An introduction to neural network methods for differential equations
Yadav, Neha; Kumar, Manoj
2015-01-01
This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed...
Exactly solvable position dependent mass schroedinger equation
International Nuclear Information System (INIS)
Koc, R.; Tuetuencueler, H.; Koercuek, E.
2002-01-01
Exact solution of the Schrodinger equation with a variable mass is presented. We have derived general expressions for the eigenstates and eigenvalues of the position dependent mass systems. We provide supersymmetric and Lie algebraic methods to discuss the position dependent mass systems
Neural network error correction for solving coupled ordinary differential equations
Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.
1992-01-01
A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.
Mass reconstruction with a neural network
International Nuclear Information System (INIS)
Loennblad, L.; Peterson, C.; Roegnvaldsson, T.
1992-01-01
A feed-forward neural network method is developed for reconstructing the invariant mass of hadronic jets appearing in a calorimeter. The approach is illustrated in W→qanti q, where W-bosons are produced in panti p reactions at SPS collider energies. The neural network method yields results that are superior to conventional methods. This neural network application differs from the classification ones in the sense that an analog number (the mass) is computed by the network, rather than a binary decision being made. As a by-product our application clearly demonstrates the need for using 'intelligent' variables in instances when the amount of training instances is limited. (orig.)
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian
2015-01-01
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Anomaly equations and the persistent mass condition
International Nuclear Information System (INIS)
Cohen, E.; Frishman, Y.
1982-01-01
Vector SU(Nsub(c)) gauge theories with nsub(f) flavors in the fundamental representation are considered. We prove that if the persistent mass condition is assumed, the two anomaly equations are identical and flavor independent for nsub(f) >= 3. Integer solutions exist only for nsub(f) = 2. The necessity of a separate discussion for 2 <= nsub(f) <= Nsub(c) is explained. (orig.)
Constructing general partial differential equations using polynomial and neural networks.
Zjavka, Ladislav; Pedrycz, Witold
2016-01-01
Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.
Schroedinger equations with indefinite effective mass
International Nuclear Information System (INIS)
Levai, G.; Znojil, M.
2012-01-01
Complete text of publication follows. The interaction of a particle with the medium around it is usually described by some potential function V (x). It is also often necessary to take into consideration the effects of this medium using a position-dependent effective mass. A wide variety of effective masses m(x) have been used in methodological studies and applications mainly restricted to one dimensional problems, including mass functions that vanish at certain locations or those reaching infinity in some limit. The common feature of these m(x) functions was that they were all non-negative. In our recent study on the PT -symmetric version of the Coulomb potential we found that an asymptotically negative effective mass is necessary for the stability of the energy spectrum. This result inspired us to investigate under which conditions can one apply mass functions that are negative at least in some domains of the coordinate space. For the sake of simplicity we considered the infinitely deep squarewell potential in one dimension V(x) = (+∞, /x/ > L > 1, 0, /x/ 0 , /x/ 0 the energy spectrum becomes unbounded from below. This is not surprising considering that with a negative mass the kinetic energy also becomes negative. In order to stabilize the spectrum we considered energy-dependent effective mass functions that kept the mass finite even for increasing values of the energy. Our first choice was m(x,E) = (1, /x/ ∈ (1,L), -tanh (E), /x/ 2 tanh λ(k) tan k(L - 1) = -1, where λ(k) = k √tanh k 2 . With this choice the energy spectrum was found to be bounded from below. Qualitatively similar results were found for our second example, where we considered a threshold energy E thr by m(x,E) = 1, /x/ ∈ (1,L) , -1, E ≥ E thr , +1, E thr ), /x/ 2 , /x/ 0 and b = b(E) > 0. This lead to the rescaled secular equation tan κa/b x tanh κ(L - a) = b. (3) This setting allowed the investigation of the special limit in which the m(x) turns into the Dirac delta function. We
Image recovery using diffusion equation embedded neural network
International Nuclear Information System (INIS)
Torkamani-Azar, F.
2001-01-01
Artificial neural networks with their inherent parallelism have been shown to perform well in many processing applications. In this paper, a new self-organizing approach for the recovery of gray level images degraded by additive noise based on embedding the diffusion equation in a neural network (without using a priori knowledge about the image point spread function, noise or original image) is described which enhances and restores gray levels of degraded images and is for application in low-level processing. Two learning features have been proposed which would be effective in the practical implementation of such a network. The recovery procedure needs some parameter estimation such as different error goals. While the required computation is not excessive, the procedure dose not require too many iterations and convergence is very fast. In addition, through the simulation the new network showed that it has superior ability to give a better quality result with a minimum of the sum of the squared error
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander
2011-01-17
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
Artificial Neural Networks and the Mass Appraisal of Real Estate
Directory of Open Access Journals (Sweden)
Gang Zhou
2018-03-01
Full Text Available With the rapid development of computer, artificial intelligence and big data technology, artificial neural networks have become one of the most powerful machine learning algorithms. In the practice, most of the applications of artificial neural networks use back propagation neural network and its variation. Besides the back propagation neural network, various neural networks have been developing in order to improve the performance of standard models. Though neural networks are well known method in the research of real estate, there is enormous space for future research in order to enhance their function. Some scholars combine genetic algorithm, geospatial information, support vector machine model, particle swarm optimization with artificial neural networks to appraise the real estate, which is helpful for the existing appraisal technology. The mass appraisal of real estate in this paper includes the real estate valuation in the transaction and the tax base valuation in the real estate holding. In this study we focus on the theoretical development of artificial neural networks and mass appraisal of real estate, artificial neural networks model evolution and algorithm improvement, artificial neural networks practice and application, and review the existing literature about artificial neural networks and mass appraisal of real estate. Finally, we provide some suggestions for the mass appraisal of China's real estate.
Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.
2018-02-01
In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.
Schrodinger equations with indefinite effective mass
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav; Levai, G.
2012-01-01
Roč. 376, č. 45 (2012), s. 3000-3005 ISSN 0375-9601 R&D Projects: GA ČR GAP203/11/1433 Institutional support: RVO:61389005 Keywords : quantum particle * effective mass * position dependence * energy dependence * stability * solvable models Subject RIV: BE - Theoretical Physics Impact factor: 1.766, year: 2012
Error estimation in the neural network solution of ordinary differential equations.
Filici, Cristian
2010-06-01
In this article a method of error estimation for the neural approximation of the solution of an Ordinary Differential Equation is presented. Some examples of the application of the method support the theory presented. Copyright 2010. Published by Elsevier Ltd.
Gauge-invariant masses through Schwinger-Dyson equations
International Nuclear Information System (INIS)
Bashir, A.; Raya, A.
2007-01-01
Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions
Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z- number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.
Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation.
Li, Shuai; Li, Yangming
2013-10-28
The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.
Ponten, S.C.; Daffertshofer, A.; Hillebrand, A.; Stam, C.J.
2010-01-01
We investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram (EEG). Thirty-two neural mass models (NMMs), each representing the lump activity
The Generalized Conversion Factor in Einstein's Mass-Energy Equation
Directory of Open Access Journals (Sweden)
Ajay Sharma
2008-07-01
Full Text Available Einstein's September 1905 paper is origin of light energy-mass inter conversion equation ($L = Delta mc^{2}$ and Einstein speculated $E = Delta mc^{2}$ from it by simply replacing $L$ by $E$. From its critical analysis it follows that $L = Delta mc^{2}$ is only true under special or ideal conditions. Under general cases the result is $L propto Delta mc^{2}$ ($E propto Delta mc^{2}$. Consequently an alternate equation $Delta E = A ub c^{2}Delta M$ has been suggested, which implies that energy emitted on annihilation of mass can be equal, less and more than predicted by $Delta E = Delta mc^{2}$. The total kinetic energy of fission fragments of U-235 or Pu-239 is found experimentally 20-60 MeV less than Q-value predicted by $Delta mc^{2}$. The mass of particle Ds (2317 discovered at SLAC, is more than current estimates. In many reactions including chemical reactions $E = Delta mc^{2}$ is not confirmed yet, but regarded as true. It implies the conversion factor than $c^{2}$ is possible. These phenomena can be explained with help of generalized mass-energy equation $Delta E = A ub c^{2}Delta M$.
Solving differential equations with unknown constitutive relations as recurrent neural networks
Energy Technology Data Exchange (ETDEWEB)
Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.; Tartakovsky, Alexandre M.
2017-12-08
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learning literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.
Nucleon Mass from a Covariant Three-Quark Faddeev Equation
International Nuclear Information System (INIS)
Eichmann, G.; Alkofer, R.; Krassnigg, A.; Nicmorus, D.
2010-01-01
We report the first study of the nucleon where the full Poincare-covariant structure of the three-quark amplitude is implemented in the Faddeev equation. We employ an interaction kernel which is consistent with contemporary studies of meson properties and aspects of chiral symmetry and its dynamical breaking, thus yielding a comprehensive approach to hadron physics. The resulting current-mass evolution of the nucleon mass compares well with lattice data and deviates only by ∼5% from the quark-diquark result obtained in previous studies.
Validating neural-network refinements of nuclear mass models
Utama, R.; Piekarewicz, J.
2018-01-01
Background: Nuclear astrophysics centers on the role of nuclear physics in the cosmos. In particular, nuclear masses at the limits of stability are critical in the development of stellar structure and the origin of the elements. Purpose: We aim to test and validate the predictions of recently refined nuclear mass models against the newly published AME2016 compilation. Methods: The basic paradigm underlining the recently refined nuclear mass models is based on existing state-of-the-art models that are subsequently refined through the training of an artificial neural network. Bayesian inference is used to determine the parameters of the neural network so that statistical uncertainties are provided for all model predictions. Results: We observe a significant improvement in the Bayesian neural network (BNN) predictions relative to the corresponding "bare" models when compared to the nearly 50 new masses reported in the AME2016 compilation. Further, AME2016 estimates for the handful of impactful isotopes in the determination of r -process abundances are found to be in fairly good agreement with our theoretical predictions. Indeed, the BNN-improved Duflo-Zuker model predicts a root-mean-square deviation relative to experiment of σrms≃400 keV. Conclusions: Given the excellent performance of the BNN refinement in confronting the recently published AME2016 compilation, we are confident of its critical role in our quest for mass models of the highest quality. Moreover, as uncertainty quantification is at the core of the BNN approach, the improved mass models are in a unique position to identify those nuclei that will have the strongest impact in resolving some of the outstanding questions in nuclear astrophysics.
Noncommutativity into Dirac Equation with mass dependent on the position
International Nuclear Information System (INIS)
Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva
2013-01-01
Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)
The isobaric multiplet mass equation for A≤71 revisited
Energy Technology Data Exchange (ETDEWEB)
Lam, Yi Hua, E-mail: lamyihua@gmail.com [CENBG (UMR 5797 — Université Bordeaux 1 — CNRS/IN2P3), Chemin du Solarium, Le Haut Vigneau, BP 120, 33175 Gradignan Cedex (France); Blank, Bertram, E-mail: blank@cenbg.in2p3.fr [CENBG (UMR 5797 — Université Bordeaux 1 — CNRS/IN2P3), Chemin du Solarium, Le Haut Vigneau, BP 120, 33175 Gradignan Cedex (France); Smirnova, Nadezda A. [CENBG (UMR 5797 — Université Bordeaux 1 — CNRS/IN2P3), Chemin du Solarium, Le Haut Vigneau, BP 120, 33175 Gradignan Cedex (France); Bueb, Jean Bernard; Antony, Maria Susai [IPHC, Université de Strasbourg, CNRS/UMR7178, 23 Rue du Loess, 67037 Strasbourg Cedex (France)
2013-11-15
Accurate mass determination of short-lived nuclides by Penning-trap spectrometers and progress in the spectroscopy of proton-rich nuclei have triggered renewed interest in the isobaric multiplet mass equation (IMME). The energy levels of the members of T=1/2,1,3/2, and 2 multiplets and the coefficients of the IMME are tabulated for A≤71. The new compilation is based on the most recent mass evaluation (AME2011) and it includes the experimental results on energies of the states evaluated up to end of 2011. Taking into account the error bars, a significant deviation from the quadratic form of the IMME for the A=9,35 quartets and the A=32 quintet is observed.
Re-evaluation of the AASHTO-flexible pavement design equation with neural network modeling.
Tiğdemir, Mesut
2014-01-01
Here we establish that equivalent single-axle loads values can be estimated using artificial neural networks without the complex design equality of American Association of State Highway and Transportation Officials (AASHTO). More importantly, we find that the neural network model gives the coefficients to be able to obtain the actual load values using the AASHTO design values. Thus, those design traffic values that might result in deterioration can be better calculated using the neural networks model than with the AASHTO design equation. The artificial neural network method is used for this purpose. The existing AASHTO flexible pavement design equation does not currently predict the pavement performance of the strategic highway research program (Long Term Pavement Performance studies) test sections very accurately, and typically over-estimates the number of equivalent single axle loads needed to cause a measured loss of the present serviceability index. Here we aimed to demonstrate that the proposed neural network model can more accurately represent the loads values data, compared against the performance of the AASHTO formula. It is concluded that the neural network may be an appropriate tool for the development of databased-nonparametric models of pavement performance.
Generalized activity equations for spiking neural network dynamics
Directory of Open Access Journals (Sweden)
Michael A Buice
2013-11-01
Full Text Available Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales - the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.
Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua
2017-01-01
To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.
Population equations for degree-heterogenous neural networks
Kähne, M.; Sokolov, I. M.; Rüdiger, S.
2017-11-01
We develop a statistical framework for studying recurrent networks with broad distributions of the number of synaptic links per neuron. We treat each group of neurons with equal input degree as one population and derive a system of equations determining the population-averaged firing rates. The derivation rests on an assumption of a large number of neurons and, additionally, an assumption of a large number of synapses per neuron. For the case of binary neurons, analytical solutions can be constructed, which correspond to steps in the activity versus degree space. We apply this theory to networks with degree-correlated topology and show that complex, multi-stable regimes can result for increasing correlations. Our work is motivated by the recent finding of subnetworks of highly active neurons and the fact that these neurons tend to be connected to each other with higher probability.
Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.
Mall, Susmita; Chakraverty, S
2016-08-01
Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.
A range of formulations to couple mass and momentum equations
International Nuclear Information System (INIS)
Darbandi, M.; Schneider, G.E.
2002-01-01
Since the innovation of control-volume-based methods, the issue of pressure-velocity decoupling has prompted the researcher to develop and employ staggered grid arrangement. The difficulties and disadvantages of staggered-grid-based schemes have encouraged the workers to investigate more in alternative scheme, i.e., the collocated-grid-based scheme. The primitive idea in collocated scheme is to couple the mass and momentum equations with the help of two types of velocity definitions instead of two types of grid arrangements. Following the work of preceding workers, we introduce a general strategy which enables the workers to develop a wide range of velocity definitions which can be properly used in collocated formulations. The developed formulations are then tested in a domain with source and sink. The results of the extended formulations are eventually discussed. (author)
Application of cellular neural network (CNN) method to the nuclear reactor dynamics equations
International Nuclear Information System (INIS)
Hadad, K.; Piroozmand, A.
2007-01-01
This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the nuclear reactor dynamic equations. An equivalent electrical circuit is analyzed and the governing equations of a bare, homogeneous reactor core are modeled via CNN. The validity of the CNN result is compared with numerical solution of the system of nonlinear governing partial differential equations (PDE) using MATLAB. Steady state as well as transient simulations, show very good comparison between the two methods. We used our CNN model to simulate space-time response of different reactivity excursions in a typical nuclear reactor. On line solution of reactor dynamic equations is used as an aid to reactor operation decision making. The complete algorithm could also be implemented using very large scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for small size nuclear reactors such as the ones used in space missions
Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.
2018-05-01
The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.
Classification of mammographic masses using generalized dynamic fuzzy neural networks
International Nuclear Information System (INIS)
Lim, Wei Keat; Er, Meng Joo
2004-01-01
In this article, computer-aided classification of mammographic masses using generalized dynamic fuzzy neural networks (GDFNN) is presented. The texture parameters, derived from first-order gradient distribution and gray-level co-occurrence matrices, were computed from the regions of interest. A total of 343 images containing 180 benign masses and 163 malignant masses from the Digital Database for Screening Mammography were analyzed. A fast approach of automatically generating fuzzy rules from training samples was implemented to classify tumors. This work is novel in that it alleviates the problem of requiring a designer to examine all the input-output relationships of a training database in order to obtain the most appropriate structure for the classifier in a conventional computer-aided diagnosis. In this approach, not only the connection weights can be adjusted, but also the structure can be self-adaptive during the learning process. By virtue of the automatic generation of the classifier by the GDFNN learning algorithm, the area under the receiver-operating characteristic curve, A z , attains 0.868±0.020, which corresponds to a true-positive fraction of 95.0% at a false positive fraction of 52.8%. The corresponding accuracy is 70.0%, the positive predictive value is 62.0%, and the negative predictive value is 91.4%
Origin of Mass. Mass and Mass-Energy Equation from Classical-Mechanics Solution
Zheng-Johansson, J. X.; Johansson, P-I.
2005-01-01
We establish the classical wave equation for a particle formed of a massless oscillatory elementary charge generally also traveling, and the resulting electromagnetic waves, of a generally Doppler-effected angular frequency $\\w$, in the vacuum in three dimensions. We obtain from the solutions the total energy of the particle wave to be $\\eng=\\hbarc\\w$, $2\\pi \\hbarc$ being a function expressed in wave-medium parameters and identifiable as the Planck constant. In respect to the train of the wav...
General Navier–Stokes-like momentum and mass-energy equations
Energy Technology Data Exchange (ETDEWEB)
Monreal, Jorge, E-mail: jmonreal@mail.usf.edu
2015-03-15
A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere
2015-04-01
This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.
Faye, Grégory; Rankin, James; Chossat, Pascal
2013-05-01
The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.
Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks
International Nuclear Information System (INIS)
Brantley, P S
2001-01-01
An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoî t
2011-01-01
simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3
Sitchin, A.
1972-01-01
Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.
DEFF Research Database (Denmark)
Sørensen, Helle Aagaard; Sperotto, Maria Maddalena; Petersen, M.
2002-01-01
The performance of matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry with neural networks in wheat variety classification is further evaluated.(1) Two principal issues were studied: (a) the number of varieties that could be classified correctly; and (b) various means of....... With the final method, it was possible to classify 30 wheat varieties with 87% correctly classified mass spectra and a correlation coefficient of 0.90....
Schrödinger equations with indefinite effective mass
International Nuclear Information System (INIS)
Znojil, Miloslav; Lévai, Géza
2012-01-01
The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass m=m(x,E) itself acquires negative values in a limited range of coordinates x and energies E. -- Highlights: ► The new concept of the locally negative effective mass introduced and studied. ► Tests presented via a few exactly solvable toy models. ► Manifest energy dependence found to guarantee the stability of the system. ► The emergence of anomalous states found related to the decrease of the energy threshold. ► Most of the toy-model properties (localization, nodal number growth) found generic.
Numerical solution of integral equations, describing mass spectrum of vector mesons
International Nuclear Information System (INIS)
Zhidkov, E.P.; Nikonov, E.G.; Sidorov, A.V.; Skachkov, N.B.; Khoromskij, B.N.
1988-01-01
The description of the numerical algorithm for solving quasipotential integral equation in impulse space is presented. The results of numerical computations of the vector meson mass spectrum and the leptonic decay width are given in comparison with the experimental data
Wave-packet revival for the Schroedinger equation with position-dependent mass
International Nuclear Information System (INIS)
Schmidt, Alexandre G.M.
2006-01-01
We study the temporal evolution of solutions of 1D Schroedinger equation with position-dependent mass inside an infinite well. Revival of wave-packet is shown to exist and partial revivals are different from the usual ones
A New Equation to Estimate Muscle Mass from Creatinine and Cystatin C.
Directory of Open Access Journals (Sweden)
Sun-wook Kim
Full Text Available With evaluation for physical performance, measuring muscle mass is an important step in detecting sarcopenia. However, there are no methods to estimate muscle mass from blood sampling.To develop a new equation to estimate total-body muscle mass with serum creatinine and cystatin C level, we designed a cross-sectional study with separate derivation and validation cohorts. Total body muscle mass and fat mass were measured using dual-energy x-ray absorptiometry (DXA in 214 adults aged 25 to 84 years who underwent physical checkups from 2010 to 2013 in a single tertiary hospital. Serum creatinine and cystatin C levels were also examined.Serum creatinine was correlated with muscle mass (P < .001, and serum cystatin C was correlated with body fat mass (P < .001 after adjusting glomerular filtration rate (GFR. After eliminating GFR, an equation to estimate total-body muscle mass was generated and coefficients were calculated in the derivation cohort. There was an agreement between muscle mass calculated by the novel equation and measured by DXA in both the derivation and validation cohort (P < .001, adjusted R2 = 0.829, β = 0.95, P < .001, adjusted R2 = 0.856, β = 1.03, respectively.The new equation based on serum creatinine and cystatin C levels can be used to estimate total-body muscle mass.
Optimal partial mass transportation and obstacle Monge-Kantorovich equation
Igbida, Noureddine; Nguyen, Van Thanh
2018-05-01
Optimal partial mass transport, which is a variant of the optimal transport problem, consists in transporting effectively a prescribed amount of mass from a source to a target. The problem was first studied by Caffarelli and McCann (2010) [6] and Figalli (2010) [12] with a particular attention to the quadratic cost. Our aim here is to study the optimal partial mass transport problem with Finsler distance costs including the Monge cost given by the Euclidian distance. Our approach is different and our results do not follow from previous works. Among our results, we introduce a PDE of Monge-Kantorovich type with a double obstacle to characterize active submeasures, Kantorovich potential and optimal flow for the optimal partial transport problem. This new PDE enables us to study the uniqueness and monotonicity results for the active submeasures. Another interesting issue of our approach is its convenience for numerical analysis and computations that we develop in a separate paper [14] (Igbida and Nguyen, 2018).
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
International Nuclear Information System (INIS)
Chithiika Ruby, V.; Senthilvelan, M.
2010-01-01
In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schroedinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schroedinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.
Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke
2018-02-01
In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Ruch, Nicole; Joss, Franziska; Jimmy, Gerda; Melzer, Katarina; Hänggi, Johanna; Mäder, Urs
2013-11-01
The aim of this study was to compare the energy expenditure (EE) estimations of activity-specific prediction equations (ASPE) and of an artificial neural network (ANNEE) based on accelerometry with measured EE. Forty-three children (age: 9.8 ± 2.4 yr) performed eight different activities. They were equipped with one tri-axial accelerometer that collected data in 1-s epochs and a portable gas analyzer. The ASPE and the ANNEE were trained to estimate the EE by including accelerometry, age, gender, and weight of the participants. To provide the activity-specific information, a decision tree was trained to recognize the type of activity through accelerometer data. The ASPE were applied to the activity-type-specific data recognized by the tree (Tree-ASPE). The Tree-ASPE precisely estimated the EE of all activities except cycling [bias: -1.13 ± 1.33 metabolic equivalent (MET)] and walking (bias: 0.29 ± 0.64 MET; P MET) and walking (bias: 0.61 ± 0.72 MET) and underestimated the EE of cycling (bias: -0.90 ± 1.18 MET; P MET, Tree-ASPE: 0.08 ± 0.21 MET) and walking (ANNEE 0.61 ± 0.72 MET, Tree-ASPE: 0.29 ± 0.64 MET) were significantly smaller in the Tree-ASPE than in the ANNEE (P < 0.05). The Tree-ASPE was more precise in estimating the EE than the ANNEE. The use of activity-type-specific information for subsequent EE prediction equations might be a promising approach for future studies.
Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time
Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)
1999-01-01
A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.
Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction.
Zineddin, Bachar; Wang, Zidong; Liu, Xiaohui
2011-11-01
Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.
International Nuclear Information System (INIS)
Morales, J.; Ovando, G.; Pena, J. J.
2010-01-01
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
Directory of Open Access Journals (Sweden)
John A. DeRuntz Jr.
2005-01-01
Full Text Available The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA. Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equations, and the total pressure applied to the structural equations on its right hand side. By formally solving for the acceleration vector from the structural system and substituting it into its place in the DAA equations, the augmentation introduces a term involving the inverse of the structural mass matrix. However there exist at least two important classes of problems in which the structural mass matrix is singular. This paper develops a method to carry out the augmentation for such problems using a generalized inverse technique.
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
International Nuclear Information System (INIS)
Ni Guang-Jiong; Xu Jian-Jun; Lou Sen-Yue
2011-01-01
Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S—2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state—-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity. (general)
International Nuclear Information System (INIS)
Ichiki, Akihisa; Shiino, Masatoshi
2007-01-01
Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analogue neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic networks requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very less, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA
Novel Equations for Estimating Lean Body Mass in Peritoneal Dialysis Patients.
Dong, Jie; Li, Yan-Jun; Xu, Rong; Yang, Zhi-Kai; Zheng, Ying-Dong
2015-12-01
♦ To develop and validate equations for estimating lean body mass (LBM) in peritoneal dialysis (PD) patients. ♦ Two equations for estimating LBM, one based on mid-arm muscle circumference (MAMC) and hand grip strength (HGS), i.e., LBM-M-H, and the other based on HGS, i.e., LBM-H, were developed and validated with LBM obtained by dual-energy X-ray absorptiometry (DEXA). The developed equations were compared to LBM estimated from creatinine kinetics (LBM-CK) and anthropometry (LBM-A) in terms of bias, precision, and accuracy. The prognostic values of LBM estimated from the equations in all-cause mortality risk were assessed. ♦ The developed equations incorporated gender, height, weight, and dialysis duration. Compared to LBM-DEXA, the bias of the developed equations was lower than that of LBM-CK and LBM-A. Additionally, LBM-M-H and LBM-H had better accuracy and precision. The prognostic values of LBM in all-cause mortality risk based on LBM-M-H, LBM-H, LBM-CK, and LBM-A were similar. ♦ Lean body mass estimated by the new equations based on MAMC and HGS was correlated with LBM obtained by DEXA and may serve as practical surrogate markers of LBM in PD patients. Copyright © 2015 International Society for Peritoneal Dialysis.
International Nuclear Information System (INIS)
Lim, S.C.; Lee, K.J.
1993-01-01
The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)
Young, Mariel; Johannesdottir, Fjola; Poole, Ken; Shaw, Colin; Stock, J T
2018-02-01
Femoral head diameter is commonly used to estimate body mass from the skeleton. The three most frequently employed methods, designed by Ruff, Grine, and McHenry, were developed using different populations to address different research questions. They were not specifically designed for application to female remains, and their accuracy for this purpose has rarely been assessed or compared in living populations. This study analyzes the accuracy of these methods using a sample of modern British women through the use of pelvic CT scans (n = 97) and corresponding information about the individuals' known height and weight. Results showed that all methods provided reasonably accurate body mass estimates (average percent prediction errors under 20%) for the normal weight and overweight subsamples, but were inaccurate for the obese and underweight subsamples (average percent prediction errors over 20%). When women of all body mass categories were combined, the methods provided reasonable estimates (average percent prediction errors between 16 and 18%). The results demonstrate that different methods provide more accurate results within specific body mass index (BMI) ranges. The McHenry Equation provided the most accurate estimation for women of small body size, while the original Ruff Equation is most likely to be accurate if the individual was obese or severely obese. The refined Ruff Equation was the most accurate predictor of body mass on average for the entire sample, indicating that it should be utilized when there is no knowledge of the individual's body size or if the individual is assumed to be of a normal body size. The study also revealed a correlation between pubis length and body mass, and an equation for body mass estimation using pubis length was accurate in a dummy sample, suggesting that pubis length can also be used to acquire reliable body mass estimates. This has implications for how we interpret body mass in fossil hominins and has particular relevance
Development and validation of a predictive equation for lean body mass in children and adolescents.
Foster, Bethany J; Platt, Robert W; Zemel, Babette S
2012-05-01
Lean body mass (LBM) is not easy to measure directly in the field or clinical setting. Equations to predict LBM from simple anthropometric measures, which account for the differing contributions of fat and lean to body weight at different ages and levels of adiposity, would be useful to both human biologists and clinicians. To develop and validate equations to predict LBM in children and adolescents across the entire range of the adiposity spectrum. Dual energy X-ray absorptiometry was used to measure LBM in 836 healthy children (437 females) and linear regression was used to develop sex-specific equations to estimate LBM from height, weight, age, body mass index (BMI) for age z-score and population ancestry. Equations were validated using bootstrapping methods and in a local independent sample of 332 children and in national data collected by NHANES. The mean difference between measured and predicted LBM was - 0.12% (95% limits of agreement - 11.3% to 8.5%) for males and - 0.14% ( - 11.9% to 10.9%) for females. Equations performed equally well across the entire adiposity spectrum, as estimated by BMI z-score. Validation indicated no over-fitting. LBM was predicted within 5% of measured LBM in the validation sample. The equations estimate LBM accurately from simple anthropometric measures.
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2012-01-01
Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.
Equation of Motion of an Interstellar Bussard Ramjet with Radiation and Mass Losses
Semay, Claude; Silvestre-Brac, Bernard
2008-01-01
An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and that of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly…
Energy Technology Data Exchange (ETDEWEB)
Abundo, Ugo [Neural Calculus Lab, J. Von Neumann Foundation, v.Clelia 15, 00181 Rome, Italy Opensharelab, Open Power Association, v.Genzano 95, 00179 Rome (Italy)
2015-03-10
An analogy is drawn among the irreversible evolution of a neural-network-based A.I., an information field associated to spacetime configurations and the behaviour of entities described by the Schrödinger equation.
Applications of Deep Neural Networks in a Top Quark Mass Measurement at the LHC
Lange, Torben; Kasieczka, Gregor
2018-01-01
In this analysis the usage of deep neural networks for an improved event selection forthe top-quark-mass measurement in the t¯ muon+jets channel for events at the CMS ext√periment for the LHC run II with a center of mass energy s = 13 TeV was investigated.The composition of the event selection with respect to different jet-assignment permutationtypes was found to have a strong inﬂuence on the systematic uncertainty of the top-quarkmass measurement. A selection based on the output of neural network trained on classifyingevent permutations of the t¯ muon+jets ﬁnal state into these permutation types could thentbe used to improve the systematical uncertainty of the current mass measurement from asystematical uncertainty of around 630 MeV to 560 MeV.
International Nuclear Information System (INIS)
Zhang Mei-Ling; Wang Xiao-Xiao; Xie Yin-Li; Jia Li-Qun; Sun Xian-Ting
2011-01-01
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results. (general)
Can we close the long term mass balance equation for pollutants in highway ponds?
DEFF Research Database (Denmark)
Bentzen, Thomas Ruby; Larsen, Torben; Rasmussen, Michael R.
2007-01-01
The paper discusses the prospects of finding the long term mass balance on basis of short term simulations. A step in this process is to see to which degree the mass balance equation can be closed by measurements. Accordingly the total accumulation of heavy metals and PAH's in 8 Danish detention...... ponds only receiving runoff from highways have been measured. The result shows that the incoming mass of heavy metals from short term runoff events is accumulated. This is not observable in the same magnitude for the toxic organic compounds. The results also show that the accumulation rates...
A modified Friedmann equation for a system with varying gravitational mass
Gorkavyi, Nick; Vasilkov, Alexander
2018-05-01
The Laser Interferometer Gravitational-Wave Observatory (LIGO) detection of gravitational waves that take away 5 per cent of the total mass of two merging black holes points out on the importance of considering varying gravitational mass of a system. Using an assumption that the energy-momentum pseudo-tensor of gravitational waves is not considered as a source of gravitational field, we analyse a perturbation of the Friedmann-Robertson-Walker metric caused by the varying gravitational mass of a system. This perturbation leads to a modified Friedmann equation that contains a term similar to the `cosmological constant'. Theoretical estimates of the effective cosmological constant quantitatively corresponds to observed cosmological acceleration.
Novel Equations for Estimating Lean Body Mass in Patients With Chronic Kidney Disease.
Tian, Xue; Chen, Yuan; Yang, Zhi-Kai; Qu, Zhen; Dong, Jie
2018-05-01
Simplified methods to estimate lean body mass (LBM), an important nutritional measure representing muscle mass and somatic protein, are lacking in nondialyzed patients with chronic kidney disease (CKD). We developed and tested 2 reliable equations for estimation of LBM in daily clinical practice. The development and validation groups both included 150 nondialyzed patients with CKD Stages 3 to 5. Two equations for estimating LBM based on mid-arm muscle circumference (MAMC) or handgrip strength (HGS) were developed and validated in CKD patients with dual-energy x-ray absorptiometry as referenced gold method. We developed and validated 2 equations for estimating LBM based on HGS and MAMC. These equations, which also incorporated sex, height, and weight, were developed and validated in CKD patients. The new equations were found to exhibit only small biases when compared with dual-energy x-ray absorptiometry, with median differences of 0.94 and 0.46 kg observed in the HGS and MAMC equations, respectively. Good precision and accuracy were achieved for both equations, as reflected by small interquartile ranges in the differences and in the percentages of estimates that were 20% of measured LBM. The bias, precision, and accuracy of each equation were found to be similar when it was applied to groups of patients divided by the median measured LBM, the median ratio of extracellular to total body water, and the stages of CKD. LBM estimated from MAMC or HGS were found to provide accurate estimates of LBM in nondialyzed patients with CKD. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.
Position-Dependent Mass Schrödinger Equation for the Morse Potential
International Nuclear Information System (INIS)
Ovando, G; Peña, J J; Morales, J; López-Bonilla, J
2017-01-01
The position dependent mass Schrödinger equation (PDMSE) has a wide range of quantum applications such as the study of semiconductors, quantum wells, quantum dots and impurities in crystals, among many others. On the other hand, the Morse potential is one of the most important potential models used to study the electronic properties of diatomic molecules. In this work, the solution of the effective mass one-dimensional Schrödinger equation for the Morse potential is presented. This is done by means of the canonical transformation method in algebraic form. The PDMSE is solved for any model of the proposed kinetic energy operators as for example the BenDaniel-Duke, Gora-Williams, Zhu-Kroemer or Li-Kuhn. Also, in order to solve the PDMSE with Morse potential, we consider a superpotential leading to a special form of the exactly solvable Schrödinger equation of constant mass for a class of multiparameter exponential-type potential along with a proper mass distribution. The proposed approach is general and can be applied in the search of new potentials suitable on science of materials by looking into the viable choices of the mass function. (paper)
Li, Chunqing; Tie, Xiaobo; Liang, Kai; Ji, Chanjuan
2016-01-01
After conducting the intensive research on the distribution of fluid's velocity and biochemical reactions in the membrane bioreactor (MBR), this paper introduces the use of the mass-transfer differential equation to simulate the distribution of the chemical oxygen demand (COD) concentration in MBR membrane pool. The solutions are as follows: first, use computational fluid dynamics to establish a flow control equation model of the fluid in MBR membrane pool; second, calculate this model by adopting direct numerical simulation to get the velocity field of the fluid in membrane pool; third, combine the data of velocity field to establish mass-transfer differential equation model for the concentration field in MBR membrane pool, and use Seidel iteration method to solve the equation model; last but not least, substitute the real factory data into the velocity and concentration field model to calculate simulation results, and use visualization software Tecplot to display the results. Finally by analyzing the nephogram of COD concentration distribution, it can be found that the simulation result conforms the distribution rule of the COD's concentration in real membrane pool, and the mass-transfer phenomenon can be affected by the velocity field of the fluid in membrane pool. The simulation results of this paper have certain reference value for the design optimization of the real MBR system.
International Nuclear Information System (INIS)
Dang Xuanju; Tan Yonghong
2005-01-01
A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated
Refining mass formulas for astrophysical applications: A Bayesian neural network approach
Utama, R.; Piekarewicz, J.
2017-10-01
Background: Exotic nuclei, particularly those near the drip lines, are at the core of one of the fundamental questions driving nuclear structure and astrophysics today: What are the limits of nuclear binding? Exotic nuclei play a critical role in both informing theoretical models as well as in our understanding of the origin of the heavy elements. Purpose: Our aim is to refine existing mass models through the training of an artificial neural network that will mitigate the large model discrepancies far away from stability. Methods: The basic paradigm of our two-pronged approach is an existing mass model that captures as much as possible of the underlying physics followed by the implementation of a Bayesian neural network (BNN) refinement to account for the missing physics. Bayesian inference is employed to determine the parameters of the neural network so that model predictions may be accompanied by theoretical uncertainties. Results: Despite the undeniable quality of the mass models adopted in this work, we observe a significant improvement (of about 40%) after the BNN refinement is implemented. Indeed, in the specific case of the Duflo-Zuker mass formula, we find that the rms deviation relative to experiment is reduced from σrms=0.503 MeV to σrms=0.286 MeV. These newly refined mass tables are used to map the neutron drip lines (or rather "drip bands") and to study a few critical r -process nuclei. Conclusions: The BNN approach is highly successful in refining the predictions of existing mass models. In particular, the large discrepancy displayed by the original "bare" models in regions where experimental data are unavailable is considerably quenched after the BNN refinement. This lends credence to our approach and has motivated us to publish refined mass tables that we trust will be helpful for future astrophysical applications.
Hof, Bas van ’t; Veldman, Arthur E.P.
2012-01-01
The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting 'MaMEC' discretizations conserve mass, momentum as well as energy, although no
Gómez Campos, Rossana; Pacheco Carrillo, Jaime; Almonacid Fierro, Alejandro; Urra Albornoz, Camilo; Cossío-Bolaños, Marco
2018-03-01
(i) To propose regression equations based on anthropometric measures to estimate fat mass (FM) using dual energy X-ray absorptiometry (DXA) as reference method, and (ii)to establish population reference standards for equation-derived FM. A cross-sectional study on 6,713 university students (3,354 males and 3,359 females) from Chile aged 17.0 to 27.0years. Anthropometric measures (weight, height, waist circumference) were taken in all participants. Whole body DXA was performed in 683 subjects. A total of 478 subjects were selected to develop regression equations, and 205 for their cross-validation. Data from 6,030 participants were used to develop reference standards for FM. Equations were generated using stepwise multiple regression analysis. Percentiles were developed using the LMS method. Equations for men were: (i) FM=-35,997.486 +232.285 *Weight +432.216 *CC (R 2 =0.73, SEE=4.1); (ii)FM=-37,671.303 +309.539 *Weight +66,028.109 *ICE (R2=0.76, SEE=3.8), while equations for women were: (iii)FM=-13,216.917 +461,302 *Weight+91.898 *CC (R 2 =0.70, SEE=4.6), and (iv) FM=-14,144.220 +464.061 *Weight +16,189.297 *ICE (R 2 =0.70, SEE=4.6). Percentiles proposed included p10, p50, p85, and p95. The developed equations provide valid and accurate estimation of FM in both sexes. The values obtained using the equations may be analyzed from percentiles that allow for categorizing body fat levels by age and sex. Copyright © 2017 SEEN y SED. Publicado por Elsevier España, S.L.U. All rights reserved.
Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation
International Nuclear Information System (INIS)
Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng
2016-01-01
We study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. The presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.
Energy Technology Data Exchange (ETDEWEB)
Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)
1976-11-01
Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.
International Nuclear Information System (INIS)
Yasuk, F.; Tekin, S.; Boztosun, I.
2010-01-01
In this study, the exact solutions of the d-dimensional Schroedinger equation with a position-dependent mass m(r)=1/(1+ζ 2 r 2 ) is presented for a free particle, V(r)=0, by using the method of point canonical transformations. The energy eigenvalues and corresponding wavefunctions for the effective potential which is to be a generalized Poeschl-Teller potential are obtained within the framework of the asymptotic iteration method.
An artificial Radial Basis Function (RBF) neural network model was developed for the prediction of mass transfer of the phospholipids from canola meal in supercritical CO2 fluid. The RBF kind of artificial neural networks (ANN) with orthogonal least squares (OLS) learning algorithm were used for mod...
Directory of Open Access Journals (Sweden)
Fábio Lúcio Santos
2009-06-01
Full Text Available This paper deals with an analytical model of a rigid rotor supported by hydrodynamic journal bearings where the plane separation technique together with the Artificial Neural Network (ANN is used to predict the location and magnitude of the correction masses for balancing the rotor bearing system. The rotating system is modeled by applying the rigid shaft Stodola-Green model, in which the shaft gyroscopic moments and rotatory inertia are accounted for, in conjunction with the hydrodynamic cylindrical journal bearing model based on the classical Reynolds equation. A linearized perturbation procedure is employed to render the lubrication equations from the Reynolds equation, which allows predicting the eight linear force coefficients associated with the bearing direct and cross-coupled stiffness and damping coefficients. The results show that the methodology presented is efficient for balancing rotor systems. This paper gives a step further in the monitoring process, since Artificial Neural Network is normally used to predict, not to correct the mass unbalance. The procedure presented can be used in turbo machinery industry to balance rotating machinery that require continuous inspections. Some simulated results will be used in order to clarify the methodology presented.
International Nuclear Information System (INIS)
Hadad, Kamal; Pirouzmand, Ahmad; Ayoobian, Navid
2008-01-01
This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (T N ) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the T N moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state T N moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations
SUSY method for the three-dimensional Schrödinger equation with effective mass
International Nuclear Information System (INIS)
Ioffe, M.V.; Kolevatova, E.V.; Nishnianidze, D.N.
2016-01-01
Highlights: • SUSY intertwining relations for the 3-dim Schrödinger equation with effective mass were studied. • The general solution of these intertwining relations with first order supercharges was obtained. • Four different options for parameters values were considered separately to find the mass functions and partner potentials. - Abstract: The three-dimensional Schrödinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtained without any preliminary constraints. Several forms of coefficient functions of the supercharges are investigated and analytical expressions for the mass function and partner potentials are found. As usual for SUSY Quantum Mechanics with nonsingular superpotentials, the spectra of intertwined Hamiltonians coincide up to zero modes of supercharges, and the corresponding wave functions are connected by intertwining relations. All models are partially integrable by construction: each of them has at least one second order symmetry operator.
Regularity and mass conservation for discrete coagulation–fragmentation equations with diffusion
Cañizo, J.A.
2010-03-01
We present a new a priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case. © 2009 Elsevier Masson SAS. All rights reserved.
Goodacre, R; Hiom, S J; Cheeseman, S L; Murdoch, D; Weightman, A J; Wade, W G
1996-02-01
Curie-point pyrolysis mass spectra were obtained from 29 oral asaccharolytic Eubacterium strains and 6 abscess isolates previously identified as Peptostreptococcus heliotrinreducens. Pyrolysis mass spectrometry (PyMS) with cluster analysis was able to clarify the taxonomic position of this group of organisms. Artificial neural networks (ANNS) were then trained by supervised learning (with the back-propagation algorithm) to recognize the strains from their pyrolysis mass spectra; all Eubacterium strains were correctly identified, and the abscess isolates were identified as un-named Eubacterium taxon C2 and were distinct from the type strain of P. heliotrinreducens. These results demonstrate that the combination of PyMS and ANNs provides a rapid and accurate identification technique.
Equation of motion of an interstellar Bussard ramjet with radiation and mass losses
International Nuclear Information System (INIS)
Semay, Claude; Silvestre-Brac, Bernard
2008-01-01
An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and that of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly reduced. However, the parametric equations in terms of the ramjet's speed for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame and the proper time indicated by the clocks on board the spaceship can still be obtained in an analytical form. The non-relativistic motion and the motion near the limit speed are studied
Equation of motion of an interstellar Bussard ramjet with radiation and mass losses
Energy Technology Data Exchange (ETDEWEB)
Semay, Claude [Groupe de Physique Nucleaire Theorique, Universite de Mons-Hainaut, Academie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons (Belgium); Silvestre-Brac, Bernard [LPSC, Universite Joseph Fourier, Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Avenue des Martyrs 53, F-38026 Grenoble-Cedex (France)], E-mail: claude.semay@umh.ac.be, E-mail: silvestre@lpsc.in2p3.fr
2008-11-15
An interstellar Bussard ramjet is a spaceship using the protons of the interstellar medium in a fusion engine to produce thrust. In recent papers, it was shown that the relativistic equation of motion of an ideal ramjet and that of a ramjet with radiation loss are analytical. When a mass loss appears, the limit speed of the ramjet is more strongly reduced. However, the parametric equations in terms of the ramjet's speed for the position of the ramjet in the inertial frame of the interstellar medium, the time in this frame and the proper time indicated by the clocks on board the spaceship can still be obtained in an analytical form. The non-relativistic motion and the motion near the limit speed are studied.
Wu, Huai-Ning; Luo, Biao
2012-12-01
It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.
Novel equations to estimate lean body mass in maintenance hemodialysis patients.
Noori, Nazanin; Kovesdy, Csaba P; Bross, Rachelle; Lee, Martin; Oreopoulos, Antigone; Benner, Deborah; Mehrotra, Rajnish; Kopple, Joel D; Kalantar-Zadeh, Kamyar
2011-01-01
Lean body mass (LBM) is an important nutritional measure representing muscle mass and somatic protein in hemodialysis patients, for whom we developed and tested equations to estimate LBM. A study of diagnostic test accuracy. The development cohort included 118 hemodialysis patients with LBM measured using dual-energy x-ray absorptiometry (DEXA) and near-infrared (NIR) interactance. The validation cohort included 612 additional hemodialysis patients with LBM measured using a portable NIR interactance technique during hemodialysis. 3-month averaged serum concentrations of creatinine, albumin, and prealbumin; normalized protein nitrogen appearance; midarm muscle circumference (MAMC); handgrip strength; and subjective global assessment of nutrition. LBM measured using DEXA in the development cohort and NIR interactance in validation cohorts. In the development cohort, DEXA and NIR interactance correlated strongly (r = 0.94, P < 0.001). DEXA-measured LBM correlated with serum creatinine level, MAMC, and handgrip strength, but not with other nutritional markers. Three regression equations to estimate DEXA-measured LBM were developed based on each of these 3 surrogates and sex, height, weight, and age (and urea reduction ratio for the serum creatinine regression). In the validation cohort, the validity of the equations was tested against the NIR interactance-measured LBM. The equation estimates correlated well with NIR interactance-measured LBM (R² ≥ 0.88), although in higher LBM ranges, they tended to underestimate it. Median (95% confidence interval) differences and interquartile range for differences between equation estimates and NIR interactance-measured LBM were 3.4 (-3.2 to 12.0) and 3.0 (1.1-5.1) kg for serum creatinine and 4.0 (-2.6 to 13.6) and 3.7 (1.3-6.0) kg for MAMC, respectively. DEXA measurements were obtained on a nondialysis day, whereas NIR interactance was performed during hemodialysis treatment, with the likelihood of confounding by volume status
Neutron Star masses from the Field Correlator Method Equation of State
Directory of Open Access Journals (Sweden)
Zappalà D.
2014-04-01
Full Text Available We analyse the hadron-quark phase transition in neutron stars by confronting the hadronic Equation of State (EoS obtained according to the microscopic Brueckner-Hartree-Fock many body theory, with the quark matter EoS derived within the Field Correlator Method. In particular, the latter EoS is only parametrized in terms of the gluon condensate and the large distance quark-antiquark potential, so that the comparison of the results of this analysis with the most recent measurements of heavy neutron star masses provides some physical constraints on these two parameters.
Chen, Guiling
2013-01-01
This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study
Dietrich, Felix
2017-01-01
Reconstructing the invariant mass in a Higgs boson decay event containing tau leptons turns out to be a challenging endeavour. The aim of this summer student project is to implement a new algorithm for this task, using deep neural networks and machine learning. The results are compared to SVFit, an existing algorithm that uses dynamical likelihood techniques. A neural network is found that reaches the accuracy of SVFit at low masses and even surpasses it at higher masses, while at the same time providing results a thousand times faster.
Renormalization-group equations of neutrino masses and flavor mixing parameters in matter
Xing, Zhi-zhong; Zhou, Shun; Zhou, Ye-Ling
2018-05-01
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a≡ 2√{2}{G}F{N}_eE to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {\\tilde{m}}_i (for i = 1 , 2 , 3). Given the standard parametrization of V , the RGEs for {{\\tilde{θ}}_{12}, {\\tilde{θ}}_{13}, {\\tilde{θ}}_{23}, \\tilde{δ}} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ- τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.
International Nuclear Information System (INIS)
Gori, F.
2006-01-01
Mass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called 'Price Increase Factor', PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (author)
Directory of Open Access Journals (Sweden)
Mahmood Akbari
2017-12-01
Full Text Available In recent years, numerous experimental tests were done on the concrete beams reinforced with the fiber-reinforced polymer (FRP. In this way, some equations were proposed to estimate the shear strength of the beams reinforced with FRP. The aim of this study is to explore the feasibility of using a feed-forward artificial neural network (ANN model to predict the ultimate shear strength of the beams strengthened with FRP composites. For this purpose, a database consists of 304 reinforced FRP concrete beams have been collected from the available articles on the analysis of shear behavior of these beams. The inputs to the ANN model consists of the 11 variables including the geometric dimensions of the section, steel reinforcement amount, FRP amount and the properties of the concrete, steel reinforcement and FRP materials while the output variable is the shear strength of the FRP beam. To assess the performance of the ANN model for estimating the shear strength of the reinforced beams, the outputs of the ANN are compared to those of equations of the Iranian code (Publication No. 345 and the American code (ACI 440. The comparisons between the outputs of Iran and American regulations with those of the proposed model indicates that the predictive power of this model is much better than the experimental codes. Specifically, for under study data, mean absolute relative error (MARE criteria is 13%, 34% and 39% for the ANN model, the American and the Iranian codes, respectively.
International Nuclear Information System (INIS)
Wu Ning; Zhang Dahua
2007-01-01
A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
International Nuclear Information System (INIS)
Cobian, Hector; Schulze-Halberg, Axel
2011-01-01
We construct Darboux transformations for time-dependent Schroedinger equations with position-dependent mass in (2 + 1) dimensions. Several examples illustrate our results, which complement and generalize former findings for the constant mass case in two spatial variables (Schulze-Halberg 2010 J. Math. Phys. 51 033521).
Alsing, Justin; Silva, Hector O.; Berti, Emanuele
2018-04-01
We infer the mass distribution of neutron stars in binary systems using a flexible Gaussian mixture model and use Bayesian model selection to explore evidence for multi-modality and a sharp cut-off in the mass distribution. We find overwhelming evidence for a bimodal distribution, in agreement with previous literature, and report for the first time positive evidence for a sharp cut-off at a maximum neutron star mass. We measure the maximum mass to be 2.0M⊙ sharp cut-off is interpreted as the maximum stable neutron star mass allowed by the equation of state of dense matter, our measurement puts constraints on the equation of state. For a set of realistic equations of state that support >2M⊙ neutron stars, our inference of mmax is able to distinguish between models at odds ratios of up to 12: 1, whilst under a flexible piecewise polytropic equation of state model our maximum mass measurement improves constraints on the pressure at 3 - 7 × the nuclear saturation density by ˜30 - 50% compared to simply requiring mmax > 2M⊙. We obtain a lower bound on the maximum sound speed attained inside the neutron star of c_s^max > 0.63c (99.8%), ruling out c_s^max c/√{3} at high significance. Our constraints on the maximum neutron star mass strengthen the case for neutron star-neutron star mergers as the primary source of short gamma-ray bursts.
Hyperfunction solutions of the zero rest mass equations and representations of LIE groups
International Nuclear Information System (INIS)
Dunne, E.G.
1984-01-01
Recently, hyperfunctions have arisen in an essential way in separate results in mathematical physics and in representation theory. In the setting of the twistor program, Wells, with others, has extended the Penrose transform to hyperfunction solutions of the zero rest mass equations, showing that the fundamental isomorphisms hold for this larger space. Meanwhile, Schmid has shown the existence of a canonical globalization of a Harish-Chandra module, V, to a representation of the group. This maximal globalization may be realized as the completion of V in a locally convex vector space in the hyperfunction topology. This thesis shows that the former is a particular case of the latter where the globalization can be done by hand. This explicit globalization is then carried out for a more general case of the Radon transform on homogeneous spaces
Trépanier, Sylvain; Mathieu, Lucie; Daigneault, Réal; Faure, Stéphane
2016-04-01
This study proposes an artificial neural networks-based method for predicting the unaltered (precursor) chemical compositions of hydrothermally altered volcanic rock. The method aims at predicting precursor's major components contents (SiO2, FeOT, MgO, CaO, Na2O, and K2O). The prediction is based on ratios of elements generally immobile during alteration processes; i.e. Zr, TiO2, Al2O3, Y, Nb, Th, and Cr, which are provided as inputs to the neural networks. Multi-layer perceptron neural networks were trained on a large dataset of least-altered volcanic rock samples that document a wide range of volcanic rock types, tectonic settings and ages. The precursors thus predicted are then used to perform mass balance calculations. Various statistics were calculated to validate the predictions of precursors' major components, which indicate that, overall, the predictions are precise and accurate. For example, rank-based correlation coefficients were calculated to compare predicted and analysed values from a least-altered test dataset that had not been used to train the networks. Coefficients over 0.87 were obtained for all components, except for Na2O (0.77), indicating that predictions for alkali might be less performant. Also, predictions are performant for most volcanic rock compositions, except for ultra-K rocks. The proposed method provides an easy and rapid solution to the often difficult task of determining appropriate volcanic precursor compositions to rocks modified by hydrothermal alteration. It is intended for large volcanic rock databases and is most useful, for example, to mineral exploration performed in complex or poorly known volcanic settings. The method is implemented as a simple C++ console program.
Directory of Open Access Journals (Sweden)
Elias .
2011-03-01
Full Text Available The case study was conducted in the area of Acacia mangium plantation at BKPH Parung Panjang, KPH Bogor. The objective of the study was to formulate equation models of tree root carbon mass and root to shoot carbon mass ratio of the plantation. It was found that carbon content in the parts of tree biomass (stems, branches, twigs, leaves, and roots was different, in which the highest and the lowest carbon content was in the main stem of the tree and in the leaves, respectively. The main stem and leaves of tree accounted for 70% of tree biomass. The root-shoot ratio of root biomass to tree biomass above the ground and the root-shoot ratio of root biomass to main stem biomass was 0.1443 and 0.25771, respectively, in which 75% of tree carbon mass was in the main stem and roots of tree. It was also found that the root-shoot ratio of root carbon mass to tree carbon mass above the ground and the root-shoot ratio of root carbon mass to tree main stem carbon mass was 0.1442 and 0.2034, respectively. All allometric equation models of tree root carbon mass of A. mangium have a high goodness-of-fit as indicated by its high adjusted R2.Keywords: Acacia mangium, allometric, root-shoot ratio, biomass, carbon mass
TBA equations for the mass gap in the O(2r) non-linear σ-models
International Nuclear Information System (INIS)
Balog, Janos; Hegedues, Arpad
2005-01-01
We propose TBA integral equations for 1-particle states in the O(n) non-linear σ-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system
Samala, Ravi K; Chan, Heang-Ping; Hadjiiski, Lubomir; Helvie, Mark A; Wei, Jun; Cha, Kenny
2016-12-01
Develop a computer-aided detection (CAD) system for masses in digital breast tomosynthesis (DBT) volume using a deep convolutional neural network (DCNN) with transfer learning from mammograms. A data set containing 2282 digitized film and digital mammograms and 324 DBT volumes were collected with IRB approval. The mass of interest on the images was marked by an experienced breast radiologist as reference standard. The data set was partitioned into a training set (2282 mammograms with 2461 masses and 230 DBT views with 228 masses) and an independent test set (94 DBT views with 89 masses). For DCNN training, the region of interest (ROI) containing the mass (true positive) was extracted from each image. False positive (FP) ROIs were identified at prescreening by their previously developed CAD systems. After data augmentation, a total of 45 072 mammographic ROIs and 37 450 DBT ROIs were obtained. Data normalization and reduction of non-uniformity in the ROIs across heterogeneous data was achieved using a background correction method applied to each ROI. A DCNN with four convolutional layers and three fully connected (FC) layers was first trained on the mammography data. Jittering and dropout techniques were used to reduce overfitting. After training with the mammographic ROIs, all weights in the first three convolutional layers were frozen, and only the last convolution layer and the FC layers were randomly initialized again and trained using the DBT training ROIs. The authors compared the performances of two CAD systems for mass detection in DBT: one used the DCNN-based approach and the other used their previously developed feature-based approach for FP reduction. The prescreening stage was identical in both systems, passing the same set of mass candidates to the FP reduction stage. For the feature-based CAD system, 3D clustering and active contour method was used for segmentation; morphological, gray level, and texture features were extracted and merged with a
Yousefi, Mina; Krzyżak, Adam; Suen, Ching Y
2018-05-01
Digital breast tomosynthesis (DBT) was developed in the field of breast cancer screening as a new tomographic technique to minimize the limitations of conventional digital mammography breast screening methods. A computer-aided detection (CAD) framework for mass detection in DBT has been developed and is described in this paper. The proposed framework operates on a set of two-dimensional (2D) slices. With plane-to-plane analysis on corresponding 2D slices from each DBT, it automatically learns complex patterns of 2D slices through a deep convolutional neural network (DCNN). It then applies multiple instance learning (MIL) with a randomized trees approach to classify DBT images based on extracted information from 2D slices. This CAD framework was developed and evaluated using 5040 2D image slices derived from 87 DBT volumes. The empirical results demonstrate that this proposed CAD framework achieves much better performance than CAD systems that use hand-crafted features and deep cardinality-restricted Bolzmann machines to detect masses in DBTs. Copyright © 2018 Elsevier Ltd. All rights reserved.
Binding and segmentation via a neural mass model trained with Hebbian and anti-Hebbian mechanisms.
Cona, Filippo; Zavaglia, Melissa; Ursino, Mauro
2012-04-01
Synchronization of neural activity in the gamma band, modulated by a slower theta rhythm, is assumed to play a significant role in binding and segmentation of multiple objects. In the present work, a recent neural mass model of a single cortical column is used to analyze the synaptic mechanisms which can warrant synchronization and desynchronization of cortical columns, during an autoassociation memory task. The model considers two distinct layers communicating via feedforward connections. The first layer receives the external input and works as an autoassociative network in the theta band, to recover a previously memorized object from incomplete information. The second realizes segmentation of different objects in the gamma band. To this end, units within both layers are connected with synapses trained on the basis of previous experience to store objects. The main model assumptions are: (i) recovery of incomplete objects is realized by excitatory synapses from pyramidal to pyramidal neurons in the same object; (ii) binding in the gamma range is realized by excitatory synapses from pyramidal neurons to fast inhibitory interneurons in the same object. These synapses (both at points i and ii) have a few ms dynamics and are trained with a Hebbian mechanism. (iii) Segmentation is realized with faster AMPA synapses, with rise times smaller than 1 ms, trained with an anti-Hebbian mechanism. Results show that the model, with the previous assumptions, can correctly reconstruct and segment three simultaneous objects, starting from incomplete knowledge. Segmentation of more objects is possible but requires an increased ratio between the theta and gamma periods.
DEFF Research Database (Denmark)
D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar
2012-01-01
and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...... flexors. Results: Males were signifantly stronger than females across all age groups. Elbow peak torque (EPT) was better preserved from 60s to 70s whereas knee peak torque (KPT) reduced significantly (PGender, thigh mass and age best...... predicted KPT (R2=0.60). Gender, forearm mass and age best predicted EPT (R2=0.75). Good crossvalidation was established for both elbow and knee models. Conclusion: This cross-sectional study of muscle strength created and validated strength scaled equations of EPT and KPT using only gender, segment mass...
International Nuclear Information System (INIS)
Shiino, Masatoshi; Yamana, Michiko
2004-01-01
We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields
Institute of Scientific and Technical Information of China (English)
李仁杰; 乔永芬; 刘洋
2002-01-01
We present a general approach to the construction of conservation laws for variable mass nonholonomic noncon-servative systems. First, we give the definition of integrating factors, and we study in detail the necessary conditionsfor the existence of the conserved quantities. Then, we establish the conservation theorem and its inverse theorem forHamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems. Finally,we give an example to illustrate the application of the results.
Institute of Scientific and Technical Information of China (English)
李仁杰; 刘洋; 等
2002-01-01
We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton's canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.
International Nuclear Information System (INIS)
Bahar, M.K.; Yasuk, F.
2012-01-01
The solutions of the effective mass Dirac equation for the Manning-Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac-Manning-Rosen problem for α = 0 or α = 1. In this case, the Manning-Rosen potential reduces to the Hulthen potential. (author)
Chen, Chi-Kan
2017-07-26
The identification of genetic regulatory networks (GRNs) provides insights into complex cellular processes. A class of recurrent neural networks (RNNs) captures the dynamics of GRN. Algorithms combining the RNN and machine learning schemes were proposed to reconstruct small-scale GRNs using gene expression time series. We present new GRN reconstruction methods with neural networks. The RNN is extended to a class of recurrent multilayer perceptrons (RMLPs) with latent nodes. Our methods contain two steps: the edge rank assignment step and the network construction step. The former assigns ranks to all possible edges by a recursive procedure based on the estimated weights of wires of RNN/RMLP (RE RNN /RE RMLP ), and the latter constructs a network consisting of top-ranked edges under which the optimized RNN simulates the gene expression time series. The particle swarm optimization (PSO) is applied to optimize the parameters of RNNs and RMLPs in a two-step algorithm. The proposed RE RNN -RNN and RE RMLP -RNN algorithms are tested on synthetic and experimental gene expression time series of small GRNs of about 10 genes. The experimental time series are from the studies of yeast cell cycle regulated genes and E. coli DNA repair genes. The unstable estimation of RNN using experimental time series having limited data points can lead to fairly arbitrary predicted GRNs. Our methods incorporate RNN and RMLP into a two-step structure learning procedure. Results show that the RE RMLP using the RMLP with a suitable number of latent nodes to reduce the parameter dimension often result in more accurate edge ranks than the RE RNN using the regularized RNN on short simulated time series. Combining by a weighted majority voting rule the networks derived by the RE RMLP -RNN using different numbers of latent nodes in step one to infer the GRN, the method performs consistently and outperforms published algorithms for GRN reconstruction on most benchmark time series. The framework of two
Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly
Dong, J. M.; Zhang, Y. H.; Zuo, W.; Gu, J. Z.; Wang, L. J.; Sun, Y.
2018-02-01
The Wigner isobaric multiplet mass equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question of the origin of the Nolen-Schiffer anomaly (NSA) found in the Coulomb displacement energy of mirror nuclei. We find that the naturally emerged CSB term in GIMME is largely responsible for explaining the NSA.
A sensitivity analysis of the mass balance equation terms in subcooled flow boiling
International Nuclear Information System (INIS)
Braz Filho, Francisco A.; Caldeira, Alexandre D.; Borges, Eduardo M.
2013-01-01
In a heated vertical channel, the subcooled flow boiling occurs when the fluid temperature reaches the saturation point, actually a small overheating, near the channel wall while the bulk fluid temperature is below this point. In this case, vapor bubbles are generated along the channel resulting in a significant increase in the heat flux between the wall and the fluid. This study is particularly important to the thermal-hydraulics analysis of Pressurized Water Reactors (PWRs). The computational fluid dynamics software FLUENT uses the Eulerian multiphase model to analyze the subcooled flow boiling. In a previous paper, the comparison of the FLUENT results with experimental data for the void fraction presented a good agreement, both at the beginning of boiling as in nucleate boiling at the end of the channel. In the region between these two points the comparison with experimental data was not so good. Thus, a sensitivity analysis of the mass balance equation terms, steam production and condensation, was performed. Factors applied to the terms mentioned above can improve the agreement of the FLUENT results to the experimental data. Void fraction calculations show satisfactory results in relation to the experimental data in pressures values of 15, 30 and 45 bars. (author)
Liu, Tao; Huang, Jie
2017-04-17
This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.
Third post-Newtonian dynamics of compact binaries: equations of motion in the centre-of-mass frame
Blanchet, L
2003-01-01
The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work, we investigate the binary's relative dynamics in the centre-of-mass frame (centre of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the centre-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved centre-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates centre-of-mass Lagrangian is equivalent, via a contact transformation of the particles' variables, to the centre-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.
International Nuclear Information System (INIS)
Debnath, S.; Maji, Smarajit; Meyur, Sanjib
2014-01-01
We have obtained exact solution of the effective mass Schrödinger equation for the generalised Hylleraas potential. The exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunctions are obtained in terms of the hypergeometric functions. Results are also given for the special case of potential parameter.
International Nuclear Information System (INIS)
Tang Xiaoyan; Shukla, Padma Kant
2008-01-01
Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein-Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures
Laurençot, Philippe
2018-03-01
Uniqueness of mass-conserving self-similar solutions to Smoluchowski's coagulation equation is shown when the coagulation kernel K is given by K(x,x_*)=2(x x_*)^{-α } , (x,x_*)\\in (0,∞)^2 , for some α >0.
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Suppression of seizures based on the multi-coupled neural mass model.
Cao, Yuzhen; Ren, Kaili; Su, Fei; Deng, Bin; Wei, Xile; Wang, Jiang
2015-10-01
Epilepsy is one of the most common serious neurological disorders, which affects approximately 1% of population in the world. In order to effectively control the seizures, we propose a novel control methodology, which combines the feedback linearization control (FLC) with the underlying mechanism of epilepsy, to achieve the suppression of seizures. The three coupled neural mass model is constructed to study the property of the electroencephalographs (EEGs). Meanwhile, with the model we research on the propagation of epileptiform waves and the synchronization of populations, which are taken as the foundation of our control method. Results show that the proposed approach not only yields excellent performances in clamping the pathological spiking patterns to the reference signals derived under the normal state but also achieves the normalization of the pathological parameter, where the parameters are estimated from EEGs with Unscented Kalman Filter. The specific contribution of this paper is to treat the epilepsy from its pathogenesis with the FLC, which provides critical theoretical basis for the clinical treatment of neurological disorders.
Characterization of K-complexes and slow wave activity in a neural mass model.
Directory of Open Access Journals (Sweden)
Arne Weigenand
2014-11-01
Full Text Available NREM sleep is characterized by two hallmarks, namely K-complexes (KCs during sleep stage N2 and cortical slow oscillations (SOs during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.
A neural mass model of interconnected regions simulates rhythm propagation observed via TMS-EEG.
Cona, F; Zavaglia, M; Massimini, M; Rosanova, M; Ursino, M
2011-08-01
Knowledge of cortical rhythms represents an important aspect of modern neuroscience, to understand how the brain realizes its functions. Recent data suggest that different regions in the brain may exhibit distinct electroencephalogram (EEG) rhythms when perturbed by Transcranial Magnetic Stimulation (TMS) and that these rhythms can change due to the connectivity among regions. In this context, in silico simulations may help the validation of these hypotheses that would be difficult to be verified in vivo. Neural mass models can be very useful to simulate specific aspects of electrical brain activity and, above all, to analyze and identify the overall frequency content of EEG in a cortical region of interest (ROI). In this work we implemented a model of connectivity among cortical regions to fit the impulse responses in three ROIs recorded during a series of TMS/EEG experiments performed in five subjects and using three different impulse intensities. In particular we investigated Brodmann Area (BA) 19 (occipital lobe), BA 7 (parietal lobe) and BA 6 (frontal lobe). Results show that the model can reproduce the natural rhythms of the three regions quite well, acting on a few internal parameters. Moreover, the model can explain most rhythm changes induced by stimulation of another region, and inter-subject variability, by estimating just a few long-range connectivity parameters among ROIs. Copyright © 2011 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Yoshinobu Tanaka
2012-01-01
Full Text Available The overall membrane pair characteristics included in the overall mass transport equation are understandable using the phenomenological equations expressed in the irreversible thermodynamics. In this investigation, the overall membrane pair characteristics (overall transport number , overall solute permeability , overall electro-osmotic permeability and overall hydraulic permeability were measured by seawater electrodialysis changing current density, temperature and salt concentration, and it was found that occasionally takes minus value. For understanding the above phenomenon, new concept of the overall concentration reflection coefficient ∗ is introduced from the phenomenological equation. This is the aim of this investigation. ∗ is defined for describing the permselectivity between solutes and water molecules in the electrodialysis system just after an electric current interruption. ∗ is expressed by the function of and . ∗ is generally larger than 1 and is positive, but occasionally ∗ becomes less than 1 and becomes negative. Negative means that ions are transferred with water molecules (solvent from desalting cells toward concentrating cells just after an electric current interruption, indicating up-hill transport or coupled transport between water molecules and solutes.
A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations
Zhang, Guoyu; Huang, Chengming; Li, Meng
2018-04-01
We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.
Directory of Open Access Journals (Sweden)
Chifu E. N.
2009-10-01
Full Text Available In this article, we formulate solutions to Einstein's geometrical field equations derived using our new approach. Our field equations exterior and interior to the mass distribution have only one unknown function determined by the mass or pressure distribution. Our obtained solutions yield the unknown function as generalizations of Newton's gravitational scalar potential. Thus, our solution puts Einstein's geometrical theory of gravity on same footing with Newton's dynamical theory; with the dependence of the field on one and only one unknown function comparable to Newton's gravitational scalar potential. Our results in this article are of much significance as the Sun and planets in the solar system are known to be more precisely oblate spheroidal in geometry. The oblate spheroidal geometries of these bodies have effects on their gravitational fields and the motions of test particles and photons in these fields.
International Nuclear Information System (INIS)
Dong Shihai; Lozada-Cassou, M.
2005-01-01
The exact solutions of two-dimensional Schrodinger equation with the position-dependent mass for a hard-core potential are obtained. The eigenvalues related to the position-dependent masses μ 1 and μ 2 , the potential well depth V 0 and the effective range r 0 can be calculated by the boundary condition. We generalize this quantum system to three-dimensional case. The special cases for l=0,1 are studied in detail. For l=0 and c=0, we find that the energy levels will increase with the parameters μ 2 , V 0 and r 0 if μ 1 >μ 2
Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka
2017-06-01
The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.
International Nuclear Information System (INIS)
Hof, Bas van’t; Veldman, Arthur E.P.
2012-01-01
The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.
International Nuclear Information System (INIS)
Pirouzmand, Ahmad; Hadad, Kamal
2011-01-01
Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.
Moisey, Lesley L; Mourtzakis, Marina; Kozar, Rosemary A; Compher, Charlene; Heyland, Daren K
2017-12-01
Lean body mass (LBM), quantified using computed tomography (CT), is a significant predictor of clinical outcomes in the critically ill. While CT analysis is precise and accurate in measuring body composition, it may not be practical or readily accessible to all patients in the intensive care unit (ICU). Here, we assessed the agreement between LBM measured by CT and four previously developed equations that predict LBM using variables (i.e. age, sex, weight, height) commonly recorded in the ICU. LBM was calculated in 327 critically ill adults using CT scans, taken at ICU admission, and 4 predictive equations (E1-4) that were derived from non-critically adults since there are no ICU-specific equations. Agreement was assessed using paired t-tests, Pearson's correlation coefficients and Bland-Altman plots. Median LBM calculated by CT was 45 kg (IQR 37-53 kg) and was significantly different (p LBM (error ranged from 7.5 to 9.9 kg), compared with LBM calculated by CT, suggesting insufficient agreement. Our data indicates a large bias is present between the calculation of LBM by CT imaging and the predictive equations that have been compared here. This underscores the need for future research toward the development of ICU-specific equations that reliably estimate LBM in a practical and cost-effective manner. Copyright © 2016 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All rights reserved.
The establishment of in-process plutonium mass equation in Rokkasho Reprocessing Plant
International Nuclear Information System (INIS)
Yamaya, Kosuke; Ebata, Takashi; Yamazaki, Yoshihiro; Kawai, Akio; Iwamoto, Tomonori
2008-01-01
At Rokkasho Reprocessing Plant (RRP), Active Test (AT) using actual spent fuels for the final confirmation of the equipment and the system has been performed toward the commercial operation. From the safeguards viewpoint, performance of material accountancy equipment is confirmed and data for evaluating parameters of the inspection equipment is obtained by making use of the AT period. RRP is applied to Near Real Time material Accountancy (NRTA). Under the NRTA scheme, the inventory at a cut-off time during process operation needs to be accounted for. There are some un-measurable inventories of plutonium in the process, which will be calculated from inventory estimation equations. The amount of these plutonium inventories calculated from the equations is so large that it is essential to improve the inventory estimation equations to be quite accurate. Therefore, correctness of the inventory estimation equations is evaluated by using process operation data obtained during AT. This paper describes the results of evaluating the inventory estimation equations by using the process operation data and the NRTA procedure under continuous operating condition as well. (author)
Yasaka, Koichiro; Akai, Hiroyuki; Abe, Osamu; Kiryu, Shigeru
2018-03-01
Purpose To investigate diagnostic performance by using a deep learning method with a convolutional neural network (CNN) for the differentiation of liver masses at dynamic contrast agent-enhanced computed tomography (CT). Materials and Methods This clinical retrospective study used CT image sets of liver masses over three phases (noncontrast-agent enhanced, arterial, and delayed). Masses were diagnosed according to five categories (category A, classic hepatocellular carcinomas [HCCs]; category B, malignant liver tumors other than classic and early HCCs; category C, indeterminate masses or mass-like lesions [including early HCCs and dysplastic nodules] and rare benign liver masses other than hemangiomas and cysts; category D, hemangiomas; and category E, cysts). Supervised training was performed by using 55 536 image sets obtained in 2013 (from 460 patients, 1068 sets were obtained and they were augmented by a factor of 52 [rotated, parallel-shifted, strongly enlarged, and noise-added images were generated from the original images]). The CNN was composed of six convolutional, three maximum pooling, and three fully connected layers. The CNN was tested with 100 liver mass image sets obtained in 2016 (74 men and 26 women; mean age, 66.4 years ± 10.6 [standard deviation]; mean mass size, 26.9 mm ± 25.9; 21, nine, 35, 20, and 15 liver masses for categories A, B, C, D, and E, respectively). Training and testing were performed five times. Accuracy for categorizing liver masses with CNN model and the area under receiver operating characteristic curve for differentiating categories A-B versus categories C-E were calculated. Results Median accuracy of differential diagnosis of liver masses for test data were 0.84. Median area under the receiver operating characteristic curve for differentiating categories A-B from C-E was 0.92. Conclusion Deep learning with CNN showed high diagnostic performance in differentiation of liver masses at dynamic CT. © RSNA, 2017 Online
International Nuclear Information System (INIS)
Erselcan, Taner; Turgut, Bulent; Dogan, Derya; Ozdemir, Semra
2002-01-01
The standardized uptake value (SUV) has gained recognition in recent years as a semiquantitative evaluation parameter in positron emission tomography (PET) studies. However, there is as yet no consensus on the way in which this index should be determined. One of the confusing factors is the normalisation procedure. Among the proposed anthropometric parameters for normalisation is lean body mass (LBM); LBM has been determined by using a predictive equation in most if not all of the studies. In the present study, we assessed the degree of agreement of various LBM predictive equations with a reference method. Secondly, we evaluated the impact of predicted LBM values on a hypothetical value of 2.5 SUV, normalised to LBM (SUV LBM ), by using various equations. The study population consisted of 153 women, aged 32.3±11.8 years (mean±SD), with a height of 1.61±0.06 m, a weight of 71.1±17.5 kg, a body surface area of 1.77±0.22 m 2 and a body mass index of 27.6±6.9 kg/m 2 . LBM (44.2±6.6 kg) was measured by a dual-energy X-ray absorptiometry (DEXA) method. A total of nine equations from the literature were evaluated, four of them from recent PET studies. Although there was significant correlation between predicted and measured LBM values, 95% limits of agreement determined by the Bland and Altman method showed a wide range of variation in predicted LBM values as compared with DEXA, no matter which predictive equation was used. Moreover, only one predictive equation was not statistically different in the comparison of means (DEXA and predicted LBM values). It was also shown that the predictive equations used in this study yield a wide range of SUV LBM values from 1.78 to 5.16 (29% less or 107% more) for an SUV of 2.5. In conclusion, this study suggests that estimation of LBM by use of a predictive equation may cause substantial error for an individual, and that if LBM is chosen for the SUV normalisation procedure, it should be measured, not predicted. (orig.)
A two-component wave equation for particles of spin 1/2 and non-zero rest mass
International Nuclear Information System (INIS)
Srivastava, T.
1981-11-01
We have discussed here the qualifications of the equation (delta 0 +sigmasup(k)deltasub(k))psi = -kappaTpsi, where deltasub(μ) is identical to delta/deltaxsup(μ), sigmasup(k) are the Pauli spin matrices, T is the linear operator which changes the sign of t, kappa=m 0 c/(h/2π) and psi a function with two components, as a suitable wave equation for a spin 1/2 particle with non-zero rest mass. We have established that both components of all its solutions satisfy the Klein-Gordon equation and that a 1-1 correspondence can be set up between its solutions and the positive energy solutions of the Dirac equation which preserves inner products (suitably defined for our case). We have then gone on to show covariance under transformations of the proper Lorentz group as also under space and time inversions and translations. Eigenfunctions of energy-momentum and spin have been explicitly found and it is shown that causality is preserved and a Green's function exists. A list appears, at the end, of points to be discussed in Part II of this paper, points which, it is hoped, will complete the acceptability of the theory. (author)
International Nuclear Information System (INIS)
Sahiner, B.; Chan, H.P.; Petrick, N.; Helvie, M.A.; Adler, D.D.; Goodsitt, M.M.; Wei, D.
1996-01-01
The authors investigated the classification of regions of interest (ROI's) on mammograms as either mass or normal tissue using a convolution neural network (CNN). A CNN is a back-propagation neural network with two-dimensional (2-D) weight kernels that operate on images. A generalized, fast and stable implementation of the CNN was developed. The input images to the CNN were obtained form the ROI's using two techniques. The first technique employed averaging and subsampling. The second technique employed texture feature extraction methods applied to small subregions inside the ROI. Features computed over different subregions were arranged as texture images, which were subsequently used as CNN inputs. The effects of CNN architecture and texture feature parameters on classification accuracy were studied. Receiver operating characteristic (ROC) methodology was used to evaluate the classification accuracy. A data set consisting of 168 ROI's containing biopsy-proven masses and 504 ROI's containing normal breast tissue was extracted from 168 mammograms by radiologists experienced in mammography. This data set was used for training and testing the CNN. With the best combination of CNN architecture and texture feature parameters, the area under the test ROC curve reached 0.87, which corresponded to a true-positive fraction of 90% at a false positive fraction of 31%. The results demonstrate the feasibility of using a CNN for classification of masses and normal tissue on mammograms
DeRuntz Jr., John A.
2005-01-01
The numerical solution of underwater shock fluid – structure interaction problems using boundary element/finite element techniques became tractable through the development of the family of Doubly Asymptotic Approximations (DAA). Practical implementation of the method has relied on the so-called augmentation of the DAA equations. The fluid and structural systems are respectively coupled by the structural acceleration vector in the surface normal direction on the right hand side of the DAA equa...
Directory of Open Access Journals (Sweden)
B. Godongwana
2010-01-01
Full Text Available This paper presents an analytical model of substrate mass transfer through the lumen of a membrane bioreactor. The model is a solution of the convective-diffusion equation in two dimensions using a regular perturbation technique. The analysis accounts for radial-convective flow as well as axial diffusion of the substrate specie. The model is applicable to the different modes of operation of membrane bioreactor (MBR systems (e.g., dead-end, open-shell, or closed-shell mode, as well as the vertical or horizontal orientation. The first-order limit of the Michaelis-Menten equation for substrate consumption was used to test the developed model against available analytical results. The results obtained from the application of this model, along with a biofilm growth kinetic model, will be useful in the derivation of an efficiency expression for enzyme production in an MBR.
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A. N. Gorbenko
2015-01-01
Full Text Available Modern rotary machines use auto-balancing devices of passive type to provide automatic balancing of rotors and reduce vibration. Most available researches on the rotor auto-balancing dynamics and stability are based on the assumption that the compensating bodies of the autobalancer, as well as the rotor imbalance, are infinitesimal values. The literature review has shown that the problems concerning the automatic balancing of rotor with its three-dimensional motion are solved approximately and require an in-depth analysis taking into consideration the final mass of the compensating bodies.The paper analyses the effect of an auto-balancer mass on the mass-inertial properties of the three-dimensional rotor motion. It gives the autonomous equations of the system motion. The work shows that attaching the point masses of compensating auto-balancer bodies and imbalance to the rotor causes an increase, however non-identical, in all components of the total inertia tensor of the mechanical system. This leads to a qualitative change in mass-inertial characteristics of the system.The composite rotor becomes an inertia anisotropic body in which the inertia moments about the two transverse own axes are not equal to each other. The rotor anisotropy results in complicated dynamic behavior of the gyroscopic rotor. In this case, the additional critical rotor speeds and the zones of instability of motion may occur.It is shown that in the case of using multi-body auto-balancer the inertial parameters of the rotor system grow into the interval values, i.e. their values are not uniquely determined and may be equal to a variety values from a certain range. Thus, the degree of inertial anisotropy and other auto-balancing parameters are the interval values as well in this case.The system of dimensionless equations of rotary machine motion, which contains the minimum required number of dimensionless parameters, has been obtained. The specific ranges of the dimensionless
DEFF Research Database (Denmark)
Hjerrild, M.; Stensballe, A.; Rasmussen, T.E.
2004-01-01
Protein phosphorylation plays a key role in cell regulation and identification of phosphorylation sites is important for understanding their functional significance. Here, we present an artificial neural network algorithm: NetPhosK (http://www.cbs.dtu.dk/services/NetPhosK/) that predicts protein...
Gardiner, Casey K; YorkWilliams, Sophie L; Bryan, Angela D; Hutchison, Kent E
2017-07-28
Obesity is a large and growing public health concern, presenting enormous economic and health costs to individuals and society. A burgeoning literature demonstrates that overweight and obese individuals display different neural processing of rewarding stimuli, including caloric substances, as compared to healthy weight individuals. However, much extant research on the neurobiology of obesity has focused on addiction models, without highlighting potentially separable neural underpinnings of caloric intake versus substance use. The present research explores these differences by examining neural response to alcoholic beverages and a sweet non-alcoholic beverage, among a sample of individuals with varying weight status and patterns of alcohol use and misuse. Participants received tastes of a sweet beverage (litchi juice) and alcoholic beverages during fMRI scanning. When controlling for alcohol use, elevated weight status was associated with increased activation in response to sweet taste in regions including the cingulate cortex, hippocampus, precuneus, and fusiform gyrus. However, weight status was not associated with neural response to alcoholic beverages. Copyright © 2017 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Hjerrild, Majbrit; Stensballe, Allan; Rasmussen, Thomas E
2011-01-01
Protein phosphorylation plays a key role in cell regulation and identification of phosphorylation sites is important for understanding their functional significance. Here, we present an artificial neural network algorithm: NetPhosK (http://www.cbs.dtu.dk/services/NetPhosK/) that predicts protein...
Directory of Open Access Journals (Sweden)
Hoyong Sung
2017-06-01
Full Text Available Background : Using BMI as an independent variable is the easiest way to estimate percent body fat. Thus far, few studies have investigated the development and cross-validation of an equation for estimating the percent body fat of Korean adults according to the BMI. The goals of this study were the development and cross-validation of an equation for estimating the percent fat of representative Korean adults using the BMI. Methods : Samples were obtained from the Korea National Health and Nutrition Examination Survey between 2008 and 2011. The samples from 2008-2009 and 2010-2011 were labeled as the validation group (n=10,624 and the cross-validation group (n=8,291, respectively. The percent fat was measured using dual-energy X-ray absorptiometry, and the body mass index, gender, and age were included as independent variables to estimate the measured percent fat. The coefficient of determination (R², standard error of estimation (SEE, and total error (TE were calculated to examine the accuracy of the developed equation. Results : The cross-validated R² was 0.731 for Model 1 and 0.735 for Model 2. The SEE was 3.978 for Model 1 and 3.951 for Model 2. The equations developed in this study are more accurate for estimating percent fat of the cross-validation group than those previously published by other researchers. Conclusion : The newly developed equations are comparatively accurate for the estimation of the percent fat of Korean adults.
Energy Technology Data Exchange (ETDEWEB)
Drago, Alessandro; Pagliara, Giuseppe [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Ferrara (Italy); Lavagno, Andrea; Pigato, Daniele [Politecnico di Torino (Italy). Dept. of Applied Science and Technology; INFN, Torino (Italy)
2016-02-15
We present several arguments which favor the scenario of two coexisting families of compact stars: hadronic stars and quark stars. Besides the well-known hyperon puzzle of the physics of compact stars, a similar puzzle exists also when considering delta resonances. We show that these particles appear at densities close to twice saturation density and must be therefore included in the calculations of the hadronic equation of state. Such an early appearance is strictly related to the value of the L parameter of the symmetry energy that has been found, in recent phenomenological studies, to lie in the range 40 < L < 62 MeV. We discuss also the threshold for the formation of deltas and hyperons for hot and lepton-rich hadronic matter. Similarly to the case of hyperons, also delta resonances cause a softening of the equation of state, which makes it difficult to obtain massive hadronic stars. Quark stars, on the other hand, can reach masses up to 2.75M {sub CircleDot} as predicted by perturbative QCD calculations. We then discuss the observational constraints on the masses and the radii of compact stars. The tension between the precise measurements of high masses and the indications of the existence of very compact stellar objects (with radii of the order of 10 km) is relieved when assuming that very massive compact stars are quark stars and very compact stars are hadronic stars. Finally, we discuss recent interesting measurements of the eccentricities of the orbits of millisecond pulsars in low mass X-ray binaries. The high values of the eccentricities found in some cases could be explained by assuming that the hadronic star, initially present in the binary system, converts to a quark star due to the increase of its central density. (orig.)
Directory of Open Access Journals (Sweden)
Ryszard Hejmanowski
2015-01-01
Full Text Available Based on the previous studies conducted by the authors, a new approach was proposed, namely the tools of artificial intelligence. One of neural networks is a multilayer perceptron network (MLP, which has already found applications in many fields of science. Sequentially, a series of calculations was made for different MLP neural network configuration and the best of them was selected. Mean square error (MSE and the correlation coefficient R were adopted as the selection criterion for the optimal network. The obtained results were characterized with a considerable dispersion. With an increase in the amount of hidden neurons, the MSE of the network increased while the correlation coefficient R decreased. Similar conclusions were drawn for the network with a small number of hidden neurons. The analysis allowed to select a network composed of 24 neurons as the best one for the issue under question. The obtained final answers of artificial neural network were presented in a histogram as differences between the calculated and expected value.
Hughes, J T; Maple-Brown, L J; Piers, L S; Meerkin, J; O'Dea, K; Ward, L C
2015-01-01
To describe the development of a single-frequency bioimpedance prediction equation for fat-free mass (FFM) suitable for adult Aboriginal and Torres Strait Islander peoples with and without diabetes or indicators of chronic kidney disease (CKD). FFM was measured by whole-body dual-energy X-ray absorptiometry in 147 adult Indigenous Australians. Height, weight, body circumference and resistance were also measured. Adults with and without diabetes and indicators of CKD were examined. A random split sample with internal cross-validation approach was used to predict and subsequently validate FFM using resistance, height, weight, age and gender against measured FFM. Among 147 adults with a median body mass index of 31 kg/m(2), the final model of FFM was FFM (kg)=0.432 (height, cm(2)/resistance, ohm)-0.086 (age, years)+0.269 (weight, kg)-6.422 (if female)+16.429. Adjusted R(2) was 0.94 and the root mean square error was 3.33 kg. The concordance was high (rc=0.97) between measured and predicted FFM across a wide range of FFM (31-85 kg). In the context of the high burden of diabetes and CKD among adult Indigenous Australians, this new equation for FFM was both accurate and precise and based on easily acquired variables (height, weight, age, gender and resistance) among a heterogeneous adult cohort.
Bandeira Diniz, João Otávio; Bandeira Diniz, Pedro Henrique; Azevedo Valente, Thales Levi; Corrêa Silva, Aristófanes; de Paiva, Anselmo Cardoso; Gattass, Marcelo
2018-03-01
The processing of medical image is an important tool to assist in minimizing the degree of uncertainty of the specialist, while providing specialists with an additional source of detect and diagnosis information. Breast cancer is the most common type of cancer that affects the female population around the world. It is also the most deadly type of cancer among women. It is the second most common type of cancer among all others. The most common examination to diagnose breast cancer early is mammography. In the last decades, computational techniques have been developed with the purpose of automatically detecting structures that maybe associated with tumors in mammography examination. This work presents a computational methodology to automatically detection of mass regions in mammography by using a convolutional neural network. The materials used in this work is the DDSM database. The method proposed consists of two phases: training phase and test phase. The training phase has 2 main steps: (1) create a model to classify breast tissue into dense and non-dense (2) create a model to classify regions of breast into mass and non-mass. The test phase has 7 step: (1) preprocessing; (2) registration; (3) segmentation; (4) first reduction of false positives; (5) preprocessing of regions segmented; (6) density tissue classification (7) second reduction of false positives where regions will be classified into mass and non-mass. The proposed method achieved 95.6% of accuracy in classify non-dense breasts tissue and 97,72% accuracy in classify dense breasts. To detect regions of mass in non-dense breast, the method achieved a sensitivity value of 91.5%, and specificity value of 90.7%, with 91% accuracy. To detect regions in dense breasts, our method achieved 90.4% of sensitivity and 96.4% of specificity, with accuracy of 94.8%. According to the results achieved by CNN, we demonstrate the feasibility of using convolutional neural networks on medical image processing techniques for
Hiramatsu, Yuya; Muramatsu, Chisako; Kobayashi, Hironobu; Hara, Takeshi; Fujita, Hiroshi
2017-03-01
Breast cancer screening with mammography and ultrasonography is expected to improve sensitivity compared with mammography alone, especially for women with dense breast. An automated breast volume scanner (ABVS) provides the operator-independent whole breast data which facilitate double reading and comparison with past exams, contralateral breast, and multimodality images. However, large volumetric data in screening practice increase radiologists' workload. Therefore, our goal is to develop a computer-aided detection scheme of breast masses in ABVS data for assisting radiologists' diagnosis and comparison with mammographic findings. In this study, false positive (FP) reduction scheme using deep convolutional neural network (DCNN) was investigated. For training DCNN, true positive and FP samples were obtained from the result of our initial mass detection scheme using the vector convergence filter. Regions of interest including the detected regions were extracted from the multiplanar reconstraction slices. We investigated methods to select effective FP samples for training the DCNN. Based on the free response receiver operating characteristic analysis, simple random sampling from the entire candidates was most effective in this study. Using DCNN, the number of FPs could be reduced by 60%, while retaining 90% of true masses. The result indicates the potential usefulness of DCNN for FP reduction in automated mass detection on ABVS images.
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Chifu E. N.
2009-07-01
Full Text Available Here, we present a profound and complete analytical solution to Einstein’s gravitational field equations exterior to astrophysically real or hypothetical time varying distribu- tions of mass or pressure within regions of spherical geometry. The single arbitrary function f in our proposed exterior metric tensor and constructed field equations makes our method unique, mathematically less combersome and astrophysically satisfactory. The obtained solution of Einstein’s gravitational field equations tends out to be a gen- eralization of Newton’s gravitational scalar potential exterior to the spherical mass or pressure distribution under consideration
The dynamic brain: from spiking neurons to neural masses and cortical fields.
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Gustavo Deco
2008-08-01
Full Text Available The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI, electroencephalogram (EEG, and magnetoencephalogram (MEG. Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the
Illien, Bertrand; Ying, Ruifeng
2009-05-11
New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2equations clearly achieve a better agreement with supplier M values. For macromolecules (M>500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.
Shotorban, Babak
2010-04-01
The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.
International Nuclear Information System (INIS)
Zheng Shi-Wang; Wang Jian-Bo; Chen Xiang-Wei; Xie Jia-Fang
2012-01-01
Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system. (general)
Kono, Kenichi; Nishida, Yusuke; Moriyama, Yoshihumi; Taoka, Masahiro; Sato, Takashi
2015-06-01
The assessment of nutritional states using fat free mass (FFM) measured with near-infrared spectroscopy (NIRS) is clinically useful. This measurement should incorporate the patient's post-dialysis weight ("dry weight"), in order to exclude the effects of any change in water mass. We therefore used NIRS to investigate the regression, independent variables, and absolute reliability of FFM in dry weight. The study included 47 outpatients from the hemodialysis unit. Body weight was measured before dialysis, and FFM was measured using NIRS before and after dialysis treatment. Multiple regression analysis was used to estimate the FFM in dry weight as the dependent variable. The measured FFM before dialysis treatment (Mw-FFM), and the difference between measured and dry weight (Mw-Dw) were independent variables. We performed Bland-Altman analysis to detect errors between the statistically estimated FFM and the measured FFM after dialysis treatment. The multiple regression equation to estimate the FFM in dry weight was: Dw-FFM = 0.038 + (0.984 × Mw-FFM) + (-0.571 × [Mw-Dw]); R(2) = 0.99). There was no systematic bias between the estimated and the measured values of FFM in dry weight. Using NIRS, FFM in dry weight can be calculated by an equation including FFM in measured weight and the difference between the measured weight and the dry weight. © 2015 The Authors. Therapeutic Apheresis and Dialysis © 2015 International Society for Apheresis.
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J. Prakash Maran
2013-09-01
Full Text Available In this study, a comparative approach was made between artificial neural network (ANN and response surface methodology (RSM to predict the mass transfer parameters of osmotic dehydration of papaya. The effects of process variables such as temperature, osmotic solution concentration and agitation speed on water loss, weight reduction, and solid gain during osmotic dehydration were investigated using a three-level three-factor Box-Behnken experimental design. Same design was utilized to train a feed-forward multilayered perceptron (MLP ANN with back-propagation algorithm. The predictive capabilities of the two methodologies were compared in terms of root mean square error (RMSE, mean absolute error (MAE, standard error of prediction (SEP, model predictive error (MPE, chi square statistic (χ2, and coefficient of determination (R2 based on the validation data set. The results showed that properly trained ANN model is found to be more accurate in prediction as compared to RSM model.
Research of processes of eutrophication of Teteriv river reservoir based on neural networks mass
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Yelnikova T.A.
2016-12-01
Full Text Available Methods of process control of eutrophication in water are based on water sampling, handling them in the laboratory and calculation of indexes of pond ecosystem. However, these methods have some significant drawbacks associated with using manual labor. The method of determining of the geometric parameters of phytoplankton through the use of neural networks for processing water samples is developed. Due to this method eutrophic processes of reservoirs of river Teteriv are investigated. A comparative analysis of eutrophic processes of reservoirs "Denyshi" and “Vidsichne” intake during 2014-2015 years are given. The differences between qualitative and quantitative composition of phytoplankton algae in two reservoirs of the river Teteriv used for water supply of Zhitomir city area are found out. The influence of exogenous and endogenous factors on the expansion of phytoplankton is researched. Research results can be used for monitoring and forecasting of ecological state of water for household purposes, used for water supply of cities.
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Peng Wang
Full Text Available In this work we propose a biologically realistic local cortical circuit model (LCCM, based on neural masses, that incorporates important aspects of the functional organization of the brain that have not been covered by previous models: (1 activity dependent plasticity of excitatory synaptic couplings via depleting and recycling of neurotransmitters and (2 realistic inter-laminar dynamics via laminar-specific distribution of and connections between neural populations. The potential of the LCCM was demonstrated by accounting for the process of auditory habituation. The model parameters were specified using Bayesian inference. It was found that: (1 besides the major serial excitatory information pathway (layer 4 to layer 2/3 to layer 5/6, there exists a parallel "short-cut" pathway (layer 4 to layer 5/6, (2 the excitatory signal flow from the pyramidal cells to the inhibitory interneurons seems to be more intra-laminar while, in contrast, the inhibitory signal flow from inhibitory interneurons to the pyramidal cells seems to be both intra- and inter-laminar, and (3 the habituation rates of the connections are unsymmetrical: forward connections (from layer 4 to layer 2/3 are more strongly habituated than backward connections (from Layer 5/6 to layer 4. Our evaluation demonstrates that the novel features of the LCCM are of crucial importance for mechanistic explanations of brain function. The incorporation of these features into a mass model makes them applicable to modeling based on macroscopic data (like EEG or MEG, which are usually available in human experiments. Our LCCM is therefore a valuable building block for future realistic models of human cognitive function.
Directory of Open Access Journals (Sweden)
Vincent A Emanuele
Full Text Available SELDI-TOF mass spectrometer's compact size and automated, high throughput design have been attractive to clinical researchers, and the platform has seen steady-use in biomarker studies. Despite new algorithms and preprocessing pipelines that have been developed to address reproducibility issues, visual inspection of the results of SELDI spectra preprocessing by the best algorithms still shows miscalled peaks and systematic sources of error. This suggests that there continues to be problems with SELDI preprocessing. In this work, we study the preprocessing of SELDI in detail and introduce improvements. While many algorithms, including the vendor supplied software, can identify peak clusters of specific mass (or m/z in groups of spectra with high specificity and low false discover rate (FDR, the algorithms tend to underperform estimating the exact prevalence and intensity of peaks in those clusters. Thus group differences that at first appear very strong are shown, after careful and laborious hand inspection of the spectra, to be less than significant. Here we introduce a wavelet/neural network based algorithm which mimics what a team of expert, human users would call for peaks in each of several hundred spectra in a typical SELDI clinical study. The wavelet denoising part of the algorithm optimally smoothes the signal in each spectrum according to an improved suite of signal processing algorithms previously reported (the LibSELDI toolbox under development. The neural network part of the algorithm combines those results with the raw signal and a training dataset of expertly called peaks, to call peaks in a test set of spectra with approximately 95% accuracy. The new method was applied to data collected from a study of cervical mucus for the early detection of cervical cancer in HPV infected women. The method shows promise in addressing the ongoing SELDI reproducibility issues.
International Nuclear Information System (INIS)
Xiong Jinbiao; Koshizuka, Seiichi; Sakai, Mikio
2011-01-01
Highlights: → We selected and evaluated five two-equation eddy-viscosity turbulence models for modeling the separated and reattaching flow. → The behavior of the models in the simple flow is not consistent with that in the separated and reattaching flow. → The Abe-Kondoh-Nagano model is the best one among the selected model. → Application of the stress limiter and the Kato-Launder modification in the Abe-Kondoh-Nagano model helps to improve prediction of the peak mass transfer coefficient in the orifice flow. → The value of turbulent Schmidt number is investigated. - Abstract: The prediction of mass transfer rate is one of the key elements for estimation of the flow accelerated corrosion (FAC) rate. Three low Reynolds number (LRN) k-ε models (Lam-Bremhorst (LB), Abe-Kondoh-Nagano (AKN) and Hwang-Lin (HL)), one LRN k-ω (Wilcox, WX) model and the k-ω SST model are tested for the computation of the high Schmidt number mass transfer, especially in the flow through an orifice. The models are tested in the computation of three types of flow: (1) the fully developed pipe flow, (2) the flow over a backward facing step, (3) the flow through an orifice. The HL model shows a good performance in predicting mass transfer in the fully developed pipe flow but fails to give reliable prediction in the flow through an orifice. The WX model and the k-ω SST model underpredict the mass transfer rate in the flow types 1 and 3. The LB model underestimates the mass transfer in the flow type 1, but shows abnormal behavior at the reattaching point in type 3. Synthetically evaluating all the models in all the computed case, the AKN model is the best one; however, the prediction is still not satisfactory. In the evaluation in the flow over a backward facing step shows k-ω SST model shows superior performance. This is interpreted as an implication that the combination of the k-ε model and the stress limiter can improve the model behavior in the recirculation bubble. Both the
Institute of Scientific and Technical Information of China (English)
ZHENG Shi-Wang; WANG Jian-Bo; CHEN Xiang-Wei; XIE Jia-Fang
2012-01-01
Operational systems of spacecraft are general variable mass mechanics systems,and their symmetries and conserved quantities imply profound physical rules of the space system.We study the Mei symmetry of Tzénoff equations for a variable mass nonholonomic system and the new conserved quantities derived.The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented.This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.%Operational systems of spacecraft are general variable mass mechanics systems, and their symmetries and conserved quantities imply profound physical rules of the space system. We study the Mei symmetry of Tzenoff equations for a variable mass nonholonomic system and the new conserved quantities derived. The function expression of the new conserved quantities and the criterion equation which deduces these conserved quantities are presented. This result has some theoretical values in further research of conservation laws obeyed by the variable mass system.
DEFF Research Database (Denmark)
Bloch, Helle Aagaard; Kesmir, Can; Petersen, Marianne Kjerstine
1999-01-01
A novel tool for variety identification of wheat (Triticum aestivum L,) has been developed: an artificial neural network (ANN) is used to classify the gliadin fraction analysed by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry (MALDI-TOFMS). The robustness...
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model
Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus
2016-01-01
Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514
Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.
Papasavvas, Christoforos A; Wang, Yujiang; Trevelyan, Andrew J; Kaiser, Marcus
2015-09-01
Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.
International Nuclear Information System (INIS)
Barbashov, B.M.
1996-01-01
Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space E 2 1 , there are two invariants of that sort, the curvature K and torsion κ. Curvatures of trajectories of the string ends with masses are always constant, K i =γ/m i (i=1,2), whereas torsions κ i obey a system of differential equations with deviating arguments. For these equations with periodic κ i (τ+nl)=κ(τ), constants of motion are obtained (part 1) and exact solutions are presented (part 2) for periods l and 2l where l is the string length in the plane of parameters τ and σ(σ 1 =0, σ 2 =l). 7 refs
Directory of Open Access Journals (Sweden)
Altuğ Arda
2017-01-01
Full Text Available We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function m(x. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.
Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I
2018-04-16
Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.
Directory of Open Access Journals (Sweden)
Mohsen Shanbeh
2011-01-01
Full Text Available One of the main methods to reduce the production costs is waste recycling which is the most important challenge for the future. Cotton wastes collected from ginning process have desirable properties which could be used during spinning process. The purpose of this study was to develop predictive models of breaking strength and mass irregularity (CV% of cotton waste rotor-spun yarns containing cotton waste collected from ginning process by using the artificial neural network trained with backpropagation algorithm. Artificial neural network models have been developed based on rotor diameter, rotor speed, navel type, opener roller speed, ginning waste proportion and yarn linear density as input parameters. The parameters of artificial neural network model, namely, learning, and momentum rate, number of hidden layers and number of hidden processing elements (neurons were optimized to get the best predictive models. The findings showed that the breaking strength and mass irregularity of rotor spun yarns could be predicted satisfactorily by artificial neural network. The maximum error in predicting the breaking strength and mass irregularity of testing data was 8.34% and 6.65%, respectively.
A neural signature of food semantics is associated with body-mass index.
Pergola, Giulio; Foroni, Francesco; Mengotti, Paola; Argiris, Georgette; Rumiati, Raffaella Ida
2017-10-01
Visual recognition of objects may rely on different features depending on the category to which they belong. Recognizing natural objects, such as fruits and plants, weighs more on their perceptual attributes, whereas recognizing man-made objects, such as tools or vehicles, weighs more upon the functions and actions they enable. Edible objects are perceptually rich but also prepared for specific functions, therefore it is unclear how perceptual and functional attributes affect their recognition. Two event-related potentials experiments investigated: (i) whether food categorization in the brain is differentially modulated by sensory and functional attributes, depending on whether the food is natural or transformed; (ii) whether these processes are modulated by participants' body mass index. In experiment 1, healthy normal-weight participants were presented with a sentence (prime) and a photograph of a food. Primes described either a sensory feature ('It tastes sweet') or a functional feature ('It is suitable for a wedding party') of the food, while photographs depicted either a natural (e.g., cherry) or a transformed food (e.g., pizza). Prime-feature pairs were either congruent or incongruent. This design aimed at modulating N400-like components elicited by semantic processing. In experiment 1, N400-like amplitude was significantly larger for transformed food than for natural food with sensory primes, and vice versa with functional primes. In experiment 2, underweight and obese women performed the same semantic task. We found that, while the N400-like component in obese participants was modulated by sensory-functional primes only for transformed food, the same modulation was found in underweight participants only for natural food. These findings suggest that the level of food transformation interacts with participants' body mass index in modulating food perception and the underlying brain processing. Crown Copyright © 2017. Published by Elsevier B.V. All rights
DEFF Research Database (Denmark)
Bloch, H.A.; Petersen, Marianne Kjerstine; Sperotto, Maria Maddalena
2001-01-01
developed, which combines analysis of alcohol-soluble wheat proteins (gliadins) using matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry with neural networks. Here we have applied the same method for the identification of both barley (Hordeum vulgare L.) and rye (Secale cereale L.......) varieties. For barley, 95% of the mass spectra were correctly classified. This is an encouraging result, since in earlier experiments only a grouping into subsets of varieties was possible. However, the method was not useful in the classification of rye, due to the strong similarity between mass spectra...
Hofsteenge, G.H.; Chin A Paw, M.J.M.; Weijs, P.J.M.
2015-01-01
Background: In clinical practice, patient friendly methods to assess body composition in obese adolescents are needed. Therefore, the bioelectrical impedance analysis (BIA) related fat-free mass (FFM) prediction equations (FFM-BIA) were evaluated in obese adolescents (age 11-18 years) compared to
Zhebel, E.; Minisini, S.; Mulder, W.A.
2012-01-01
We solve the three-dimensional acoustic wave equation, discretized on tetrahedral meshes. Two methods are considered: mass-lumped continuous finite elements and the symmetric interior-penalty discontinuous Galerkin method (SIP-DG). Combining the spatial discretization with the leap-frog
Liu, Fei; Wang, Jiang; Liu, Chen; Li, Huiyan; Deng, Bin; Fietkiewicz, Chris; Loparo, Kenneth A.
2016-12-01
An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.
Kilgour, Robert D; Cardiff, Katrina; Rosenthall, Leonard; Lucar, Enriqueta; Trutschnigg, Barbara; Vigano, Antonio
2016-01-01
Measurements of body composition using dual-energy X-ray absorptiometry (DXA) and single abdominal images from computed tomography (CT) in advanced cancer patients (ACP) have important diagnostic and prognostic value. The question arises as to whether CT scans can serve as surrogates for DXA in terms of whole-body fat-free mass (FFM), whole-body fat mass (FM), and appendicular skeletal muscle (ASM) mass. Predictive equations to estimate body composition for ACP from CT images have been proposed (Mourtzakis et al. 2008; Appl. Physiol. Nutr. Metabol. 33(5): 997-1006); however, these equations have yet to be validated in an independent cohort of ACP. Thus, this study evaluated the accuracy of these equations in estimating FFM, FM, and ASM mass using CT images at the level of the third lumbar vertebrae and compared these values with DXA measurements. FFM, FM, and ASM mass were estimated from the prediction equations proposed by Mourtzakis and colleagues (2008) using single abdominal CT images from 43 ACP and were compared with whole-body DXA scans using Spearman correlations and Bland-Altman analyses. Despite a moderate to high correlation between the actual (DXA) and predicted (CT) values for FM (rho = 0.93; p ≤ 0.001), FFM (rho = 0.78; p ≤ 0.001), and ASM mass (rho = 0.70; p ≤ 0.001), Bland-Altman analyses revealed large range-of-agreement differences between the 2 methods (29.39 kg for FFM, 15.47 kg for FM, and 3.99 kg for ASM mass). Based on the magnitude of these differences, we concluded that prediction equations using single abdominal CT images have poor accuracy, cannot be considered as surrogates for DXA, and may have limited clinical utility.
Energy Technology Data Exchange (ETDEWEB)
Kim, Woo Hyoung; Kim, Chang Guhn; Kim, Dae Weung [Wonkwang Univ. School of Medicine, Iksan (Korea, Republic of)
2012-09-15
Standardized uptake values (SUVs)normalized by lean body mass (LBM)determined by CT were compared with those normalized by LBM estimated using predictive equations (PEs)in normal liver, spleen, and aorta using {sup 18}F FDG PET/CT. Fluorine 18 fluorodeoxyglucose (F FDG)positron emission tomography/computed tomography (PET/CT)was conducted on 453 patients. LBM determined by CT was defined in 3 ways (LBM{sup CT1}-3). Five PEs were used for comparison (LBM{sup PE1}-5). Tissue SUV normalized by LBM (SUL) was calculated using LBM from each method (SUL{sup CT1}-3, SUL{sup PE1}-5). Agreement between methods was assessed by Bland Altman analysis. Percentage difference and percentage error were also calculated. For all liver SUL{sup CTS} vs. liver SUL{sup PES} except liver SUL{sup PE3}, the range of biases, SDs of percentage difference and percentage errors were -0.17-0.24 SUL, 6.15-10.17%, and 25.07-38.91%, respectively. For liver SUL{sup CTs} vs. liver SUL{sup PE3}, the corresponding figures were 0.47-0.69 SUL, 10.90-11.25%, and 50.85-51.55%, respectively, showing the largest percentage errors and positive biases. Irrespective of magnitudes of the biases, large percentage errors of 25.07-51.55% were observed between liver SUL{sup CT1}-3 and liver SUL{sup PE1}-5. The results of spleen and aorta SUL{sup CTs} and SUL{sup PEs} comparison were almost identical to those for liver. The present study demonstrated substantial errors in individual SUL{sup PEs} compared with SUL{sup CTs} as a reference value. Normalization of SUV by LBM determined by CT rather than PEs may be a useful approach to reduce errors in individual SUL{sup PEs}.
International Nuclear Information System (INIS)
Kim, Woo Hyoung; Kim, Chang Guhn; Kim, Dae Weung
2012-01-01
Standardized uptake values (SUVs)normalized by lean body mass (LBM)determined by CT were compared with those normalized by LBM estimated using predictive equations (PEs)in normal liver, spleen, and aorta using 18 F FDG PET/CT. Fluorine 18 fluorodeoxyglucose (F FDG)positron emission tomography/computed tomography (PET/CT)was conducted on 453 patients. LBM determined by CT was defined in 3 ways (LBM CT1 -3). Five PEs were used for comparison (LBM PE1 -5). Tissue SUV normalized by LBM (SUL) was calculated using LBM from each method (SUL CT1 -3, SUL PE1 -5). Agreement between methods was assessed by Bland Altman analysis. Percentage difference and percentage error were also calculated. For all liver SUL CTS vs. liver SUL PES except liver SUL PE3 , the range of biases, SDs of percentage difference and percentage errors were -0.17-0.24 SUL, 6.15-10.17%, and 25.07-38.91%, respectively. For liver SUL CTs vs. liver SUL PE3 , the corresponding figures were 0.47-0.69 SUL, 10.90-11.25%, and 50.85-51.55%, respectively, showing the largest percentage errors and positive biases. Irrespective of magnitudes of the biases, large percentage errors of 25.07-51.55% were observed between liver SUL CT1 -3 and liver SUL PE1 -5. The results of spleen and aorta SUL CTs and SUL PEs comparison were almost identical to those for liver. The present study demonstrated substantial errors in individual SUL PEs compared with SUL CTs as a reference value. Normalization of SUV by LBM determined by CT rather than PEs may be a useful approach to reduce errors in individual SUL PEs
Samala, Ravi K.; Chan, Heang-Ping; Hadjiiski, Lubomir; Helvie, Mark A.; Richter, Caleb; Cha, Kenny
2018-02-01
Deep-learning models are highly parameterized, causing difficulty in inference and transfer learning. We propose a layered pathway evolution method to compress a deep convolutional neural network (DCNN) for classification of masses in DBT while maintaining the classification accuracy. Two-stage transfer learning was used to adapt the ImageNet-trained DCNN to mammography and then to DBT. In the first-stage transfer learning, transfer learning from ImageNet trained DCNN was performed using mammography data. In the second-stage transfer learning, the mammography-trained DCNN was trained on the DBT data using feature extraction from fully connected layer, recursive feature elimination and random forest classification. The layered pathway evolution encapsulates the feature extraction to the classification stages to compress the DCNN. Genetic algorithm was used in an iterative approach with tournament selection driven by count-preserving crossover and mutation to identify the necessary nodes in each convolution layer while eliminating the redundant nodes. The DCNN was reduced by 99% in the number of parameters and 95% in mathematical operations in the convolutional layers. The lesion-based area under the receiver operating characteristic curve on an independent DBT test set from the original and the compressed network resulted in 0.88+/-0.05 and 0.90+/-0.04, respectively. The difference did not reach statistical significance. We demonstrated a DCNN compression approach without additional fine-tuning or loss of performance for classification of masses in DBT. The approach can be extended to other DCNNs and transfer learning tasks. An ensemble of these smaller and focused DCNNs has the potential to be used in multi-target transfer learning.
Directory of Open Access Journals (Sweden)
Julio Rojas Naccha
2012-09-01
Full Text Available The predictive ability of Artificial Neural Network (ANN on the effect of the concentration (30, 40, 50 y 60 % w/w and temperature (30, 40 y 50°C of fructooligosaccharides solution, in the mass, moisture, volume and solids of osmodehydrated yacon cubes, and in the coefficients of the water means effective diffusivity with and without shrinkage was evaluated. The Feedforward type ANN with the Backpropagation training algorithms and the Levenberg-Marquardt weight adjustment was applied, using the following topology: 10-5 goal error, 0.01 learning rate, 0.5 moment coefficient, 2 input neurons, 6 output neurons, one hidden layer with 18 neurons, 15 training stages and logsig-pureline transfer functions. The overall average error achieved by the ANN was 3.44% and correlation coefficients were bigger than 0.9. No significant differences were found between the experimental values and the predicted values achieved by the ANN and with the predicted values achieved by a statistical model of second-order polynomial regression (p > 0.95.
Directory of Open Access Journals (Sweden)
Basabdatta Sen Bhattacharya
2016-11-01
Full Text Available Experimental studies on the Lateral Geniculate Nucleus (LGN of mammals and rodents show that the inhibitory interneurons (IN receive around 47.1% of their afferents from the retinal spiking neurons, and constitute around 20 - 25% of the LGN cell population. However, there is a definite gap in knowledge about the role and impact of IN on thalamocortical dynamics in both experimental and model-based research. We use a neural mass computational model of the LGN with three neural populations viz. IN, thalamocortical relay (TCR, thalamic reticular nucleus (TRN, to study the causality of IN on LGN oscillations and state-transitions. The synaptic information transmission in the model is implemented with kinetic modelling, facilitating the linking of low-level cellular attributes with high-level population dynamics. The model is parameterised and tuned to simulate both Local Field Potential (LFP of LGN and electroencephalogram (EEG of visual cortex in an awake resting state with eyes closed and dominant frequency within the alpha (8-13 Hz band. The results show that: First, the response of the TRN is suppressed in the presence of IN in the circuit; disconnecting the IN from the circuit effects a dramatic change in the model output, displaying high amplitude synchronous oscillations within the alpha band in both TCR and TRN. These observations conform to experimental reports implicating the IN as the primary inhibitory modulator of LGN dynamics in a cognitive state, and that reduced cognition is achieved by suppressing the TRN response. Second, the model validates steady state visually evoked potential response in humans corresponding to periodic input stimuli; however, when the IN is disconnected from the circuit, the output power spectra do not reflect the input frequency. This agrees with experimental reports underpinning the role of IN in efficient retino-geniculate information transmission. Third, a smooth transition from alpha to theta band is
Pan, Kuo-Chuan; Liebendörfer, Matthias; Couch, Sean M.; Thielemann, Friedrich-Karl
2018-04-01
We investigate axisymmetric black hole (BH) formation and its gravitational wave (GW) and neutrino signals with self-consistent core-collapse supernova simulations of a non-rotating 40 M ⊙ progenitor star using the isotropic diffusion source approximation for the neutrino transport and a modified gravitational potential for general relativistic effects. We consider four different neutron star (NS) equations of state (EoS): LS220, SFHo, BHBΛϕ, and DD2, and study the impact of the EoS on BH formation dynamics and GW emission. We find that the BH formation time is sensitive to the EoS from 460 to >1300 ms and is delayed in multiple dimensions for ∼100–250 ms due to the finite entropy effects. Depending on the EoS, our simulations show the possibility that shock revival can occur along with the collapse of the proto-neutron star (PNS) to a BH. The gravitational waveforms contain four major features that are similar to previous studies but show extreme values: (1) a low-frequency signal (∼300–500 Hz) from core-bounce and prompt convection, (2) a strong signal from the PNS g-mode oscillation among other features, (3) a high-frequency signal from the PNS inner-core convection, and (4) signals from the standing accretion shock instability and convection. The peak frequency at the onset of BH formation reaches to ∼2.3 kHz. The characteristic amplitude of a 10 kpc object at peak frequency is detectable but close to the noise threshold of the Advanced LIGO and KAGRA, suggesting that the next-generation GW detector will need to improve the sensitivity at the kHz domain to better observe stellar-mass BH formation from core-collapse supernovae or failed supernovae.
Leung, Y M; Cave, N J; Hodgson, B A S
2018-06-27
To develop an equation that accurately estimates fat-free mass (FFM) and the ratio of FFM to skeletal size or mass, using morphometric measurements in lean working farm dogs, and to examine the association between FFM derived from body condition score (BCS) and FFM measured using isotope dilution. Thirteen Huntaway and seven Heading working dogs from sheep and beef farms in the Waikato region of New Zealand were recruited based on BCS (BCS 4) using a nine-point scale. Bodyweight, BCS, and morphometric measurements (head length and circumference, body length, thoracic girth, and fore and hind limb length) were recorded for each dog, and body composition was measured using an isotopic dilution technique. A new variable using morphometric measurements, termed skeletal size, was created using principal component analysis. Models for predicting FFM, leanST (FFM minus skeletal mass) and ratios of FFM and leanST to skeletal size or mass were generated using multiple linear regression analysis. Mean FFM of the 20 dogs, measured by isotope dilution, was 22.1 (SD 4.4) kg and the percentage FFM of bodyweight was 87.0 (SD 5.0)%. Median BCS was 3.0 (min 1, max 6). Bodyweight, breed, age and skeletal size or mass were associated with measured FFM (pFFM and measured FFM (R 2 =0.96), and for the ratio of predicted FFM to skeletal size and measured values (R 2 =0.99). Correlation coefficients were higher for the ratio FFM and leanST to skeletal size than for ratios using skeletal mass. There was a positive correlation between BCS-derived fat mass as a percentage of bodyweight and fat mass percentage determined using isotope dilution (R 2 =0.65). As expected, the predictive equation was accurate in estimating FFM when tested on the same group of dogs used to develop the equation. The significance of breed, independent of skeletal size, in predicting FFM indicates that individual breed formulae may be required. Future studies that apply these equations on a greater population of
International Nuclear Information System (INIS)
Quigg, Chris
2007-01-01
In the classical physics we inherited from Isaac Newton, mass does not arise, it simply is. The mass of a classical object is the sum of the masses of its parts. Albert Einstein showed that the mass of a body is a measure of its energy content, inviting us to consider the origins of mass. The protons we accelerate at Fermilab are prime examples of Einsteinian matter: nearly all of their mass arises from stored energy. Missing mass led to the discovery of the noble gases, and a new form of missing mass leads us to the notion of dark matter. Starting with a brief guided tour of the meanings of mass, the colloquium will explore the multiple origins of mass. We will see how far we have come toward understanding mass, and survey the issues that guide our research today.
Hofsteenge, Geesje H; Chinapaw, Mai J M; Weijs, Peter J M
2015-10-15
In clinical practice, patient friendly methods to assess body composition in obese adolescents are needed. Therefore, the bioelectrical impedance analysis (BIA) related fat-free mass (FFM) prediction equations (FFM-BIA) were evaluated in obese adolescents (age 11-18 years) compared to FFM measured by dual-energy x-ray absorptiometry (FFM-DXA) and a new population specific FFM-BIA equation is developed. After an overnight fast, the subjects attended the outpatient clinic. After measuring height and weight, a full body scan by dual-energy x-ray absorptiometry (DXA) and a BIA measurement was performed. Thirteen predictive FFM-BIA equations based on weight, height, age, resistance, reactance and/or impedance were systematically selected and compared to FFM-DXA. Accuracy of FFM-BIA equations was evaluated by the percentage adolescents predicted within 5% of FFM-DXA measured, the mean percentage difference between predicted and measured values (bias) and the Root Mean Squared prediction Error (RMSE). Multiple linear regression was conducted to develop a new BIA equation. Validation was based on 103 adolescents (60% girls), age 14.5 (sd1.7) years, weight 94.1 (sd15.6) kg and FFM-DXA of 56.1 (sd9.8) kg. The percentage accurate estimations varied between equations from 0 to 68%; bias ranged from -29.3 to +36.3% and RMSE ranged from 2.8 to 12.4 kg. An alternative prediction equation was developed: FFM = 0.527 * H(cm)(2)/Imp + 0.306 * weight - 1.862 (R(2) = 0.92, SEE = 2.85 kg). Percentage accurate prediction was 76%. Compared to DXA, the Gray equation underestimated the FFM with 0.4 kg (55.7 ± 8.3), had an RMSE of 3.2 kg, 63% accurate prediction and the smallest bias of (-0.1%). When split by sex, the Gray equation had the narrowest range in accurate predictions, bias, and RMSE. For the assessment of FFM with BIA, the Gray-FFM equation appears to be the most accurate, but 63% is still not at an acceptable accuracy level for obese adolescents. The new equation appears to
International Nuclear Information System (INIS)
Carver, M.B.; Hanley, D.V.; Chaplin, K.R.
1979-02-01
MAKSIMA-CHEMIST was written to compute the kinetics of simultaneous chemical reactions. The ordinary differential equations, which are automatically derived from the stated chemical equations, are difficult to integrate, as they are coupled in a highly nonlinear manner and frequently involve a large range in the magnitude of the reaction rates. They form a classic 'stiff' differential equaton set which can be integrated efficiently only by recently developed advanced techniques. The new program also contains provision for higher order chemical reactions, and has a dynamic storage and decision feature. This permits it to accept any number of chemical reactions and species, and choose an integraton scheme which will perform most efficiently within the available memory. Sparse matrix techniques are used when the size and structure of the equation set is suitable. Finally, a number of post-analysis options are available, including printer and Calcomp plots of transient response of selected species, and graphical representation of the reaction matrix. (auth)
Bhatnagar, Shashank; Alemu, Lmenew
2018-02-01
In this work we calculate the mass spectra of charmonium for 1 P ,…,4 P states of 0++ and 1++, for 1 S ,…,5 S states of 0-+, and for 1 S ,…,4 D states of 1- along with the two-photon decay widths of the ground and first excited states of 0++ quarkonia for the process O++→γ γ in the framework of a QCD-motivated Bethe-Salpeter equation (BSE). In this 4 ×4 BSE framework, the coupled Salpeter equations are first shown to decouple for the confining part of the interaction (under the heavy-quark approximation) and are analytically solved, and later the one-gluon-exchange interaction is perturbatively incorporated, leading to mass spectral equations for various quarkonia. The analytic forms of wave functions obtained are used for the calculation of the two-photon decay widths of χc 0. Our results are in reasonable agreement with data (where available) and other models.
DEFF Research Database (Denmark)
Săftoiu, Adrian; Vilmann, Peter; Gorunescu, Florin
2012-01-01
By using strain assessment, real-time endoscopic ultrasound (EUS) elastography provides additional information about a lesion's characteristics in the pancreas. We assessed the accuracy of real-time EUS elastography in focal pancreatic lesions using computer-aided diagnosis by artificial neural...... network analysis....
Abell, Caitlyn E; Stalder, Kenneth J; Hendricks, Haven B; Fitzgerald, Robert F
2012-07-01
The objectives of this study were to develop a prediction equation for carcass knife-separable lean within and across USDA cull sow market weight classes (MWC) and to determine carcass and individual primal cut knife separable lean content from cull sows. There were significant percent lean and fat differences in the primal cuts across USDA MWC. The two lighter USDA MWC had a greater percent carcass lean and lower percent fat compared to the two heavier MWC. In general, hot carcass weight explained the majority of carcass lean variation. Additionally, backfat was a significant variation source when predicting cull sow carcass lean. The findings support using a single lean prediction equation across MWC to assist processors when making cull sow purchasing decisions and determine the mix of animals from various USDA MWC that will meet their needs when making pork products with defined lean:fat content. Copyright © 2012 Elsevier Ltd. All rights reserved.
Alien calculus and a Schwinger-Dyson equation: two-point function with a nonperturbative mass scale
Bellon, Marc P.; Clavier, Pierre J.
2018-02-01
Starting from the Schwinger-Dyson equation and the renormalization group equation for the massless Wess-Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.
International Nuclear Information System (INIS)
Burger, Florian
2012-01-01
In this thesis we report about an investigation of the finite temperature crossover/phase transition of quantum chromodynamics and the evaluation of the thermodynamic equation of state. To this end the lattice method and the Wilson twisted mass discretisation of the quark action are used. This formulation is known to have an automatic improvement of lattice artifacts and thus an improved continuum limit behaviour. This work presents first robust results using this action for the non-vanishing temperature case. We investigate the chiral limit of the two flavour phase transition with several small values of the pion mass in order to address the open question of the order of the transition in the limit of vanishing quark mass. For the currently simulated pion masses in the range of 300 to 700 MeV we present evidence that the finite temperature transition is a crossover transition rather than a genuine phase transition. The chiral limit is investigated by comparing the scaling of the observed crossover temperature with the mass including several possible scenarios. Complementary to this approach the chiral condensate as the order parameter for the spontaneous breaking of chiral symmetry is analysed in comparison with the O(4) universal scaling function which characterises a second order transition. With respect to thermodynamics the equation of state is obtained from the trace anomaly employing the temperature integral method which provides the pressure and energy density in the crossover region. The continuum limit of the trace anomaly is studied by considering several values of N τ and the tree-level correction technique.
DEFF Research Database (Denmark)
Nilsson, Torben; Bassani, Maria R.; Larsen, Thomas Ostenfeld
1996-01-01
different agar media, replicates of the same species grouped together. Likewise, a satisfactory classification was achieved by multivariate analysis of the data for various isolates of the cheese-associated fungi Aspergillus versicolor, P. discolor, P. roqueforti, P. solitum, P. verrucosum, P. commune and P......Curie point pyrolysis/mass spectrometry of Penicillium species was performed with 530 degrees C Curie point foils. The mass spectra were submitted to principal component analysis, canonical variates analysis and hierarchical cluster analysis, producing a final dendrogram by the use of average....... palitans. However, some difficulties appeared in distinguishing the closely related species P. commune and P. palitans. Such difficulties became greater on including more isolates and limiting the analysis to five of the species. The use of back-propagation artificial neural networks, in contrast, resulted...
Ando, Hisae; Gotoh, Koro; Fujiwara, Kansuke; Anai, Manabu; Chiba, Seiichi; Masaki, Takayuki; Kakuma, Tetsuya; Shibata, Hirotaka
2017-07-17
We examined whether glucagon-like peptide-1 (GLP-1) affects β-cell mass and proliferation through neural pathways, from hepatic afferent nerves to pancreatic efferent nerves via the central nervous system, in high-fat diet (HFD)-induced obese rats. The effects of chronic administration of GLP-1 (7-36) and liraglutide, a GLP-1 receptor agonist, on pancreatic morphological alterations, c-fos expression and brain-derived neurotrophic factor (BDNF) content in the hypothalamus, and glucose metabolism were investigated in HFD-induced obese rats that underwent hepatic afferent vagotomy (VgX) and/or pancreatic efferent sympathectomy (SpX). Chronic GLP-1 (7-36) administration to HFD-induced obese rats elevated c-fos expression and BDNF content in the hypothalamus, followed by a reduction in pancreatic β-cell hyperplasia and insulin content, thus resulting in improved glucose tolerance. These responses were abolished by VgX and SpX. Moreover, administration of liraglutide similarly activated the hypothalamic neural pathways, thus resulting in a more profound amelioration of glucose tolerance than native GLP-1 (7-36). These data suggest that GLP-1 normalizes the obesity-induced compensatory increase in β-cell mass and glucose intolerance through a neuronal relay system consisting of hepatic afferent nerves, the hypothalamus, and pancreatic efferent nerves.
Săftoiu, Adrian; Vilmann, Peter; Gorunescu, Florin; Janssen, Jan; Hocke, Michael; Larsen, Michael; Iglesias-Garcia, Julio; Arcidiacono, Paolo; Will, Uwe; Giovannini, Marc; Dietrich, Cristoph F; Havre, Roald; Gheorghe, Cristian; McKay, Colin; Gheonea, Dan Ionuţ; Ciurea, Tudorel
2012-01-01
By using strain assessment, real-time endoscopic ultrasound (EUS) elastography provides additional information about a lesion's characteristics in the pancreas. We assessed the accuracy of real-time EUS elastography in focal pancreatic lesions using computer-aided diagnosis by artificial neural network analysis. We performed a prospective, blinded, multicentric study at of 258 patients (774 recordings from EUS elastography) who were diagnosed with chronic pancreatitis (n = 47) or pancreatic adenocarcinoma (n = 211) from 13 tertiary academic medical centers in Europe (the European EUS Elastography Multicentric Study Group). We used postprocessing software analysis to compute individual frames of elastography movies recorded by retrieving hue histogram data from a dynamic sequence of EUS elastography into a numeric matrix. The data then were analyzed in an extended neural network analysis, to automatically differentiate benign from malignant patterns. The neural computing approach had 91.14% training accuracy (95% confidence interval [CI], 89.87%-92.42%) and 84.27% testing accuracy (95% CI, 83.09%-85.44%). These results were obtained using the 10-fold cross-validation technique. The statistical analysis of the classification process showed a sensitivity of 87.59%, a specificity of 82.94%, a positive predictive value of 96.25%, and a negative predictive value of 57.22%. Moreover, the corresponding area under the receiver operating characteristic curve was 0.94 (95% CI, 0.91%-0.97%), which was significantly higher than the values obtained by simple mean hue histogram analysis, for which the area under the receiver operating characteristic was 0.85. Use of the artificial intelligence methodology via artificial neural networks supports the medical decision process, providing fast and accurate diagnoses. Copyright © 2012 AGA Institute. Published by Elsevier Inc. All rights reserved.
Mukherjee, B; Nivedita, M; Mukherjee, D
2014-05-01
Modelling system dynamics in a hyper-eutrophic lake is quite complex especially with a constant influx of detergents and sewage material which continually changes the state variables and interferes with the assessment of the chemical rhythm occurring in polluted conditions as compared to unpolluted systems. In this paper, a carbon and nutrient mass balance model for predicting system dynamics in a complex environment was studied. Studies were conducted at Ranchi lake to understand the altered environmental dynamics in hyper-eutrophic conditions, and its impact on the plankton community. The lake was monitored regularly for five years (2007 - 2011) and the data collected on the carbon flux, nitrates, phosphates and silicates was used to design a mass balance model for evaluating and predicting the system. The model was then used to correlate the chemical rhythm with that of the phytoplankton dynamics and diversity. Nitrates and phosphates were not limiting (mean nitrate and phosphate concentrations were 1.74 and 0.83 mgl⁻¹ respectively). Free carbon dioxide was found to control the system and, interacting with other parameters determined the diversity and dynamics of the plankton community. N/P ratio determined which group of phytoplankton dominated the community, above 5 it favoured the growth of chlorophyceae while below 5 cyanobacteria dominates. TOC/TIC ratio determined the abundance. The overall system was controlled by the availability of free carbon dioxide which served as a limiting factor.
Chatterjee, D.; Gulminelli, F.; Raduta, Ad. R.; Margueron, J.
2017-12-01
The question of correlations among empirical equation of state (EoS) parameters constrained by nuclear observables is addressed in a Thomas-Fermi meta-modeling approach. A recently proposed meta-modeling for the nuclear EoS in nuclear matter is augmented with a single finite size term to produce a minimal unified EoS functional able to describe the smooth part of the nuclear ground state properties. This meta-model can reproduce the predictions of a large variety of models, and interpolate continuously between them. An analytical approximation to the full Thomas-Fermi integrals is further proposed giving a fully analytical meta-model for nuclear masses. The parameter space is sampled and filtered through the constraint of nuclear mass reproduction with Bayesian statistical tools. We show that this simple analytical meta-modeling has a predictive power on masses, radii, and skins comparable to full Hartree-Fock or extended Thomas-Fermi calculations with realistic energy functionals. The covariance analysis on the posterior distribution shows that no physical correlation is present between the different EoS parameters. Concerning nuclear observables, a strong correlation between the slope of the symmetry energy and the neutron skin is observed, in agreement with previous studies.
Directory of Open Access Journals (Sweden)
Hao Li
2016-01-01
Full Text Available 1,1,1,2,3,3,3-Heptafluoropropane (R227ea is a good refrigerant that reduces greenhouse effects and ozone depletion. In practical applications, we usually have to know the compressed liquid densities at different temperatures and pressures. However, the measurement requires a series of complex apparatus and operations, wasting too much manpower and resources. To solve these problems, here, Song and Mason equation, support vector machine (SVM, and artificial neural networks (ANNs were used to develop theoretical and machine learning models, respectively, in order to predict the compressed liquid densities of R227ea with only the inputs of temperatures and pressures. Results show that compared with the Song and Mason equation, appropriate machine learning models trained with precise experimental samples have better predicted results, with lower root mean square errors (RMSEs (e.g., the RMSE of the SVM trained with data provided by Fedele et al. [1] is 0.11, while the RMSE of the Song and Mason equation is 196.26. Compared to advanced conventional measurements, knowledge-based machine learning models are proved to be more time-saving and user-friendly.
Gill, Jatinder; Singh, Jagdev
2018-07-01
In this work, an experimental investigation is carried out with R134a and LPG refrigerant mixture for depicting mass flow rate through straight and helical coil adiabatic capillary tubes in a vapor compression refrigeration system. Various experiments were conducted under steady-state conditions, by changing capillary tube length, inner diameter, coil diameter and degree of subcooling. The results showed that mass flow rate through helical coil capillary tube was found lower than straight capillary tube by about 5-16%. Dimensionless correlation and Artificial Neural Network (ANN) models were developed to predict mass flow rate. It was found that dimensionless correlation and ANN model predictions agreed well with experimental results and brought out an absolute fraction of variance of 0.961 and 0.988, root mean square error of 0.489 and 0.275 and mean absolute percentage error of 4.75% and 2.31% respectively. The results suggested that ANN model shows better statistical prediction than dimensionless correlation model.
He, Xueqin; Han, Lujia; Ge, Jinyi; Huang, Guangqun
2018-04-01
This study establishes an optimal mathematical modelling to rationally describe the dynamic changes and spatial distribution of temperature and oxygen concentration in the aerobic composting process using coupling mass-heat-momentum transfer based on the microbial mechanism. Two different conditional composting experiments, namely continuous aeration and intermittent aeration, were performed to verify the proposed model. The results show that the model accurately predicted the dynamic changes in temperature (case I: R 2 = 0.93, RMSE = 1.95 K; case II: R 2 = 0.86, RMSE = 4.69 K) and oxygen concentration (case I: R 2 = 0.90, RMSE = 1.26%; case II: R 2 = 0.75, RMSE = 2.93%) in the central point of compost substrates. It also systematically simulated fluctuations in oxygen concentration caused by boundary conditions and the spatial distribution of the actual temperature and oxygen concentration. The proposed model exhibits good applicability in simulating the actual working conditions of aerobic composting process. Copyright © 2018 Elsevier Ltd. All rights reserved.
Hayes, Alison J; Clarke, Philip M; Lung, Tom Wc
2011-09-25
Many studies have documented the bias in body mass index (BMI) determined from self-reported data on height and weight, but few have examined the change in bias over time. Using data from large, nationally-representative population health surveys, we examined change in bias in height and weight reporting among Australian adults between 1995 and 2008. Our study dataset included 9,635 men and women in 1995 and 9,141 in 2007-2008. We investigated the determinants of the bias and derived correction equations using 2007-2008 data, which can be applied when only self-reported anthropometric data are available. In 1995, self-reported BMI (derived from height and weight) was 1.2 units (men) and 1.4 units (women) lower than measured BMI. In 2007-2008, there was still underreporting, but the amount had declined to 0.6 units (men) and 0.7 units (women) below measured BMI. The major determinants of reporting error in 2007-2008 were age, sex, measured BMI, and education of the respondent. Correction equations for height and weight derived from 2007-2008 data and applied to self-reported data were able to adjust for the bias and were accurate across all age and sex strata. The diminishing reporting bias in BMI in Australia means that correction equations derived from 2007-2008 data may not be transferable to earlier self-reported data. Second, predictions of future overweight and obesity in Australia based on trends in self-reported information are likely to be inaccurate, as the change in reporting bias will affect the apparent increase in self-reported obesity prevalence.
Kawamura, Takumu; Giacomazzo, Bruno; Kastaun, Wolfgang; Ciolfi, Riccardo; Endrizzi, Andrea; Baiotti, Luca; Perna, Rosalba
2016-09-01
We present fully general-relativistic magnetohydrodynamic simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and hence power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we observe the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to a BH. Such larger fields make it possible, for at least one of our models, to resolve the magnetorotational instability and hence further amplify the magnetic field in the disk. However, by the end of our simulations, we do not (yet) observe a magnetically dominated funnel nor a relativistic outflow. With respect to the recent simulations of Ruiz et al. [Astrophys. J. 824, L6 (2016)], we evolve models with lower and more plausible initial magnetic field strengths and (for computational reasons) we do not evolve the accretion disk for the long time scales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure aligned with the BH spin axis, we expect that the results found by Ruiz et al. (who only considered an equal-mass system with an ideal fluid EOS) should be general and—at least from a qualitative point of view—independent of the mass ratio, magnetic field
DEFF Research Database (Denmark)
Jacobsen, Susanne; Nesic, Ljiljana; Petersen, Marianne Kjerstine
2001-01-01
Analyzing a gliadin extract by matrix assisted laser desorption/ionization-time of flight-mass spectrometry (MALDI- TOF-MS) combined with an artificial neural network (ANN) is a suitable method for identification of wheat varieties. However, the ANN can not distinguish between all different wheat...
Kim, Chang Guhn; Kim, Woo Hyoung; Kim, Myoung Hyoun; Kim, Dae-Weung
2013-06-01
The purpose of this study was to estimate lean body mass (LBM) using CT (LBM CTs) and compare the results with LBM estimates of four different predictive equations (LBM PEs) to assess whether LBM CTs and LBM PEs can be used interchangeably for SUV normalization. Whole-body F-18 FDG PET/CT studies were conducted on 392 patients. LBM CT1 is modified adipose tissue-free body mass, and LBM CT2 is adipose tissue-free body mass. Four different PEs were used for comparison (LBM PE1-4). Agreement between the two measurement methods was assessed by Bland-Altman analysis. We calculated the difference between two methods (bias), the percentage of difference, and the limits of agreement, expressed as a percentage. For LBM CTs vs. LBM PEs, except LBM PE3, the ranges of biases and limits of agreement were -3.77 to 3.81 kg and 26.60-35.05 %, respectively, indicating the wide limits of agreement and differing magnitudes of bias. For LBM CTs vs. LBM PE3, LBM PE3 had wider limits of agreement and greater positive bias (44.28-46.19 % and 10.49 to 14.04 kg, respectively), showing unacceptably large discrepancies between LBM CTs and LBM PE3. This study demonstrated that there are substantial discrepancies between individual LBM CTs and LBM PEs, and this should be taken into account when LBM CTs and LBM PEs are used interchangeably between patients.
Almeida, Lucas; de Azevedo, José Luiz Lima; Kerr, Rodrigo; Araujo, Moacyr; Mata, Mauricio M.
2018-03-01
The equation of state of seawater (EOS) provides a simple way to link the properties of seawater that are the most important for ocean dynamics and the ocean-atmosphere climate system. In 2010, the set of equations used to derive all thermodynamic properties of seawater were updated using a thermodynamic approach. The new approach, named TEOS-10, results in better estimates of seawater properties, such as salinity and temperature, when compared to the previous EOS version (EOS-80). Since several physical processes in the oceans are driven by these properties, improvements in the EOS performance are expected to lead to a better and more realistic representation of the ocean. This work focuses on assessing the main differences of the: (i) contribution of water masses to a total mixture, (ii) baroclinic velocity, and (iii) volume and heat transport, as calculated by the EOS-80 and by the TEOS-10, along four zonal transects at 26.5°N, 10°N, 11°S, and 34.5°S in the Atlantic Ocean. The density differences (always between TEOS-10 and EOS-80) increase with depth and hence the results indicate that the most significant difference in the water mass contributions was found for Antarctic Bottom Water. Within that layer, the differences reach up to 10% on its fraction of the mixture when calculated by the TEOS-10, although the difference in the North Atlantic Deep Water contribution was not negligible either. The estimated baroclinic velocities showed considerable differences in all studied areas, being more significant over boundary current systems. The Gulf Stream presented lower velocity, while the Brazil Current presented increasing velocity when using TEOS-10. The comparison between values computed for volume transported by the Atlantic Meridional Overturning Circulation showed a total difference of about +6%, which cannot be neglected when considering the space and time variability involved. The heat transport showed significant differences in the study areas at the
Directory of Open Access Journals (Sweden)
Claire M Nightingale
Full Text Available BACKGROUND: Bioelectrical impedance analysis (BIA is a potentially valuable method for assessing lean mass and body fat levels in children from different ethnic groups. We examined the need for ethnic- and gender-specific equations for estimating fat free mass (FFM from BIA in children from different ethnic groups and examined their effects on the assessment of ethnic differences in body fat. METHODS: Cross-sectional study of children aged 8-10 years in London Primary schools including 325 South Asians, 250 black African-Caribbeans and 289 white Europeans with measurements of height, weight and arm-leg impedance (Z; Bodystat 1500. Total body water was estimated from deuterium dilution and converted to FFM. Multilevel models were used to derive three types of equation {A: FFM = linear combination(height+weight+Z; B: FFM = linear combination(height(2/Z; C: FFM = linear combination(height(2/Z+weight}. RESULTS: Ethnicity and gender were important predictors of FFM and improved model fit in all equations. The models of best fit were ethnicity and gender specific versions of equation A, followed by equation C; these provided accurate assessments of ethnic differences in FFM and FM. In contrast, the use of generic equations led to underestimation of both the negative South Asian-white European FFM difference and the positive black African-Caribbean-white European FFM difference (by 0.53 kg and by 0.73 kg respectively for equation A. The use of generic equations underestimated the positive South Asian-white European difference in fat mass (FM and overestimated the positive black African-Caribbean-white European difference in FM (by 4.7% and 10.1% respectively for equation A. Consistent results were observed when the equations were applied to a large external data set. CONCLUSIONS: Ethnic- and gender-specific equations for predicting FFM from BIA provide better estimates of ethnic differences in FFM and FM in children, while generic equations
Nightingale, Claire M; Rudnicka, Alicja R; Owen, Christopher G; Donin, Angela S; Newton, Sian L; Furness, Cheryl A; Howard, Emma L; Gillings, Rachel D; Wells, Jonathan C K; Cook, Derek G; Whincup, Peter H
2013-01-01
Bioelectrical impedance analysis (BIA) is a potentially valuable method for assessing lean mass and body fat levels in children from different ethnic groups. We examined the need for ethnic- and gender-specific equations for estimating fat free mass (FFM) from BIA in children from different ethnic groups and examined their effects on the assessment of ethnic differences in body fat. Cross-sectional study of children aged 8-10 years in London Primary schools including 325 South Asians, 250 black African-Caribbeans and 289 white Europeans with measurements of height, weight and arm-leg impedance (Z; Bodystat 1500). Total body water was estimated from deuterium dilution and converted to FFM. Multilevel models were used to derive three types of equation {A: FFM = linear combination(height+weight+Z); B: FFM = linear combination(height(2)/Z); C: FFM = linear combination(height(2)/Z+weight)}. Ethnicity and gender were important predictors of FFM and improved model fit in all equations. The models of best fit were ethnicity and gender specific versions of equation A, followed by equation C; these provided accurate assessments of ethnic differences in FFM and FM. In contrast, the use of generic equations led to underestimation of both the negative South Asian-white European FFM difference and the positive black African-Caribbean-white European FFM difference (by 0.53 kg and by 0.73 kg respectively for equation A). The use of generic equations underestimated the positive South Asian-white European difference in fat mass (FM) and overestimated the positive black African-Caribbean-white European difference in FM (by 4.7% and 10.1% respectively for equation A). Consistent results were observed when the equations were applied to a large external data set. Ethnic- and gender-specific equations for predicting FFM from BIA provide better estimates of ethnic differences in FFM and FM in children, while generic equations can misrepresent these ethnic differences.
Nightingale, Claire M.; Rudnicka, Alicja R.; Owen, Christopher G.; Donin, Angela S.; Newton, Sian L.; Furness, Cheryl A.; Howard, Emma L.; Gillings, Rachel D.; Wells, Jonathan C. K.; Cook, Derek G.; Whincup, Peter H.
2013-01-01
Background Bioelectrical impedance analysis (BIA) is a potentially valuable method for assessing lean mass and body fat levels in children from different ethnic groups. We examined the need for ethnic- and gender-specific equations for estimating fat free mass (FFM) from BIA in children from different ethnic groups and examined their effects on the assessment of ethnic differences in body fat. Methods Cross-sectional study of children aged 8–10 years in London Primary schools including 325 South Asians, 250 black African-Caribbeans and 289 white Europeans with measurements of height, weight and arm-leg impedance (Z; Bodystat 1500). Total body water was estimated from deuterium dilution and converted to FFM. Multilevel models were used to derive three types of equation {A: FFM = linear combination(height+weight+Z); B: FFM = linear combination(height2/Z); C: FFM = linear combination(height2/Z+weight)}. Results Ethnicity and gender were important predictors of FFM and improved model fit in all equations. The models of best fit were ethnicity and gender specific versions of equation A, followed by equation C; these provided accurate assessments of ethnic differences in FFM and FM. In contrast, the use of generic equations led to underestimation of both the negative South Asian-white European FFM difference and the positive black African-Caribbean-white European FFM difference (by 0.53 kg and by 0.73 kg respectively for equation A). The use of generic equations underestimated the positive South Asian-white European difference in fat mass (FM) and overestimated the positive black African-Caribbean-white European difference in FM (by 4.7% and 10.1% respectively for equation A). Consistent results were observed when the equations were applied to a large external data set. Conclusions Ethnic- and gender-specific equations for predicting FFM from BIA provide better estimates of ethnic differences in FFM and FM in children, while generic equations can
Fraser, L K; Edwards, K L; Cade, J E; Clarke, G P
2011-10-01
To assess the association between the consumption of fast food (FF) and body mass index (BMI) of teenagers in a large UK birth cohort. A structural equation modelling (SEM) approach was chosen to allow direct statistical testing of a theoretical model. SEM is a combination of confirmatory factor and path analysis, which allows for the inclusion of latent (unmeasured) variables. This approach was used to build two models: the effect of FF outlet visits and food choices and the effect of FF exposure on consumption and BMI. A total of 3620 participants had data for height and weight from the age 13 clinic and the frequency of FF outlet visits, and so were included in these analyses. This SEM model of food choices showed that increased frequency of eating at FF outlets is positively associated with higher consumption of unhealthy foods (β=0.29, Pfoods (β=-1.02, Pfoods and were more likely to have higher BMISDS than those teenagers who did not eat frequently at FF restaurants. Teenagers who were exposed to more takeaway foods at home ate more frequently at FF restaurants and eating at FF restaurants was also associated with lower intakes of vegetables and raw fruit in this cohort.
International Nuclear Information System (INIS)
Deaton, M. Brett; Duez, Matthew D.; Foucart, Francois; O'Connor, Evan; Ott, Christian D.; Scheel, Mark A.; Szilagyi, Bela; Kidder, Lawrence E.; Muhlberger, Curran D.
2013-01-01
Neutrino emission significantly affects the evolution of the accretion tori formed in black hole-neutron star mergers. It removes energy from the disk, alters its composition, and provides a potential power source for a gamma-ray burst. To study these effects, simulations in general relativity with a hot microphysical equation of state (EOS) and neutrino feedback are needed. We present the first such simulation, using a neutrino leakage scheme for cooling to capture the most essential effects and considering a moderate mass (1.4 M ☉ neutron star, 5.6 M ☉ black hole), high-spin (black hole J/M 2 = 0.9) system with the K 0 = 220 MeV Lattimer-Swesty EOS. We find that about 0.08 M ☉ of nuclear matter is ejected from the system, while another 0.3 M ☉ forms a hot, compact accretion disk. The primary effects of the escaping neutrinos are (1) to make the disk much denser and more compact, (2) to cause the average electron fraction Y e of the disk to rise to about 0.2 and then gradually decrease again, and (3) to gradually cool the disk. The disk is initially hot (T ∼ 6 MeV) and luminous in neutrinos (L ν ∼ 10 54 erg s –1 ), but the neutrino luminosity decreases by an order of magnitude over 50 ms of post-merger evolution
Bade, Richard; Bijlsma, Lubertus; Miller, Thomas H; Barron, Leon P; Sancho, Juan Vicente; Hernández, Felix
2015-12-15
The recent development of broad-scope high resolution mass spectrometry (HRMS) screening methods has resulted in a much improved capability for new compound identification in environmental samples. However, positive identifications at the ng/L concentration level rely on analytical reference standards for chromatographic retention time (tR) and mass spectral comparisons. Chromatographic tR prediction can play a role in increasing confidence in suspect screening efforts for new compounds in the environment, especially when standards are not available, but reliable methods are lacking. The current work focuses on the development of artificial neural networks (ANNs) for tR prediction in gradient reversed-phase liquid chromatography and applied along with HRMS data to suspect screening of wastewater and environmental surface water samples. Based on a compound tR dataset of >500 compounds, an optimized 4-layer back-propagation multi-layer perceptron model enabled predictions for 85% of all compounds to within 2min of their measured tR for training (n=344) and verification (n=100) datasets. To evaluate the ANN ability for generalization to new data, the model was further tested using 100 randomly selected compounds and revealed 95% prediction accuracy within the 2-minute elution interval. Given the increasing concern on the presence of drug metabolites and other transformation products (TPs) in the aquatic environment, the model was applied along with HRMS data for preliminary identification of pharmaceutically-related compounds in real samples. Examples of compounds where reference standards were subsequently acquired and later confirmed are also presented. To our knowledge, this work presents for the first time, the successful application of an accurate retention time predictor and HRMS data-mining using the largest number of compounds to preliminarily identify new or emerging contaminants in wastewater and surface waters. Copyright © 2015 Elsevier B.V. All rights
Tan, Juzhong; Kerr, William L
2018-08-01
Roasting is a critical step in chocolate processing, where moisture content is decreased and unique flavors and texture are developed. The determination of the degree of roasting in cocoa beans is important to ensure the quality of chocolate. Determining the degree of roasting relies on human specialists or sophisticated chemical analyses that are inaccessible to small manufacturers and farmers. In this study, an electronic nose system was constructed consisting of an array of gas sensors and used to detect volatiles emanating from cocoa beans roasted for 0, 20, 30 and 40 min. The several signals were used to train a three-layer artificial neural network (ANN). Headspace samples were also analyzed by gas chromatography/mass spectrometry (GC/MS), with 23 select volatiles used to train a separate ANN. Both ANNs were used to predict the degree of roasting of cocoa beans. The electronic nose had a prediction accuracy of 94.4% using signals from sensors TGS 813, 826, 822, 830, 830, 2620, 2602 and 2610. In comparison, the GC/MS predicted the degree of roasting with an accuracy of 95.8%. The electronic nose system is able to predict the extent of roasting, as well as a more sophisticated approach using GC/MS. © 2018 Society of Chemical Industry. © 2018 Society of Chemical Industry.
Gerstner, Wulfram
2017-01-01
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957
Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram
2017-04-01
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.
Energy Technology Data Exchange (ETDEWEB)
Deaton, M. Brett; Duez, Matthew D. [Department of Physics and Astronomy, Washington State University, Pullman, WA 99164 (United States); Foucart, Francois; O' Connor, Evan [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8 (Canada); Ott, Christian D.; Scheel, Mark A.; Szilagyi, Bela [TAPIR, MC 350-17, California Institute of Technology, Pasadena, CA 91125 (United States); Kidder, Lawrence E.; Muhlberger, Curran D., E-mail: mbdeaton@wsu.edu, E-mail: m.duez@wsu.edu [Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853 (United States)
2013-10-10
Neutrino emission significantly affects the evolution of the accretion tori formed in black hole-neutron star mergers. It removes energy from the disk, alters its composition, and provides a potential power source for a gamma-ray burst. To study these effects, simulations in general relativity with a hot microphysical equation of state (EOS) and neutrino feedback are needed. We present the first such simulation, using a neutrino leakage scheme for cooling to capture the most essential effects and considering a moderate mass (1.4 M{sub ☉} neutron star, 5.6 M{sub ☉} black hole), high-spin (black hole J/M {sup 2} = 0.9) system with the K{sub 0} = 220 MeV Lattimer-Swesty EOS. We find that about 0.08 M{sub ☉} of nuclear matter is ejected from the system, while another 0.3 M{sub ☉} forms a hot, compact accretion disk. The primary effects of the escaping neutrinos are (1) to make the disk much denser and more compact, (2) to cause the average electron fraction Y{sub e} of the disk to rise to about 0.2 and then gradually decrease again, and (3) to gradually cool the disk. The disk is initially hot (T ∼ 6 MeV) and luminous in neutrinos (L{sub ν} ∼ 10{sup 54} erg s{sup –1}), but the neutrino luminosity decreases by an order of magnitude over 50 ms of post-merger evolution.
Directory of Open Access Journals (Sweden)
Analiza M. Silva
2013-01-01
Full Text Available Simple methods to assess both fat (FM and fat-free mass (FFM are required in paediatric populations. Several bioelectrical impedance instruments (BIAs and anthropometric equations have been developed using different criterion methods (multicomponent models for assessing FM and FFM. Through childhood, FFM density increases while FFM hydration decreases until reaching adult values. Therefore, multicomponent models should be used as the gold standard method for developing simple techniques because two-compartment models (2C model rely on the assumed adult values of FFM density and hydration (1.1 g/cm3 and 73.2%, respectively. This study will review BIA and/or anthropometric-based equations for assessing body composition in paediatric populations. We reviewed English language articles from MEDLINE (1985–2012 with the selection of predictive equations developed for assessing FM and FFM using three-compartment (3C and 4C models as criterion. Search terms included children, adolescent, childhood, adolescence, 4C model, 3C model, multicomponent model, equation, prediction, DXA, BIA, resistance, anthropometry, skinfold, FM, and FFM. A total of 14 studies (33 equations were selected with the majority developed using DXA as the criterion method with a limited number of studies providing cross-validation results. Overall, the selected equations are useful for epidemiological studies, but some concerns still arise on an individual basis.
Supersymmetric quasipotential equations
International Nuclear Information System (INIS)
Zaikov, R.P.
1981-01-01
A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru
Applications of neural network to numerical analyses
International Nuclear Information System (INIS)
Takeda, Tatsuoki; Fukuhara, Makoto; Ma, Xiao-Feng; Liaqat, Ali
1999-01-01
Applications of a multi-layer neural network to numerical analyses are described. We are mainly concerned with the computed tomography and the solution of differential equations. In both cases as the objective functions for the training process of the neural network we employed residuals of the integral equation or the differential equations. This is different from the conventional neural network training where sum of the squared errors of the output values is adopted as the objective function. For model problems both the methods gave satisfactory results and the methods are considered promising for some kind of problems. (author)
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Directory of Open Access Journals (Sweden)
Deimel Christian
2014-03-01
Full Text Available The most common method for simulating cavitating flows is using the governing flow equations in a form with a variable density and treats both phases as incompressible in combination with a transport equation for the vapour volume fraction. This approach is commonly referred to as volume of fluid method (VoF. To determine the transition of the liquid phase to vapour and vice versa, a relation for the mass transfer is needed. Several models exist, based on slightly differing physical assumptions, for example derivation from the dynamics of single bubbles or large bubble clusters. In our simulation, we use the model of Sauer and Schnerr which is based on the Rayleigh equation. One common problem of all mass transfer models is the use of model constants which often need to be tuned with regard to the examined problem. Furthermore, these models often overpredict the turbulent dynamic viscosity in the two-phase region which counteracts the development of transient shedding behaviour and is compensated by the modification proposed by Reboud. In the presented study, we vary the parameters of the Sauer-Schnerr model with Reboud modification that we implemented into an OpenFOAM solver to match numerical to experimental data.
Neural networks with discontinuous/impact activations
Akhmet, Marat
2014-01-01
This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided. This book also: Explores questions related to the biological underpinning for models of neural networks\\ Considers neural networks modeling using differential equations with impulsive and piecewise constant argument discontinuities Provides all necessary mathematical basics for application to the theory of neural networks Neural Networks with Discontinuous/Impact Activations is an ideal book for researchers and professionals in the field of engineering mathematics that have an interest in app...
International Nuclear Information System (INIS)
Denby, Bruce; Lindsey, Clark; Lyons, Louis
1992-01-01
The 1980s saw a tremendous renewal of interest in 'neural' information processing systems, or 'artificial neural networks', among computer scientists and computational biologists studying cognition. Since then, the growth of interest in neural networks in high energy physics, fueled by the need for new information processing technologies for the next generation of high energy proton colliders, can only be described as explosive
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear differential equations
International Nuclear Information System (INIS)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
Neural Network to Solve Concave Games
Liu, Zixin; Wang, Nengfa
2014-01-01
The issue on neural network method to solve concave games is concerned. Combined with variational inequality, Ky Fan inequality, and projection equation, concave games are transformed into a neural network model. On the basis of the Lyapunov stable theory, some stability results are also given. Finally, two classic games’ simulation results are given to illustrate the theoretical results.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Munro, Kelly; Miller, Thomas H; Martins, Claudia P B; Edge, Anthony M; Cowan, David A; Barron, Leon P
2015-05-29
The modelling and prediction of reversed-phase chromatographic retention time (tR) under gradient elution conditions for 166 pharmaceuticals in wastewater extracts is presented using artificial neural networks for the first time. Radial basis function, multilayer perceptron and generalised regression neural networks were investigated and a comparison of their predictive ability for model solutions discussed. For real world application, the effect of matrix complexity on tR measurements is presented. Measured tR for some compounds in influent wastewater varied by >1min in comparison to tR in model solutions. Similarly, matrix impact on artificial neural network predictive ability was addressed towards developing a more robust approach for routine screening applications. Overall, the best neural network had a predictive accuracy of <1.3min at the 75th percentile of all measured tR data in wastewater samples (<10% of the total runtime). Coefficients of determination for 30 blind test compounds in wastewater matrices lay at or above R(2)=0.92. Finally, the model was evaluated for application to the semi-targeted identification of pharmaceutical residues during a weeklong wastewater sampling campaign. The model successfully identified native compounds at a rate of 83±4% and 73±5% in influent and effluent extracts, respectively. The use of an HRMS database and the optimised ANN model was also applied to shortlisting of 37 additional compounds in wastewater. Ultimately, this research will potentially enable faster identification of emerging contaminants in the environment through more efficient post-acquisition data mining. Copyright © 2015 Elsevier B.V. All rights reserved.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Esch, Hendrik
In this thesis a measurement of the top quark mass in topologies that have been enhanced with single-top quark decays in the $t$-channel produced via weak interactions is presented. The dataset consists of proton-proton collisions at a centre-of-mass energy of $\\sqrt{s}=8\\,\\mathrm{TeV}$ collected with the ATLAS detector at the LHC with a total integrated luminosity of $\\mathcal{L}_{\\mathrm{int}} =20.3\\,\\mathrm{fb^{-1}}$. Selected events contain exactly one charged lepton - which can be either an electron or a muon -, missing transverse energy and two jets with exactly one of the two being $b$-tagged. The techniques of $b$-tagging used to identify jets induced by heavy quarks is explained further. In addition, the signal is enhanced using a neural network based discriminant that combines the ability to discriminate between signal and background of several correlated variables. To determine the mass of the top quark a template method is used in combination with the mass sensitive variable, $m(\\ell b)$, which i...
Richardson, Andrea S.; Meyer, Katie A.; Howard, Annie Green; Boone-Heinonen, Janne; Popkin, Barry M.; Evenson, Kelly R.; Shikany, James M.; Lewis, Cora E.; Gordon-Larsen, Penny
2016-01-01
Objectives To examine longitudinal pathways from multiple types of neighborhood restaurants and food stores to BMI, through dietary behaviors. Methods We used data from participants (n=5114) in the United States-based Coronary Artery Risk Development in Young Adults study and a structural equation model to estimate longitudinal (1985–86 to 2005–06) pathways simultaneously from neighborhood fast food restaurants, sit-down restaurants, supermarkets, and convenience stores to BMI through dietary behaviors, controlling for socioeconomic status (SES) and physical activity. Results Higher numbers of neighborhood fast food restaurants and lower numbers of sit-down restaurants were associated with higher consumption of an obesogenic fast food-type diet. The pathways from food stores to BMI through diet were inconsistent in magnitude and statistical significance. Conclusions Efforts to decrease the numbers of neighborhood fast food restaurants and to increase the numbers of sit-down restaurant options could influence diet behaviors. Availability of neighborhood fast food and sit-down restaurants may play comparatively stronger roles than food stores in shaping dietary behaviors and BMI. PMID:26454248
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
International Nuclear Information System (INIS)
Smith, Patrick I.
2003-01-01
Physicists use large detectors to measure particles created in high-energy collisions at particle accelerators. These detectors typically produce signals indicating either where ionization occurs along the path of the particle, or where energy is deposited by the particle. The data produced by these signals is fed into pattern recognition programs to try to identify what particles were produced, and to measure the energy and direction of these particles. Ideally, there are many techniques used in this pattern recognition software. One technique, neural networks, is particularly suitable for identifying what type of particle caused by a set of energy deposits. Neural networks can derive meaning from complicated or imprecise data, extract patterns, and detect trends that are too complex to be noticed by either humans or other computer related processes. To assist in the advancement of this technology, Physicists use a tool kit to experiment with several neural network techniques. The goal of this research is interface a neural network tool kit into Java Analysis Studio (JAS3), an application that allows data to be analyzed from any experiment. As the final result, a physicist will have the ability to train, test, and implement a neural network with the desired output while using JAS3 to analyze the results or output. Before an implementation of a neural network can take place, a firm understanding of what a neural network is and how it works is beneficial. A neural network is an artificial representation of the human brain that tries to simulate the learning process [5]. It is also important to think of the word artificial in that definition as computer programs that use calculations during the learning process. In short, a neural network learns by representative examples. Perhaps the easiest way to describe the way neural networks learn is to explain how the human brain functions. The human brain contains billions of neural cells that are responsible for processing
Evolvable synthetic neural system
Curtis, Steven A. (Inventor)
2009-01-01
An evolvable synthetic neural system includes an evolvable neural interface operably coupled to at least one neural basis function. Each neural basis function includes an evolvable neural interface operably coupled to a heuristic neural system to perform high-level functions and an autonomic neural system to perform low-level functions. In some embodiments, the evolvable synthetic neural system is operably coupled to one or more evolvable synthetic neural systems in a hierarchy.
Institute of Scientific and Technical Information of China (English)
李东; 魏亚玲; 马青华; 张大鹏
2015-01-01
According to the three processes that have been experienced successively by the output of coal-bed methane and withdrawal water from coal rock’s bedding, joint and fracture systems, this paper puts forward a“Desorption-Diffusion-Seepage”tandem mass transfer model and corresponding equations. When the three mass transfer processes are in a state of balance, according to the mass conservation law,it can be deduced that the interface radius r1 between the diffusion area and seepage area has nothing to do with coal-bed’s thickness.%根据煤层气和采出水在煤岩的层理、节理和裂缝系统中产出需先后经历的”解吸—扩散—渗流”3个过程，提出“解、扩、渗”串联传质模型和相应方程。3个传质过程处于平衡状态时，根据发生于扩散区与渗流区交界面处的质量守恒定律，可以推断扩散区与渗流区交界面半径r1与煤层厚度无关。
International Nuclear Information System (INIS)
Crowe, C.T.
1975-01-01
General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources
Higher order field equations. II
International Nuclear Information System (INIS)
Tolhoek, H.A.
1977-01-01
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)
International Nuclear Information System (INIS)
Gori, F.
2006-01-01
The time evolution of the price of resources sold to the market and of the price difference, between sold and extracted resources, is investigated in case of no accumulation of the resources; i.e. when the resources are extracted and sold to the market at the same mass flow rate. The price evolution of sold resources varies with time according to the relation between the price increase factor, PIF, of sold and extracted resources. The price evolutions of sold resources and price difference are investigated according to the relation between extraction rate and interest rate of extracted and sold resources. The price of sold resources and the price difference increase with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is greater than the critical price of sold resources, which depends on the initial price of extracted resources and the interest rate of non-extracted and extracted resources. The price of sold resources and the price difference decrease with time if the PIF of sold resources is greater than the PIF of extracted resources and the initial price is smaller than the critical price of sold resources. The other cases are discussed extensively in the paper. (author)
Energy Technology Data Exchange (ETDEWEB)
Luque, A., E-mail: a.luque@upm.es [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain); Mellor, A.; Tobías, I.; Antolín, E.; Linares, P.G.; Ramiro, I.; Martí, A. [Instituto de Energía Solar, Universidad Politécnica de Madrid (Spain)
2013-03-15
The effective mass Schrödinger equation of a QD of parallelepipedic shape with a square potential well is solved by diagonalizing the exact Hamiltonian matrix developed in a basis of separation-of-variables wavefunctions. The expected below bandgap bound states are found not to differ very much from the former approximate calculations. In addition, the presence of bound states within the conduction band is confirmed. Furthermore, filamentary states bounded in two dimensions and extended in one dimension and layered states with only one dimension bounded, all within the conduction band—which are similar to those originated in quantum wires and quantum wells—coexist with the ordinary continuum spectrum of plane waves. All these subtleties are absent in spherically shaped quantum dots, often used for modeling.
Application of neural network to CT
International Nuclear Information System (INIS)
Ma, Xiao-Feng; Takeda, Tatsuoki
1999-01-01
This paper presents a new method for two-dimensional image reconstruction by using a multilayer neural network. Multilayer neural networks are extensively investigated and practically applied to solution of various problems such as inverse problems or time series prediction problems. From learning an input-output mapping from a set of examples, neural networks can be regarded as synthesizing an approximation of multidimensional function (that is, solving the problem of hypersurface reconstruction, including smoothing and interpolation). From this viewpoint, neural networks are well suited to the solution of CT image reconstruction. Though a conventionally used object function of a neural network is composed of a sum of squared errors of the output data, we can define an object function composed of a sum of residue of an integral equation. By employing an appropriate line integral for this integral equation, we can construct a neural network that can be used for CT. We applied this method to some model problems and obtained satisfactory results. As it is not necessary to discretized the integral equation using this reconstruction method, therefore it is application to the problem of complicated geometrical shapes is also feasible. Moreover, in neural networks, interpolation is performed quite smoothly, as a result, inverse mapping can be achieved smoothly even in case of including experimental and numerical errors, However, use of conventional back propagation technique for optimization leads to an expensive computation cost. To overcome this drawback, 2nd order optimization methods or parallel computing will be applied in future. (J.P.N.)
Compositeness condition in the renormalization group equation
International Nuclear Information System (INIS)
Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko
1990-01-01
The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)
Greenland Ice Sheet Mass Balance
Reeh, N.
1984-01-01
Mass balance equation for glaciers; areal distribution and ice volumes; estimates of actual mass balance; loss by calving of icebergs; hydrological budget for Greenland; and temporal variations of Greenland mass balance are examined.
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
Local Dynamics in Trained Recurrent Neural Networks.
Rivkind, Alexander; Barak, Omri
2017-06-23
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task-related neural dynamics, we study trained recurrent neural networks. We develop a mean field theory for reservoir computing networks trained to have multiple fixed point attractors. Our main result is that the dynamics of the network's output in the vicinity of attractors is governed by a low-order linear ordinary differential equation. The stability of the resulting equation can be assessed, predicting training success or failure. As a consequence, networks of rectified linear units and of sigmoidal nonlinearities are shown to have diametrically different properties when it comes to learning attractors. Furthermore, a characteristic time constant, which remains finite at the edge of chaos, offers an explanation of the network's output robustness in the presence of variability of the internal neural dynamics. Finally, the proposed theory predicts state-dependent frequency selectivity in the network response.
Local Dynamics in Trained Recurrent Neural Networks
Rivkind, Alexander; Barak, Omri
2017-06-01
Learning a task induces connectivity changes in neural circuits, thereby changing their dynamics. To elucidate task-related neural dynamics, we study trained recurrent neural networks. We develop a mean field theory for reservoir computing networks trained to have multiple fixed point attractors. Our main result is that the dynamics of the network's output in the vicinity of attractors is governed by a low-order linear ordinary differential equation. The stability of the resulting equation can be assessed, predicting training success or failure. As a consequence, networks of rectified linear units and of sigmoidal nonlinearities are shown to have diametrically different properties when it comes to learning attractors. Furthermore, a characteristic time constant, which remains finite at the edge of chaos, offers an explanation of the network's output robustness in the presence of variability of the internal neural dynamics. Finally, the proposed theory predicts state-dependent frequency selectivity in the network response.
Causal electromagnetic interaction equations
International Nuclear Information System (INIS)
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Finite connectivity attractor neural networks
International Nuclear Information System (INIS)
Wemmenhove, B; Coolen, A C C
2003-01-01
We study a family of diluted attractor neural networks with a finite average number of (symmetric) connections per neuron. As in finite connectivity spin glasses, their equilibrium properties are described by order parameter functions, for which we derive an integral equation in replica symmetric approximation. A bifurcation analysis of this equation reveals the locations of the paramagnetic to recall and paramagnetic to spin-glass transition lines in the phase diagram. The line separating the retrieval phase from the spin-glass phase is calculated at zero temperature. All phase transitions are found to be continuous
DEFF Research Database (Denmark)
Bloch, Helle Aagaard; Kesmir, Can; Petersen, Marianne Kjerstine
1999-01-01
of this novelmethod with respect to various experimental parameters has been tested. The results can be summarised: (i)With this approach 97% of the wheat varieties can be classified correctly with a corresponding correlationcoefficient of 1.0, (ii) The method is fast since the time of extracting gliadins from flour......A novel tool for variety identification of wheat (Triticum aestivum L.) has been developed: an artificialneural network (ANN) is used to classify the gliadin fraction analysed by matrix-assisted laserdesorption/ionisation time-of-flight mass spectrometry (MALDI-TOFMS). The robustness...... by the identity of the operator making theanalysis. This study demonstrates that a combination of an ANN and MALDI-TOFMS analysis of thegliadin fraction provides a fast and reliable tool for the variety identification of wheat. Copyright 1999 JohnWiley & Sons, Ltd....
Directory of Open Access Journals (Sweden)
Schwindling Jerome
2010-04-01
Full Text Available This course presents an overview of the concepts of the neural networks and their aplication in the framework of High energy physics analyses. After a brief introduction on the concept of neural networks, the concept is explained in the frame of neuro-biology, introducing the concept of multi-layer perceptron, learning and their use as data classifer. The concept is then presented in a second part using in more details the mathematical approach focussing on typical use cases faced in particle physics. Finally, the last part presents the best way to use such statistical tools in view of event classifers, putting the emphasis on the setup of the multi-layer perceptron. The full article (15 p. corresponding to this lecture is written in french and is provided in the proceedings of the book SOS 2008.
Dynamic decomposition of spatiotemporal neural signals.
Directory of Open Access Journals (Sweden)
Luca Ambrogioni
2017-05-01
Full Text Available Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals.
Jansen, Karen; De Groote, Friedl; Massaad, Firas; Meyns, Pieter; Jonkers, Ilse
2012-01-01
Leg kinematics during backward walking (BW) are very similar to the time-reversed kinematics during forward walking (FW). This suggests that the underlying muscle activation pattern could originate from a simple time reversal, as well. Experimental electromyography studies have confirmed that this is the case for some muscles. Furthermore, it has been hypothesized that muscles showing a time reversal should also exhibit a reversal in function [from accelerating the body center of mass (COM) to decelerating]. However, this has not yet been verified in simulation studies. In the present study, forward simulations were used to study the effects of muscles on the acceleration of COM in FW and BW. We found that a reversal in function was indeed present in the muscle control of the horizontal movement of COM (e.g., tibialis anterior and gastrocnemius). In contrast, muscles' antigravity contributions maintained their function for both directions of movement. An important outcome of the present study is therefore that similar muscles can be used to achieve opposite functional demands at the level of control of the COM when walking direction is reversed. However, some muscles showed direction-specific contributions (i.e., dorsiflexors). We concluded that the changes in muscle contributions imply that a simple time reversal would be insufficient to produce BW from FW. We therefore propose that BW utilizes extra elements, presumably supraspinal, in addition to a common spinal drive. These additions are needed for propulsion and require a partial reconfiguration of lower level common networks. PMID:22423005
Testa, Massimo
1990-01-01
In the large quark mass limit, an argument which identifies the mass of the heavy-light pseudoscalar or scalar bound state with the renormalized mass of the heavy quark is given. The following equation is discussed: m(sub Q) = m(sub B), where m(sub Q) and m(sub B) are respectively the mass of the heavy quark and the mass of the pseudoscalar bound state.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
AN ENERGY FUNCTION APPROACH FOR FINDING ROOTS OF CHARACTERISTIC EQUATION
Deepak Mishra; Prem K. Kalra
2011-01-01
In this paper, an energy function approach for finding roots of a characteristic equation has been proposed. Finding the roots of a characteristics equation is considered as an optimization problem. We demonstrated that this problem can be solved with the application of feedback type neural network. The proposed approach is fast and robust against variation of parameter.
Faugeras, Olivier; Touboul, Jonathan; Cessac, Bruno
2009-01-01
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential. At the second (mesoscopic) scale, interacting populations of neurons are described individually by similar equations. The equations describing the dynamical and the stationary mean-field behaviors are considered as functional equations on a set of stochastic processes. Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution. This method is proved to converge to the unique solution and we characterize its complexity and convergence rate. We also provide partial results for the stationary problem on infinite time intervals. These results shed some new light on such neural mass models as the one of Jansen and Rit (1995): their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis. Our numerical experiments confirm that the framework we propose and the numerical methods we derive from it provide a new and powerful tool for the exploration of neural behaviors at different scales.
Neural network modeling of air pollution in tunnels according to indirect measurements
International Nuclear Information System (INIS)
Kaverzneva, T; Lazovskaya, T; Tarkhov, D; Vasilyev, A
2016-01-01
The article deals with the problem of providing the necessary parameters of air of the working area in dead-end tunnels in the case of ventilation systems powered off. An ill-posed initialboundary problem for the diffusion equation is used as a mathematical model for a description and analysis of mass transfer processes in the tunnel. The neural network approach is applied to construct an approximate solution (regularization) of the identification problem in the case of the approximate measurement data and the set of interval parameters of the modeled system. Two types of model measurements included binary data are considered. The direct problem solution and the inverse problem regularization for the offered neural network approach are constructed uniformly. (paper)
Dynamics in a delayed-neural network
International Nuclear Information System (INIS)
Yuan Yuan
2007-01-01
In this paper, we consider a neural network of four identical neurons with time-delayed connections. Some parameter regions are given for global, local stability and synchronization using the theory of functional differential equations. The root distributions in the corresponding characteristic transcendental equation are analyzed, Pitchfork bifurcation, Hopf and equivariant Hopf bifurcations are investigated by revealing the center manifolds and normal forms. Numerical simulations are shown the agreements with the theoretical results
An integral transform of the Salpeter equation
International Nuclear Information System (INIS)
Krolikowski, W.
1980-03-01
We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)
Equations of motion derived from a generalization of Einstein's equation for the gravitational field
International Nuclear Information System (INIS)
Mociutchi, C.
1980-01-01
The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)
GMDH and neural networks applied in temperature sensors monitoring
International Nuclear Information System (INIS)
Bueno, Elaine Inacio; Pereira, Iraci Martinez; Silva, Antonio Teixeira e
2009-01-01
In this work a monitoring system was developed based on the Group Method of Data Handling (GMDH) and Neural Networks (ANNs) methodologies. This methodology was applied to the IEA-R1 research reactor at IPEN by using a database obtained from a theoretical model of the reactor. The IEA-R1 research reactor is a pool type reactor of 5 MW, cooled and moderated by light water, and uses graphite and beryllium as reflector. The theoretical model was developed using the Matlab GUIDE toolbox. The equations are based in the IEA-R1 mass and energy inventory balance and physical as well as operational aspects are taken into consideration. This methodology was developed by using the GMDH algorithm as input variables to the ANNs. The results obtained using the GMDH and ANNs were better than that obtained using only ANNs. (author)
Spike Neural Models Part II: Abstract Neural Models
Directory of Open Access Journals (Sweden)
Johnson, Melissa G.
2018-02-01
Full Text Available Neurons are complex cells that require a lot of time and resources to model completely. In spiking neural networks (SNN though, not all that complexity is required. Therefore simple, abstract models are often used. These models save time, use less computer resources, and are easier to understand. This tutorial presents two such models: Izhikevich's model, which is biologically realistic in the resulting spike trains but not in the parameters, and the Leaky Integrate and Fire (LIF model which is not biologically realistic but does quickly and easily integrate input to produce spikes. Izhikevich's model is based on Hodgkin-Huxley's model but simplified such that it uses only two differentiation equations and four parameters to produce various realistic spike patterns. LIF is based on a standard electrical circuit and contains one equation. Either of these two models, or any of the many other models in literature can be used in a SNN. Choosing a neural model is an important task that depends on the goal of the research and the resources available. Once a model is chosen, network decisions such as connectivity, delay, and sparseness, need to be made. Understanding neural models and how they are incorporated into the network is the first step in creating a SNN.
Generalized Callan-Symanzik equations and the Renormalization Group
International Nuclear Information System (INIS)
MacDowell, S.W.
1975-01-01
A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian; Sparber, Christof; Markowich, Peter A.
2014-01-01
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass
Recurrent Neural Network for Computing Outer Inverse.
Živković, Ivan S; Stanimirović, Predrag S; Wei, Yimin
2016-05-01
Two linear recurrent neural networks for generating outer inverses with prescribed range and null space are defined. Each of the proposed recurrent neural networks is based on the matrix-valued differential equation, a generalization of dynamic equations proposed earlier for the nonsingular matrix inversion, the Moore-Penrose inversion, as well as the Drazin inversion, under the condition of zero initial state. The application of the first approach is conditioned by the properties of the spectrum of a certain matrix; the second approach eliminates this drawback, though at the cost of increasing the number of matrix operations. The cases corresponding to the most common generalized inverses are defined. The conditions that ensure stability of the proposed neural network are presented. Illustrative examples present the results of numerical simulations.
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.
1982-05-01
A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.
Using fundamental equations to describe basic phenomena
DEFF Research Database (Denmark)
Jakobsen, Arne; Rasmussen, Bjarne D.
1999-01-01
When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equatio...
Hardware implementation of stochastic spiking neural networks.
Rosselló, Josep L; Canals, Vincent; Morro, Antoni; Oliver, Antoni
2012-08-01
Spiking Neural Networks, the last generation of Artificial Neural Networks, are characterized by its bio-inspired nature and by a higher computational capacity with respect to other neural models. In real biological neurons, stochastic processes represent an important mechanism of neural behavior and are responsible of its special arithmetic capabilities. In this work we present a simple hardware implementation of spiking neurons that considers this probabilistic nature. The advantage of the proposed implementation is that it is fully digital and therefore can be massively implemented in Field Programmable Gate Arrays. The high computational capabilities of the proposed model are demonstrated by the study of both feed-forward and recurrent networks that are able to implement high-speed signal filtering and to solve complex systems of linear equations.
Antenna analysis using neural networks
Smith, William T.
1992-01-01
Conventional computing schemes have long been used to analyze problems in electromagnetics (EM). The vast majority of EM applications require computationally intensive algorithms involving numerical integration and solutions to large systems of equations. The feasibility of using neural network computing algorithms for antenna analysis is investigated. The ultimate goal is to use a trained neural network algorithm to reduce the computational demands of existing reflector surface error compensation techniques. Neural networks are computational algorithms based on neurobiological systems. Neural nets consist of massively parallel interconnected nonlinear computational elements. They are often employed in pattern recognition and image processing problems. Recently, neural network analysis has been applied in the electromagnetics area for the design of frequency selective surfaces and beam forming networks. The backpropagation training algorithm was employed to simulate classical antenna array synthesis techniques. The Woodward-Lawson (W-L) and Dolph-Chebyshev (D-C) array pattern synthesis techniques were used to train the neural network. The inputs to the network were samples of the desired synthesis pattern. The outputs are the array element excitations required to synthesize the desired pattern. Once trained, the network is used to simulate the W-L or D-C techniques. Various sector patterns and cosecant-type patterns (27 total) generated using W-L synthesis were used to train the network. Desired pattern samples were then fed to the neural network. The outputs of the network were the simulated W-L excitations. A 20 element linear array was used. There were 41 input pattern samples with 40 output excitations (20 real parts, 20 imaginary). A comparison between the simulated and actual W-L techniques is shown for a triangular-shaped pattern. Dolph-Chebyshev is a different class of synthesis technique in that D-C is used for side lobe control as opposed to pattern
Differential equations and applications recent advances
2014-01-01
Differential Equations and Applications : Recent Advances focus on the latest developments in Nonlinear Dynamical Systems, Neural Networks, Fluid Dynamics, Fractional Differential Systems, Mathematical Modelling and Qualitative Theory. Different aspects such as Existence, Stability, Controllability, Viscosity and Numerical Analysis for different systems have been discussed in this book. This book will be of great interest and use to researchers in Applied Mathematics, Engineering and Mathematical Physics.
Representation of neural networks as Lotka-Volterra systems
International Nuclear Information System (INIS)
Moreau, Yves; Vandewalle, Joos; Louies, Stephane; Brenig, Leon
1999-01-01
We study changes of coordinates that allow the representation of the ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models--also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form, where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoied. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network
Approximate radiative solutions of the Einstein equations
International Nuclear Information System (INIS)
Kuusk, P.; Unt, V.
1976-01-01
In this paper the external field of a bounded source emitting gravitational radiation is considered. A successive approximation method is used to integrate the Einstein equations in Bondi's coordinates (Bondi et al, Proc. R. Soc.; A269:21 (1962)). A method of separation of angular variables is worked out and the approximate Einstein equations are reduced to key equations. The losses of mass, momentum, and angular momentum due to gravitational multipole radiation are found. It is demonstrated that in the case of proper treatment a real mass occurs instead of a mass aspect in a solution of the Einstein equations. In an appendix Bondi's new function is given in terms of sources. (author)
Vrentas, James S
2013-01-01
The book first covers the five elements necessary to formulate and solve mass transfer problems, that is, conservation laws and field equations, boundary conditions, constitutive equations, parameters in constitutive equations, and mathematical methods that can be used to solve the partial differential equations commonly encountered in mass transfer problems. Jump balances, Green’s function solution methods, and the free-volume theory for the prediction of self-diffusion coefficients for polymer–solvent systems are among the topics covered. The authors then use those elements to analyze a wide variety of mass transfer problems, including bubble dissolution, polymer sorption and desorption, dispersion, impurity migration in plastic containers, and utilization of polymers in drug delivery. The text offers detailed solutions, along with some theoretical aspects, for numerous processes including viscoelastic diffusion, moving boundary problems, diffusion and reaction, membrane transport, wave behavior, sedime...
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
A neural theory of visual attention
DEFF Research Database (Denmark)
Bundesen, Claus; Habekost, Thomas; Kyllingsbæk, Søren
2005-01-01
A neural theory of visual attention (NTVA) is presented. NTVA is a neural interpretation of C. Bundesen's (1990) theory of visual attention (TVA). In NTVA, visual processing capacity is distributed across stimuli by dynamic remapping of receptive fields of cortical cells such that more processing...... resources (cells) are devoted to behaviorally important objects than to less important ones. By use of the same basic equations used in TVA, NTVA accounts for a wide range of known attentional effects in human performance (reaction times and error rates) and a wide range of effects observed in firing rates...
Equations of macrotransport in reactor fuel assemblies
International Nuclear Information System (INIS)
Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.
1986-01-01
The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given
Hybrid discrete-time neural networks.
Cao, Hongjun; Ibarz, Borja
2010-11-13
Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Energy Technology Data Exchange (ETDEWEB)
Ritter, G.X.; Sussner, P. [Univ. of Florida, Gainesville, FL (United States)
1996-12-31
The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition problems. In this theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. Thresholding usually follows the linear operation in order to provide for nonlinearity of the network. In this paper we introduce a novel class of neural networks, called morphological neural networks, in which the operations of multiplication and addition are replaced by addition and maximum (or minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, morphological network computation is nonlinear before thresholding. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. In this paper we consider some of these differences and provide some particular examples of morphological neural network.
Neural tube defects are birth defects of the brain, spine, or spinal cord. They happen in the ... that she is pregnant. The two most common neural tube defects are spina bifida and anencephaly. In ...
Embedding recurrent neural networks into predator-prey models.
Moreau, Yves; Louiès, Stephane; Vandewalle, Joos; Brenig, Leon
1999-03-01
We study changes of coordinates that allow the embedding of ordinary differential equations describing continuous-time recurrent neural networks into differential equations describing predator-prey models-also called Lotka-Volterra systems. We transform the equations for the neural network first into quasi-monomial form (Brenig, L. (1988). Complete factorization and analytic solutions of generalized Lotka-Volterra equations. Physics Letters A, 133(7-8), 378-382), where we express the vector field of the dynamical system as a linear combination of products of powers of the variables. In practice, this transformation is possible only if the activation function is the hyperbolic tangent or the logistic sigmoid. From this quasi-monomial form, we can directly transform the system further into Lotka-Volterra equations. The resulting Lotka-Volterra system is of higher dimension than the original system, but the behavior of its first variables is equivalent to the behavior of the original neural network. We expect that this transformation will permit the application of existing techniques for the analysis of Lotka-Volterra systems to recurrent neural networks. Furthermore, our results show that Lotka-Volterra systems are universal approximators of dynamical systems, just as are continuous-time neural networks.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
DEFF Research Database (Denmark)
Andersen, Rikke K; Johansen, Mathias; Blaabjerg, Morten
2007-01-01
By combining new and established protocols we have developed a procedure for isolation and propagation of neural precursor cells from the forebrain subventricular zone (SVZ) of newborn rats. Small tissue blocks of the SVZ were dissected and propagated en bloc as free-floating neural tissue...... content, thus allowing experimental studies of neural precursor cells and their niche...
Constitutive equations for two-phase flows
International Nuclear Information System (INIS)
Boure, J.A.
1974-12-01
The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr
Non-invasive neural stimulation
Tyler, William J.; Sanguinetti, Joseph L.; Fini, Maria; Hool, Nicholas
2017-05-01
Neurotechnologies for non-invasively interfacing with neural circuits have been evolving from those capable of sensing neural activity to those capable of restoring and enhancing human brain function. Generally referred to as non-invasive neural stimulation (NINS) methods, these neuromodulation approaches rely on electrical, magnetic, photonic, and acoustic or ultrasonic energy to influence nervous system activity, brain function, and behavior. Evidence that has been surmounting for decades shows that advanced neural engineering of NINS technologies will indeed transform the way humans treat diseases, interact with information, communicate, and learn. The physics underlying the ability of various NINS methods to modulate nervous system activity can be quite different from one another depending on the energy modality used as we briefly discuss. For members of commercial and defense industry sectors that have not traditionally engaged in neuroscience research and development, the science, engineering and technology required to advance NINS methods beyond the state-of-the-art presents tremendous opportunities. Within the past few years alone there have been large increases in global investments made by federal agencies, foundations, private investors and multinational corporations to develop advanced applications of NINS technologies. Driven by these efforts NINS methods and devices have recently been introduced to mass markets via the consumer electronics industry. Further, NINS continues to be explored in a growing number of defense applications focused on enhancing human dimensions. The present paper provides a brief introduction to the field of non-invasive neural stimulation by highlighting some of the more common methods in use or under current development today.
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Institute of Scientific and Technical Information of China (English)
郑世旺; 王建波; 陈向炜; 李彦敏; 解加芳
2012-01-01
航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.%The operational system of the spacecraft is general a variable mass one,of which the symmetry and the conserved quantity imply physical rules of the space system.In this paper,Tzénoff equations of the variable mass nonholonomic system are derived,from which the Lie symmetries of Tzénoff equations for the variable mass nonholonomic system and conserved quantities are derived and are researched.The function expressions of conserved quantities and the criterion equations which deduce these conserved quantities are presented.This result has some theoretical value for further research of the conservation laws obeyed by the variable mass system.
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Neural electrical activity and neural network growth.
Gafarov, F M
2018-05-01
The development of central and peripheral neural system depends in part on the emergence of the correct functional connectivity in its input and output pathways. Now it is generally accepted that molecular factors guide neurons to establish a primary scaffold that undergoes activity-dependent refinement for building a fully functional circuit. However, a number of experimental results obtained recently shows that the neuronal electrical activity plays an important role in the establishing of initial interneuronal connections. Nevertheless, these processes are rather difficult to study experimentally, due to the absence of theoretical description and quantitative parameters for estimation of the neuronal activity influence on growth in neural networks. In this work we propose a general framework for a theoretical description of the activity-dependent neural network growth. The theoretical description incorporates a closed-loop growth model in which the neural activity can affect neurite outgrowth, which in turn can affect neural activity. We carried out the detailed quantitative analysis of spatiotemporal activity patterns and studied the relationship between individual cells and the network as a whole to explore the relationship between developing connectivity and activity patterns. The model, developed in this work will allow us to develop new experimental techniques for studying and quantifying the influence of the neuronal activity on growth processes in neural networks and may lead to a novel techniques for constructing large-scale neural networks by self-organization. Copyright © 2018 Elsevier Ltd. All rights reserved.
Equation-oriented specification of neural models for simulations
Directory of Open Access Journals (Sweden)
Marcel eStimberg
2014-02-01
Full Text Available Simulating biological neuronal networks is a core method of research in computational neuroscience. A full specification of such a network model includes a description of the dynamics and state changes of neurons and synapses, as well as the synaptic connectivity patterns and the initial values of all parameters. A standard approach in neuronal modelling software is to build models based on a library of pre-defined models and mechanisms; if a model component does not yet exist, it has to be defined in a special-purpose or general low-level language and potentially be compiled and linked with the simulator. Here we propose an alternative approach that allows flexible definition of models by writing textual descriptions based on mathematical notation. We demonstrate that this approach allows the definition of a wide range of models with minimal syntax. Furthermore, such explicit model descriptions allow the generation of executable code for various target languages and devices, since the description is not tied to an implementation. Finally, this approach also has advantages for readability and reproducibility, because the model description is fully explicit, and because it can be automatically parsed and transformed into formatted descriptions.The presented approach has been implemented in the Brian2 simulator.
Efficient mass calibration of magnetic sector mass spectrometers
International Nuclear Information System (INIS)
Roddick, J.C.
1996-01-01
Magnetic sector mass spectrometers used for automatic acquisition of precise isotopic data are usually controlled with Hall probes and software that uses polynomial equations to define and calibrate the mass-field relations required for mass focusing. This procedure requires a number of reference masses and careful tuning to define and maintain an accurate mass calibration. A simplified equation is presented and applied to several different magnetically controlled mass spectrometers. The equation accounts for nonlinearity in typical Hall probe controlled mass-field relations, reduces calibration to a linear fitting procedure, and is sufficiently accurate to permit calibration over a mass range of 2 to 200 amu with only two defining masses. Procedures developed can quickly correct for normal drift in calibrations and compensate for drift during isotopic analysis over a limited mass range such as a single element. The equation is: Field A·Mass 1/2 + B·(Mass) p where A, B, and p are constants. The power value p has a characteristic value for a Hall probe/controller and is insensitive to changing conditions, thus reducing calibration to a linear regression to determine optimum A and B. (author). 1 ref., 1 tab., 6 figs
Efficient mass calibration of magnetic sector mass spectrometers
Energy Technology Data Exchange (ETDEWEB)
Roddick, J C
1997-12-31
Magnetic sector mass spectrometers used for automatic acquisition of precise isotopic data are usually controlled with Hall probes and software that uses polynomial equations to define and calibrate the mass-field relations required for mass focusing. This procedure requires a number of reference masses and careful tuning to define and maintain an accurate mass calibration. A simplified equation is presented and applied to several different magnetically controlled mass spectrometers. The equation accounts for nonlinearity in typical Hall probe controlled mass-field relations, reduces calibration to a linear fitting procedure, and is sufficiently accurate to permit calibration over a mass range of 2 to 200 amu with only two defining masses. Procedures developed can quickly correct for normal drift in calibrations and compensate for drift during isotopic analysis over a limited mass range such as a single element. The equation is: Field A{center_dot}Mass{sup 1/2} + B{center_dot}(Mass){sup p} where A, B, and p are constants. The power value p has a characteristic value for a Hall probe/controller and is insensitive to changing conditions, thus reducing calibration to a linear regression to determine optimum A and B. (author). 1 ref., 1 tab., 6 figs.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Probabilistic delay differential equation modeling of event-related potentials.
Ostwald, Dirk; Starke, Ludger
2016-08-01
"Dynamic causal models" (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach. Copyright © 2016 Elsevier Inc. All rights reserved.
Invariant relations in Boussinesq-type equations
International Nuclear Information System (INIS)
Meletlidou, Efi; Pouget, Joeel; Maugin, Gerard; Aifantis, Elias
2004-01-01
A wide class of partial differential equations have at least three conservation laws that remain invariant for certain solutions of them and especially for solitary wave solutions. These conservation laws can be considered as the energy, pseudomomentum and mass integrals of these solutions. We investigate the invariant relation between the energy and the pseudomomentum for solitary waves in two Boussinesq-type equations that come from the theory of elasticity and lattice models
Quarkonia from charmonium and renormalization group equations
International Nuclear Information System (INIS)
Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.
1978-01-01
A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Modified Einstein and Navier–Stokes Equations
Bulyzhenkov, I. É.
2018-05-01
The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.
Modified Einstein and Navier-Stokes Equations
Bulyzhenkov, I. É.
2018-05-01
The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.
General particle transport equation. Final report
International Nuclear Information System (INIS)
Lafi, A.Y.; Reyes, J.N. Jr.
1994-12-01
The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence
Chaotic diagonal recurrent neural network
International Nuclear Information System (INIS)
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)
Relativistic equations of state at finite temperature
International Nuclear Information System (INIS)
Santos, A.M.S.; Menezes, D.P.
2004-01-01
In this work we study the effects of temperature on the equations of state obtained within a relativistic model with and without β equilibrium, over a wide range of densities. We integrate the TOV equations. We also compare the results of the equation of state, effective mass and strangeness fraction from the TM1, NL3 and GL sets of parameters, as well as investigating the importance of antiparticles in the treatment. The have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars. (author)
Is the Langevin phase equation an efficient model for oscillating neurons?
Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru
2009-12-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Is the Langevin phase equation an efficient model for oscillating neurons?
International Nuclear Information System (INIS)
Ota, Keisuke; Tsunoda, Takamasa; Aonishi, Toru; Omori, Toshiaki; Okada, Masato; Watanabe, Shigeo; Miyakawa, Hiroyoshi
2009-01-01
The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.
Evolvable Neural Software System
Curtis, Steven A.
2009-01-01
The Evolvable Neural Software System (ENSS) is composed of sets of Neural Basis Functions (NBFs), which can be totally autonomously created and removed according to the changing needs and requirements of the software system. The resulting structure is both hierarchical and self-similar in that a given set of NBFs may have a ruler NBF, which in turn communicates with other sets of NBFs. These sets of NBFs may function as nodes to a ruler node, which are also NBF constructs. In this manner, the synthetic neural system can exhibit the complexity, three-dimensional connectivity, and adaptability of biological neural systems. An added advantage of ENSS over a natural neural system is its ability to modify its core genetic code in response to environmental changes as reflected in needs and requirements. The neural system is fully adaptive and evolvable and is trainable before release. It continues to rewire itself while on the job. The NBF is a unique, bilevel intelligence neural system composed of a higher-level heuristic neural system (HNS) and a lower-level, autonomic neural system (ANS). Taken together, the HNS and the ANS give each NBF the complete capabilities of a biological neural system to match sensory inputs to actions. Another feature of the NBF is the Evolvable Neural Interface (ENI), which links the HNS and ANS. The ENI solves the interface problem between these two systems by actively adapting and evolving from a primitive initial state (a Neural Thread) to a complicated, operational ENI and successfully adapting to a training sequence of sensory input. This simulates the adaptation of a biological neural system in a developmental phase. Within the greater multi-NBF and multi-node ENSS, self-similar ENI s provide the basis for inter-NBF and inter-node connectivity.
Statistical mechanics of attractor neural network models with synaptic depression
International Nuclear Information System (INIS)
Igarashi, Yasuhiko; Oizumi, Masafumi; Otsubo, Yosuke; Nagata, Kenji; Okada, Masato
2009-01-01
Synaptic depression is known to control gain for presynaptic inputs. Since cortical neurons receive thousands of presynaptic inputs, and their outputs are fed into thousands of other neurons, the synaptic depression should influence macroscopic properties of neural networks. We employ simple neural network models to explore the macroscopic effects of synaptic depression. Systems with the synaptic depression cannot be analyzed due to asymmetry of connections with the conventional equilibrium statistical-mechanical approach. Thus, we first propose a microscopic dynamical mean field theory. Next, we derive macroscopic steady state equations and discuss the stabilities of steady states for various types of neural network models.
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Directory of Open Access Journals (Sweden)
Lehnert B.
2011-04-01
Full Text Available A point-mass concept has been elaborated from the equations of the gravitational field. One application of these deductions results in a black hole configuration of the Schwarzschild type, having no electric charge and no angular momentum. The critical mass of a gravitational collapse with respect to the nuclear binding energy is found to be in the range of 0.4 to 90 solar masses. A second application is connected with the spec- ulation about an extended symmetric law of gravitation, based on the options of positive and negative mass for a particle at given positive energy. This would make masses of equal polarity attract each other, while masses of opposite polarity repel each other. Matter and antimatter are further proposed to be associated with the states of positive and negative mass. Under fully symmetric conditions this could provide a mechanism for the separation of antimatter from matter at an early stage of the universe.
Directory of Open Access Journals (Sweden)
Lehnert B.
2011-04-01
Full Text Available A point-mass concept has been elaborated from the equations of the gravitational field. One application of these deductions results in a black hole configuration of the Schwarzschild type, having no electric charge and no angular momentum. The critical mass of a gravitational collapse with respect to the nuclear binding energy is found to be in the range of 0.4 to 90 solar masses. A second application is connected with the speculation about an extended symmetric law of gravitation, based on the options of positive and negative mass for a particle at given positive energy. This would make masses of equal polarity attract each other, while masses of opposite polarity repel each other. Matter and antimatter are further proposed to be associated with the states of positive and negative mass. Under fully symmetric conditions this could provide a mechanism for the separation of antimatter from matter at an early stage of the universe.
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
A neuro approach to solve fuzzy Riccati differential equations
Energy Technology Data Exchange (ETDEWEB)
Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)
2015-10-22
There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.
Non-autonomous equations with unpredictable solutions
Akhmet, Marat; Fen, Mehmet Onur
2018-06-01
To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and uniqueness of the unpredictable solution for a delay differential equation are proved as well as for quasilinear discrete systems. As a corollary of the theorem, a similar assertion for a quasilinear ordinary differential equation is formulated. The results are demonstrated numerically, and an application to Hopfield neural networks is provided. In particular, Poincaré chaos near periodic orbits is observed. The completed research contributes to the theory of chaos as well as to the theory of differential and discrete equations, considering unpredictable solutions.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
artificial neural network model for low strength rc beam shear capacity
African Journals Online (AJOL)
User
RESEARCH PAPER. Keywords: Shear strength, reinforced concrete, Artificial Neural Network, design equations ... searchers using artificial intelligence to im- prove on theoretical ...... benefit to humanity or a waste of time?” The. Structural ...
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
DEFF Research Database (Denmark)
Jørgensen, Ivan Harald Holger; Bogason, Gudmundur; Bruun, Erik
1995-01-01
This paper proposes a new way to estimate the flow in a micromechanical flow channel. A neural network is used to estimate the delay of random temperature fluctuations induced in a fluid. The design and implementation of a hardware efficient neural flow estimator is described. The system...... is implemented using switched-current technique and is capable of estimating flow in the μl/s range. The neural estimator is built around a multiplierless neural network, containing 96 synaptic weights which are updated using the LMS1-algorithm. An experimental chip has been designed that operates at 5 V...
Federal Laboratory Consortium — As part of the Electrical and Computer Engineering Department and The Institute for System Research, the Neural Systems Laboratory studies the functionality of the...
Top tagging with deep neural networks [Vidyo
CERN. Geneva
2017-01-01
Recent literature on deep neural networks for top tagging has focussed on image based techniques or multivariate approaches using high level jet substructure variables. Here, we take a sequential approach to this task by using anordered sequence of energy deposits as training inputs. Unlike previous approaches, this strategy does not result in a loss of information during pixelization or the calculation of high level features. We also propose new preprocessing methods that do not alter key physical quantities such as jet mass. We compare the performance of this approach to standard tagging techniques and present results evaluating the robustness of the neural network to pileup.
Nuclear fission with a Langevin equation
International Nuclear Information System (INIS)
Boilley, D.; Suraud, E.; Abe, Yasuhisa
1992-01-01
A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with a constant mass. Fission rates calculated at different temperatures are shown and compared with previous available results. (author) 23 refs.; 7 figs
Recurrent Neural Network Approach Based on the Integral Representation of the Drazin Inverse.
Stanimirović, Predrag S; Živković, Ivan S; Wei, Yimin
2015-10-01
In this letter, we present the dynamical equation and corresponding artificial recurrent neural network for computing the Drazin inverse for arbitrary square real matrix, without any restriction on its eigenvalues. Conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the Drazin inverse are considered. Several illustrative examples present the results of computer simulations.
Neural Networks: Implementations and Applications
Vonk, E.; Veelenturf, L.P.J.; Jain, L.C.
1996-01-01
Artificial neural networks, also called neural networks, have been used successfully in many fields including engineering, science and business. This paper presents the implementation of several neural network simulators and their applications in character recognition and other engineering areas
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1994-01-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
African Journals Online (AJOL)
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an
The generalized Fermat equation
Beukers, F.
2006-01-01
This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Critical Branching Neural Networks
Kello, Christopher T.
2013-01-01
It is now well-established that intrinsic variations in human neural and behavioral activity tend to exhibit scaling laws in their fluctuations and distributions. The meaning of these scaling laws is an ongoing matter of debate between isolable causes versus pervasive causes. A spiking neural network model is presented that self-tunes to critical…
Consciousness and neural plasticity
DEFF Research Database (Denmark)
changes or to abandon the strong identity thesis altogether. Were one to pursue a theory according to which consciousness is not an epiphenomenon to brain processes, consciousness may in fact affect its own neural basis. The neural correlate of consciousness is often seen as a stable structure, that is...
Gravity and body mass regulation
Warren, L. E.; Horwitz, B. A.; Fuller, C. A.
1997-01-01
The effects of altered gravity on body mass, food intake, energy expenditure, and body composition are examined. Metabolic adjustments are reviewed in maintenance of energy balance, neural regulation, and humoral regulation are discussed. Experiments with rats indicate that genetically obese rats respond differently to hypergravity than lean rats.
PWR system simulation and parameter estimation with neural networks
International Nuclear Information System (INIS)
Akkurt, Hatice; Colak, Uener
2002-01-01
A detailed nonlinear model for a typical PWR system has been considered for the development of simulation software. Each component in the system has been represented by appropriate differential equations. The SCILAB software was used for solving nonlinear equations to simulate steady-state and transient operational conditions. Overall system has been constructed by connecting individual components to each other. The validity of models for individual components and overall system has been verified. The system response against given transients have been analyzed. A neural network has been utilized to estimate system parameters during transients. Different transients have been imposed in training and prediction stages with neural networks. Reactor power and system reactivity during the transient event have been predicted by the neural network. Results show that neural networks estimations are in good agreement with the calculated response of the reactor system. The maximum errors are within ±0.254% for power and between -0.146 and 0.353% for reactivity prediction cases. Steam generator parameters, pressure and water level, are also successfully predicted by the neural network employed in this study. The noise imposed on the input parameters of the neural network deteriorates the power estimation capability whereas the reactivity estimation capability is not significantly affected
PWR system simulation and parameter estimation with neural networks
Energy Technology Data Exchange (ETDEWEB)
Akkurt, Hatice; Colak, Uener E-mail: uc@nuke.hacettepe.edu.tr
2002-11-01
A detailed nonlinear model for a typical PWR system has been considered for the development of simulation software. Each component in the system has been represented by appropriate differential equations. The SCILAB software was used for solving nonlinear equations to simulate steady-state and transient operational conditions. Overall system has been constructed by connecting individual components to each other. The validity of models for individual components and overall system has been verified. The system response against given transients have been analyzed. A neural network has been utilized to estimate system parameters during transients. Different transients have been imposed in training and prediction stages with neural networks. Reactor power and system reactivity during the transient event have been predicted by the neural network. Results show that neural networks estimations are in good agreement with the calculated response of the reactor system. The maximum errors are within {+-}0.254% for power and between -0.146 and 0.353% for reactivity prediction cases. Steam generator parameters, pressure and water level, are also successfully predicted by the neural network employed in this study. The noise imposed on the input parameters of the neural network deteriorates the power estimation capability whereas the reactivity estimation capability is not significantly affected.
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Local instant conservation equations
International Nuclear Information System (INIS)
Delaje, Dzh.
1984-01-01
Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
A recurrent neural network with ever changing synapses
Heerema, M.; van Leeuwen, W.A.
2000-01-01
A recurrent neural network with noisy input is studied analytically, on the basis of a Discrete Time Master Equation. The latter is derived from a biologically realizable learning rule for the weights of the connections. In a numerical study it is found that the fixed points of the dynamics of the
Dynamics of neural cryptography.
Ruttor, Andreas; Kinzel, Wolfgang; Kanter, Ido
2007-05-01
Synchronization of neural networks has been used for public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.
Dynamics of neural cryptography
International Nuclear Information System (INIS)
Ruttor, Andreas; Kinzel, Wolfgang; Kanter, Ido
2007-01-01
Synchronization of neural networks has been used for public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible
Dynamics of neural cryptography
Ruttor, Andreas; Kinzel, Wolfgang; Kanter, Ido
2007-05-01
Synchronization of neural networks has been used for public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.
Gong, Shuqing; Yang, Shaofu; Guo, Zhenyuan; Huang, Tingwen
2018-06-01
The paper is concerned with the synchronization problem of inertial memristive neural networks with time-varying delay. First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations. Then, a novel controller with a linear diffusive term and discontinuous sign term is designed. By using the controller, the sufficient conditions for assuring the global exponential synchronization of the derive and response neural networks are derived based on Lyapunov stability theory and some inequality techniques. Finally, several numerical simulations are provided to substantiate the effectiveness of the theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Energy Technology Data Exchange (ETDEWEB)
Labrador, I.; Carrasco, R.; Martinez, L.
1996-07-01
This paper describes a practical introduction to the use of Artificial Neural Networks. Artificial Neural Nets are often used as an alternative to the traditional symbolic manipulation and first order logic used in Artificial Intelligence, due the high degree of difficulty to solve problems that can not be handled by programmers using algorithmic strategies. As a particular case of Neural Net a Multilayer Perception developed by programming in C language on OS9 real time operating system is presented. A detailed description about the program structure and practical use are included. Finally, several application examples that have been treated with the tool are presented, and some suggestions about hardware implementations. (Author) 15 refs.
International Nuclear Information System (INIS)
Labrador, I.; Carrasco, R.; Martinez, L.
1996-01-01
This paper describes a practical introduction to the use of Artificial Neural Networks. Artificial Neural Nets are often used as an alternative to the traditional symbolic manipulation and first order logic used in Artificial Intelligence, due the high degree of difficulty to solve problems that can not be handled by programmers using algorithmic strategies. As a particular case of Neural Net a Multilayer Perception developed by programming in C language on OS9 real time operating system is presented. A detailed description about the program structure and practical use are included. Finally, several application examples that have been treated with the tool are presented, and some suggestions about hardware implementations. (Author) 15 refs
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Quantum linear Boltzmann equation
International Nuclear Information System (INIS)
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Covariant field equations in supergravity
Energy Technology Data Exchange (ETDEWEB)
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
International Nuclear Information System (INIS)
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
An implicit spectral formula for generalized linear Schroedinger equations
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan
2009-01-01
We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)
Statistically derived conservation equations for fluid particle flows
International Nuclear Information System (INIS)
Reyes, J.N. Jr.
1989-01-01
The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior
General method for reducing the two-body Dirac equation
International Nuclear Information System (INIS)
Galeao, A.P.; Ferreira, P.L.
1992-01-01
A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)
Guiding-center equations for electrons in ultraintense laser fields
International Nuclear Information System (INIS)
Moore, J.E.; Fisch, N.J.
1994-01-01
The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increase of the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
Sourcing for Parameter Estimation and Study of Logistic Differential Equation
Winkel, Brian J.
2012-01-01
This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…
A generalised groundwater flow equation using the concept of non ...
African Journals Online (AJOL)
The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of ...
A class of convergent neural network dynamics
Fiedler, Bernold; Gedeon, Tomáš
1998-01-01
We consider a class of systems of differential equations in Rn which exhibits convergent dynamics. We find a Lyapunov function and show that every bounded trajectory converges to the set of equilibria. Our result generalizes the results of Cohen and Grossberg (1983) for convergent neural networks. It replaces the symmetry assumption on the matrix of weights by the assumption on the structure of the connections in the neural network. We prove the convergence result also for a large class of Lotka-Volterra systems. These are naturally defined on the closed positive orthant. We show that there are no heteroclinic cycles on the boundary of the positive orthant for the systems in this class.
Separation prediction in two dimensional boundary layer flows using artificial neural networks
International Nuclear Information System (INIS)
Sabetghadam, F.; Ghomi, H.A.
2003-01-01
In this article, the ability of artificial neural networks in prediction of separation in steady two dimensional boundary layer flows is studied. Data for network training is extracted from numerical solution of an ODE obtained from Von Karman integral equation with approximate one parameter Pohlhousen velocity profile. As an appropriate neural network, a two layer radial basis generalized regression artificial neural network is used. The results shows good agreements between the overall behavior of the flow fields predicted by the artificial neural network and the actual flow fields for some cases. The method easily can be extended to unsteady separation and turbulent as well as compressible boundary layer flows. (author)
Robustness Analysis of Hybrid Stochastic Neural Networks with Neutral Terms and Time-Varying Delays
Directory of Open Access Journals (Sweden)
Chunmei Wu
2015-01-01
Full Text Available We analyze the robustness of global exponential stability of hybrid stochastic neural networks subject to neutral terms and time-varying delays simultaneously. Given globally exponentially stable hybrid stochastic neural networks, we characterize the upper bounds of contraction coefficients of neutral terms and time-varying delays by using the transcendental equation. Moreover, we prove theoretically that, for any globally exponentially stable hybrid stochastic neural networks, if additive neutral terms and time-varying delays are smaller than the upper bounds arrived, then the perturbed neural networks are guaranteed to also be globally exponentially stable. Finally, a numerical simulation example is given to illustrate the presented criteria.
ANNarchy: a code generation approach to neural simulations on parallel hardware
Vitay, Julien; Dinkelbach, Helge Ü.; Hamker, Fred H.
2015-01-01
Many modern neural simulators focus on the simulation of networks of spiking neurons on parallel hardware. Another important framework in computational neuroscience, rate-coded neural networks, is mostly difficult or impossible to implement using these simulators. We present here the ANNarchy (Artificial Neural Networks architect) neural simulator, which allows to easily define and simulate rate-coded and spiking networks, as well as combinations of both. The interface in Python has been designed to be close to the PyNN interface, while the definition of neuron and synapse models can be specified using an equation-oriented mathematical description similar to the Brian neural simulator. This information is used to generate C++ code that will efficiently perform the simulation on the chosen parallel hardware (multi-core system or graphical processing unit). Several numerical methods are available to transform ordinary differential equations into an efficient C++code. We compare the parallel performance of the simulator to existing solutions. PMID:26283957
MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion
Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong
This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.
DEFF Research Database (Denmark)
Krogh, Anders Stærmose; Riis, Søren Kamaric
1999-01-01
A general framework for hybrids of hidden Markov models (HMMs) and neural networks (NNs) called hidden neural networks (HNNs) is described. The article begins by reviewing standard HMMs and estimation by conditional maximum likelihood, which is used by the HNN. In the HNN, the usual HMM probability...... parameters are replaced by the outputs of state-specific neural networks. As opposed to many other hybrids, the HNN is normalized globally and therefore has a valid probabilistic interpretation. All parameters in the HNN are estimated simultaneously according to the discriminative conditional maximum...... likelihood criterion. The HNN can be viewed as an undirected probabilistic independence network (a graphical model), where the neural networks provide a compact representation of the clique functions. An evaluation of the HNN on the task of recognizing broad phoneme classes in the TIMIT database shows clear...
International Nuclear Information System (INIS)
Carter, B.; McLenaghan, R.G.
1982-01-01
It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)
Neural networks for aircraft control
Linse, Dennis
1990-01-01
Current research in Artificial Neural Networks indicates that networks offer some potential advantages in adaptation and fault tolerance. This research is directed at determining the possible applicability of neural networks to aircraft control. The first application will be to aircraft trim. Neural network node characteristics, network topology and operation, neural network learning and example histories using neighboring optimal control with a neural net are discussed.
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian
2014-10-08
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
Chaplot, Devendra Singh; Parisotto, Emilio; Salakhutdinov, Ruslan
2018-01-01
Localization is the problem of estimating the location of an autonomous agent from an observation and a map of the environment. Traditional methods of localization, which filter the belief based on the observations, are sub-optimal in the number of steps required, as they do not decide the actions taken by the agent. We propose "Active Neural Localizer", a fully differentiable neural network that learns to localize accurately and efficiently. The proposed model incorporates ideas of tradition...
Neural cryptography with feedback.
Ruttor, Andreas; Kinzel, Wolfgang; Shacham, Lanir; Kanter, Ido
2004-04-01
Neural cryptography is based on a competition between attractive and repulsive stochastic forces. A feedback mechanism is added to neural cryptography which increases the repulsive forces. Using numerical simulations and an analytic approach, the probability of a successful attack is calculated for different model parameters. Scaling laws are derived which show that feedback improves the security of the system. In addition, a network with feedback generates a pseudorandom bit sequence which can be used to encrypt and decrypt a secret message.
A new formulation of equations of compressible fluids by analogy with Maxwell's equations
International Nuclear Information System (INIS)
Kambe, Tsutomu
2010-01-01
A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.
A discussion of the relativistic equal-time equation
International Nuclear Information System (INIS)
Chengrui, Q.; Danhua, Q.
1981-03-01
Ruan Tu-nan et al have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limit M 2 → infinite in the ladder approximation of single photon exchange. We show that up to order O(α 4 ) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of order O(α 6 ). (author)
Transport equation solving methods
International Nuclear Information System (INIS)
Granjean, P.M.
1984-06-01
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Global existence of periodic solutions on a simplified BAM neural network model with delays
International Nuclear Information System (INIS)
Zheng Baodong; Zhang Yazhuo; Zhang Chunrui
2008-01-01
A simplified n-dimensional BAM neural network model with delays is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu [Wu J. Symmetric functional-differential equations and neural networks with memory. Trans Am Math Soc 1998;350:4799-838], and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney [Li MY, Muldowney J. On Bendixson's criterion. J Differ Equations 1994;106:27-39]. Finally, computer simulations are performed to illustrate the analytical results found
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano; Gomes, Diogo A.; Machado Velho, Roberto
2017-01-01
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
An Adjoint-based Numerical Method for a class of nonlinear Fokker-Planck Equations
Festa, Adriano
2017-03-22
Here, we introduce a numerical approach for a class of Fokker-Planck (FP) equations. These equations are the adjoint of the linearization of Hamilton-Jacobi (HJ) equations. Using this structure, we show how to transfer the properties of schemes for HJ equations to the FP equations. Hence, we get numerical schemes with desirable features such as positivity and mass-preservation. We illustrate this approach in examples that include mean-field games and a crowd motion model.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Iteration of adjoint equations
International Nuclear Information System (INIS)
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Analysis of wave equation in electromagnetic field by Proca equation
International Nuclear Information System (INIS)
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Solution of Deformed Einstein Equations and Quantum Black Holes
International Nuclear Information System (INIS)
Dil, Emre; Kolay, Erdinç
2016-01-01
Recently, one- and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight into the deformed Einstein equations and consider the solutions of these equations for the extremal quantum black holes. We then represent the implications of the solutions, such that the deformation parameters lead the charged black holes to have a smaller mass than the usual Reissner-Nordström black holes. This reduction in mass of a usual black hole can be considered as a transition from classical to quantum black hole regime.
On the deformed Einstein equations and quantum black holes
International Nuclear Information System (INIS)
Dil, E; Ersanli, C C; Kolay, E
2016-01-01
Recently q -deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give the solutions of deformed Einstein equations by considering these equations for the charged black holes. Also we present the implications of the solutions, such as the deformation parameters lead the charged black holes to have a smaller mass than the classical Reissner- Nordstrom black holes. The reduction in mass of a classical black hole can be viewed as a transition from classical to quantum black hole regime. (paper)
Field-theoretic approach to fluctuation effects in neural networks
International Nuclear Information System (INIS)
Buice, Michael A.; Cowan, Jack D.
2007-01-01
A well-defined stochastic theory for neural activity, which permits the calculation of arbitrary statistical moments and equations governing them, is a potentially valuable tool for theoretical neuroscience. We produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes. Assuming that neural network activity is Markovian, we construct the effective spike model, which describes both neural fluctuations and response. This analysis leads to a systematic expansion of corrections to mean field theory, which for the effective spike model is a simple version of the Wilson-Cowan equation. We argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation. More general models (which may incorporate refractoriness) can exhibit other universality classes, such as dynamic isotropic percolation. Because of the extremely high connectivity in typical networks, it is expected that higher-order terms in the systematic expansion are small for experimentally accessible measurements, and thus, consistent with measurements in neocortical slice preparations, we expect mean field exponents for the transition. We provide a quantitative criterion for the relative magnitude of each term in the systematic expansion, analogous to the Ginsburg criterion. Experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience
Chemical potential and the gap equation
International Nuclear Information System (INIS)
Chen Huan; Yuan Wei; Chang Lei; Liu Yuxin; Klaehn, Thomas; Roberts, Craig D.
2008-01-01
In general, the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are μ independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex, but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realize chiral symmetry in the Nambu-Goldstone mode, and in the chiral limit, with increasing chemical potential, they exhibit a first-order chiral symmetry restoring transition at μ≅M(0), where M(p 2 ) is the dressed-quark mass function.
Smooth function approximation using neural networks.
Ferrari, Silvia; Stengel, Robert F
2005-01-01
An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the function's input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.
Indian Academy of Sciences (India)
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Indian Academy of Sciences (India)
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
African Journals Online (AJOL)
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
Indian Academy of Sciences (India)
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Guiding center drift equations
International Nuclear Information System (INIS)
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
Michaelis - Menten equation for degradation of insoluble substrate
DEFF Research Database (Denmark)
Andersen, Morten; Kari, Jeppe; Borch, Kim
2017-01-01
substrate it is difficult to assess whether the requirement of the MM equation is met. In this paper we study a simple kinetic model, where removal of attack sites expose new ones which preserve the total accessible substrate, and denote this approach the substrate conserving model. The kinetic equations...... are solved in closed form, both steady states and progress curves, for any admissible values of initial conditions and rate constants. The model is shown to merge with the MM equation and the reverse MM equation when these are valid. The relation between available molar concentration of attack sites and mass...
Evaluation of peak power prediction equations in male basketball players.
Duncan, Michael J; Lyons, Mark; Nevill, Alan M
2008-07-01
This study compared peak power estimated using 4 commonly used regression equations with actual peak power derived from force platform data in a group of adolescent basketball players. Twenty-five elite junior male basketball players (age, 16.5 +/- 0.5 years; mass, 74.2 +/- 11.8 kg; height, 181.8 +/- 8.1 cm) volunteered to participate in the study. Actual peak power was determined using a countermovement vertical jump on a force platform. Estimated peak power was determined using countermovement jump height and body mass. All 4 prediction equations were significantly related to actual peak power (all p jump prediction equations, 12% for the Canavan and Vescovi equation, and 6% for the Sayers countermovement jump equation. In all cases peak power was underestimated.
Parallel consensual neural networks.
Benediktsson, J A; Sveinsson, J R; Ersoy, O K; Swain, P H
1997-01-01
A new type of a neural-network architecture, the parallel consensual neural network (PCNN), is introduced and applied in classification/data fusion of multisource remote sensing and geographic data. The PCNN architecture is based on statistical consensus theory and involves using stage neural networks with transformed input data. The input data are transformed several times and the different transformed data are used as if they were independent inputs. The independent inputs are first classified using the stage neural networks. The output responses from the stage networks are then weighted and combined to make a consensual decision. In this paper, optimization methods are used in order to weight the outputs from the stage networks. Two approaches are proposed to compute the data transforms for the PCNN, one for binary data and another for analog data. The analog approach uses wavelet packets. The experimental results obtained with the proposed approach show that the PCNN outperforms both a conjugate-gradient backpropagation neural network and conventional statistical methods in terms of overall classification accuracy of test data.
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Evolution equations for extended dihadron fragmentation functions
International Nuclear Information System (INIS)
Ceccopieri, F.A.; Bacchetta, A.
2007-03-01
We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, M h , of the hadron pair. We first rederive the known results on M h -integrated functions using Jet Calculus techniques, and then we present the evolution equations for extended dihadron fragmentation functions. Our results are relevant for the analysis of experimental measurements of two-particle-inclusive processes at different energies. (orig.)
On generalized fractional vibration equation
International Nuclear Information System (INIS)
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-01-01
Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
Larson, V. H.
1982-01-01
The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
equateIRT: An R Package for IRT Test Equating
Directory of Open Access Journals (Sweden)
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
Neural Architectures for Control
Peterson, James K.
1991-01-01
The cerebellar model articulated controller (CMAC) neural architectures are shown to be viable for the purposes of real-time learning and control. Software tools for the exploration of CMAC performance are developed for three hardware platforms, the MacIntosh, the IBM PC, and the SUN workstation. All algorithm development was done using the C programming language. These software tools were then used to implement an adaptive critic neuro-control design that learns in real-time how to back up a trailer truck. The truck backer-upper experiment is a standard performance measure in the neural network literature, but previously the training of the controllers was done off-line. With the CMAC neural architectures, it was possible to train the neuro-controllers on-line in real-time on a MS-DOS PC 386. CMAC neural architectures are also used in conjunction with a hierarchical planning approach to find collision-free paths over 2-D analog valued obstacle fields. The method constructs a coarse resolution version of the original problem and then finds the corresponding coarse optimal path using multipass dynamic programming. CMAC artificial neural architectures are used to estimate the analog transition costs that dynamic programming requires. The CMAC architectures are trained in real-time for each obstacle field presented. The coarse optimal path is then used as a baseline for the construction of a fine scale optimal path through the original obstacle array. These results are a very good indication of the potential power of the neural architectures in control design. In order to reach as wide an audience as possible, we have run a seminar on neuro-control that has met once per week since 20 May 1991. This seminar has thoroughly discussed the CMAC architecture, relevant portions of classical control, back propagation through time, and adaptive critic designs.
DEFF Research Database (Denmark)
Runehov, Anne Leona Cesarine
Are religious spiritual experiences merely the product of the human nervous system? Anne L.C. Runehov investigates the potential of contemporary neuroscience to explain religious experiences. Following the footsteps of Michael Persinger, Andrew Newberg and Eugene d'Aquili she defines...... the terminological bounderies of "religious experiences" and explores the relevant criteria for the proper evaluation of scientific research, with a particular focus on the validity of reductionist models. Runehov's theis is that the perspectives looked at do not necessarily exclude each other but can be merged....... The question "sacred or neural?" becomes a statement "sacred and neural". The synergies thus produced provide manifold opportunities for interdisciplinary dialogue and research....
Deconvolution using a neural network
Energy Technology Data Exchange (ETDEWEB)
Lehman, S.K.
1990-11-15
Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.
Introduction to Artificial Neural Networks
DEFF Research Database (Denmark)
Larsen, Jan
1999-01-01
The note addresses introduction to signal analysis and classification based on artificial feed-forward neural networks.......The note addresses introduction to signal analysis and classification based on artificial feed-forward neural networks....
High mass planets and low mass stars
International Nuclear Information System (INIS)
Stevenson, D.J.
1986-01-01
The paper on theoretical models of brown dwarf stars was presented to the workshop on ''Astrophysics of brown dwarfs'', Virginia, USA, 1985. The ingredients in the models i.e. equation of state, entropy and the infrared opacity are described. An analytical model is developed which is based on a polytrope (n = 3/4) but which neglects thermonuclear reactions. The model forms the basis of scaling laws for luminosity, mass, opacity and age. Complicating factors in brown dwarf evolution are also discussed. (U.K.)
Spaced Learning Enhances Subsequent Recognition Memory by Reducing Neural Repetition Suppression
Xue, Gui; Mei, Leilei; Chen, Chuansheng; Lu, Zhong-Lin; Poldrack, Russell; Dong, Qi
2011-01-01
Spaced learning usually leads to better recognition memory as compared with massed learning, yet the underlying neural mechanisms remain elusive. One open question is whether the spacing effect is achieved by reducing neural repetition suppression. In this fMRI study, participants were scanned while intentionally memorizing 120 novel faces, half…
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Macroscopic balance equations for two-phase flow models
International Nuclear Information System (INIS)
Hughes, E.D.
1979-01-01
The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Electroweak evolution equations
International Nuclear Information System (INIS)
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Baertsch, N. A.
2013-01-01
Reduced respiratory neural activity elicits a rebound increase in phrenic and hypoglossal motor output known as inactivity-induced phrenic and hypoglossal motor facilitation (iPMF and iHMF, respectively). We hypothesized that, similar to other forms of respiratory plasticity, iPMF and iHMF are pattern sensitive. Central respiratory neural activity was reversibly reduced in ventilated rats by hyperventilating below the CO2 apneic threshold to create brief intermittent neural apneas (5, ∼1.5 min each, separated by 5 min), a single brief massed neural apnea (7.5 min), or a single prolonged neural apnea (30 min). Upon restoration of respiratory neural activity, long-lasting (>60 min) iPMF was apparent following brief intermittent and prolonged, but not brief massed, neural apnea. Further, brief intermittent and prolonged neural apnea elicited an increase in the maximum phrenic response to high CO2, suggesting that iPMF is associated with an increase in phrenic dynamic range. By contrast, only prolonged neural apnea elicited iHMF, which was transient in duration (<15 min). Intermittent, massed, and prolonged neural apnea all elicited a modest transient facilitation of respiratory frequency. These results indicate that iPMF, but not iHMF, is pattern sensitive, and that the response to respiratory neural inactivity is motor pool specific. PMID:23493368
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Mass-Radius diagram for compact stars
International Nuclear Information System (INIS)
Carvalho, G A; Jr, R M Marinho; Malheiro, M
2015-01-01
The compact stars represent the final stage in the evolution of ordinary stars, they are formed when a star ceases its nuclear fuel, in this point the process that sustain its stability will stop. After this, the internal pressure can no longer stand the gravitational force and the star colapses [2]. In this work we investigate the structure of these stars which are described by the equations of Tolman-Openheimer-Volkof (TOV) [1]. These equations show us how the pressure varies with the mass and radius of the star. We consider the TOV equations for both relativistic and non-relativistic cases. In the case of compact stars (white dwarfs and neutron stars) the internal pressure that balances the gravitational pressure is essentialy the pressure coming from the degeneracy of fermions. To have solved the TOV equations we need a equation of state that shows how this internal pressure is related to the energy density or mass density. Instead of using politropic equations of state we have solved the equations numericaly using the exact relativistic energy equation for the model of fermion gas at zero temperature. We obtain results for the mass-radius relation for white dwarfs and we compared with the results obtained using the politropic equations of state. In addition we discussed a good fit for the mass-radius relation. (paper)
An integrated approach to determine phenomenological equations in metallic systems
Ghamarian, Iman
It is highly desirable to be able to make predictions of properties in metallic materials based upon the composition of the material and the microstructure. Unfortunately, the complexity of real, multi-component, multi-phase engineering alloys makes the provision of constituent-based (i.e., composition or microstructure) phenomenological equations extremely difficult. Due to these difficulties, qualitative predictions are frequently used to study the influence of microstructure or composition on the properties. Neural networks were used as a tool to get a quantitative model from a database. However, the developed model is not a phenomenological model. In this study, a new method based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and monte carlo was proposed. These three methods, when coupled in the manner described in this study, allows for the extraction of phenomenological equations with a concurrent analysis of uncertainty. This approach has been applied to a multi-component, multi-phase microstructure exhibiting phases with varying spatial and morphological distributions. Specifically, this approach has been applied to derive a phenomenological equation for the prediction of yield strength in alpha+beta processed Ti-6-4. The equation is consistent with not only the current dataset but also, where available, the limited information regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium.
DEFF Research Database (Denmark)
Hansen, Lars Kai; Salamon, Peter
1990-01-01
We propose several means for improving the performance an training of neural networks for classification. We use crossvalidation as a tool for optimizing network parameters and architecture. We show further that the remaining generalization error can be reduced by invoking ensembles of similar...... networks....
Neural correlates of consciousness
African Journals Online (AJOL)
neural cells.1 Under this approach, consciousness is believed to be a product of the ... possible only when the 40 Hz electrical hum is sustained among the brain circuits, ... expect the brain stem ascending reticular activating system. (ARAS) and the ... related synchrony of cortical neurons.11 Indeed, stimulation of brainstem ...
Neural Networks and Micromechanics
Kussul, Ernst; Baidyk, Tatiana; Wunsch, Donald C.
The title of the book, "Neural Networks and Micromechanics," seems artificial. However, the scientific and technological developments in recent decades demonstrate a very close connection between the two different areas of neural networks and micromechanics. The purpose of this book is to demonstrate this connection. Some artificial intelligence (AI) methods, including neural networks, could be used to improve automation system performance in manufacturing processes. However, the implementation of these AI methods within industry is rather slow because of the high cost of conducting experiments using conventional manufacturing and AI systems. To lower the cost, we have developed special micromechanical equipment that is similar to conventional mechanical equipment but of much smaller size and therefore of lower cost. This equipment could be used to evaluate different AI methods in an easy and inexpensive way. The proved methods could be transferred to industry through appropriate scaling. In this book, we describe the prototypes of low cost microequipment for manufacturing processes and the implementation of some AI methods to increase precision, such as computer vision systems based on neural networks for microdevice assembly and genetic algorithms for microequipment characterization and the increase of microequipment precision.
Introduction to neural networks
International Nuclear Information System (INIS)
Pavlopoulos, P.
1996-01-01
This lecture is a presentation of today's research in neural computation. Neural computation is inspired by knowledge from neuro-science. It draws its methods in large degree from statistical physics and its potential applications lie mainly in computer science and engineering. Neural networks models are algorithms for cognitive tasks, such as learning and optimization, which are based on concepts derived from research into the nature of the brain. The lecture first gives an historical presentation of neural networks development and interest in performing complex tasks. Then, an exhaustive overview of data management and networks computation methods is given: the supervised learning and the associative memory problem, the capacity of networks, the Perceptron networks, the functional link networks, the Madaline (Multiple Adalines) networks, the back-propagation networks, the reduced coulomb energy (RCE) networks, the unsupervised learning and the competitive learning and vector quantization. An example of application in high energy physics is given with the trigger systems and track recognition system (track parametrization, event selection and particle identification) developed for the CPLEAR experiment detectors from the LEAR at CERN. (J.S.). 56 refs., 20 figs., 1 tab., 1 appendix
Wang, Cong; Hill, David J
2006-01-01
One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an appropriately designed adaptive neural controller is capable of learning closed-loop system dynamics during tracking control to a periodic reference orbit. Among various neural network (NN) architectures, the localized radial basis function (RBF) network is employed. A property of persistence of excitation (PE) for RBF networks is established, and a partial PE condition of closed-loop signals, i.e., the PE condition of a regression subvector constructed out of the RBFs along a periodic state trajectory, is proven to be satisfied. Accurate NN approximation for closed-loop system dynamics is achieved in a local region along the periodic state trajectory, and a learning ability is implemented during a closed-loop feedback control process. Second, based on the deterministic learning mechanism, a neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve closed-loop stability and improved control performance. The significance of this paper is that the presented deterministic learning mechanism and the neural learning control scheme provide elementary components toward the development of a biologically-plausible learning and control methodology. Simulation studies are included to demonstrate the effectiveness of the approach.
National Research Council Canada - National Science Library
Omidvar, Omid; Elliott, David L
1997-01-01
... is reprinted with permission from A. Barto, "Reinforcement Learning," Handbook of Brain Theory and Neural Networks, M.A. Arbib, ed.. The MIT Press, Cambridge, MA, pp. 804-809, 1995. Chapter 4, Figures 4-5 and 7-9 and Tables 2-5, are reprinted with permission, from S. Cho, "Map Formation in Proprioceptive Cortex," International Jour...
DEFF Research Database (Denmark)
Vuust, Peter; Gebauer, Line K; Witek, Maria A G
2014-01-01
. According to this theory, perception and learning is manifested through the brain’s Bayesian minimization of the error between the input to the brain and the brain’s prior expectations. Fourth, empirical studies of neural and behavioral effects of syncopation, polyrhythm and groove will be reported, and we...
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.
The Lorentz-Dirac equation in light of quantum theory
International Nuclear Information System (INIS)
Nikishov, A.I.
1996-01-01
To high accuracy, an electron in ultrarelativistic motion 'sees' an external field in its rest frame as a crossed field (E=H, E·H=0). In this case, quantum expressions allow the introduction of a local intensity of the radiation, which determines the radiative term of the force of radiative reaction. For γ=(1-v2)-1/2>> 1 this term is much larger than the mass term, i.e., the term with xd3do. Under these conditions, the reduced Lorentz-Dirac equation, which is obtained from the full Lorentz-Dirac equation by eliminating the terms xd3do and xe on the right side using the equation of motion without taking into account the force of radiative reaction, is equivalent to good accuracy to the original Lorentz-Dirac equation. Exact solutions to the reduced Lorentz-Dirac equation are obtained for a constant field and the field of a plane wave. For γ∼1 a local expression for the radiative term cannot be obtained quantitatively from the quantum expressions. In this case the mass (Lorentz-Dirac) terms in the original and reduced Lorentz-Dirac equations are not small compared to the radiative term. The predictions of these equations, which depend appreciably on the mass terms, are therefore less reliable
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
2013-01-01
Background This study aims to improve accuracy of Bioelectrical Impedance Analysis (BIA) prediction equations for estimating fat free mass (FFM) of the elderly by using non-linear Back Propagation Artificial Neural Network (BP-ANN) model and to compare the predictive accuracy with the linear regression model by using energy dual X-ray absorptiometry (DXA) as reference method. Methods A total of 88 Taiwanese elderly adults were recruited in this study as subjects. Linear regression equations and BP-ANN prediction equation were developed using impedances and other anthropometrics for predicting the reference FFM measured by DXA (FFMDXA) in 36 male and 26 female Taiwanese elderly adults. The FFM estimated by BIA prediction equations using traditional linear regression model (FFMLR) and BP-ANN model (FFMANN) were compared to the FFMDXA. The measuring results of an additional 26 elderly adults were used to validate than accuracy of the predictive models. Results The results showed the significant predictors were impedance, gender, age, height and weight in developed FFMLR linear model (LR) for predicting FFM (coefficient of determination, r2 = 0.940; standard error of estimate (SEE) = 2.729 kg; root mean square error (RMSE) = 2.571kg, P < 0.001). The above predictors were set as the variables of the input layer by using five neurons in the BP-ANN model (r2 = 0.987 with a SD = 1.192 kg and relatively lower RMSE = 1.183 kg), which had greater (improved) accuracy for estimating FFM when compared with linear model. The results showed a better agreement existed between FFMANN and FFMDXA than that between FFMLR and FFMDXA. Conclusion When compared the performance of developed prediction equations for estimating reference FFMDXA, the linear model has lower r2 with a larger SD in predictive results than that of BP-ANN model, which indicated ANN model is more suitable for estimating FFM. PMID:23388042
Neural-fuzzy control of adept one SCARA
International Nuclear Information System (INIS)
Er, M.J.; Toh, B.H.; Toh, B.Y.
1998-01-01
This paper presents an Intelligent Control Strategy for the Adept One SCARA (Selective Compliance Assembly Robot Arm). It covers the design and simulation study of a Neural-Fuzzy Controller (NFC) for the SCARA with a view of tracking a predetermined trajectory of motion in the joint space. The SCARA was simulated as a three-axis manipulator with the dynamics of the tool (fourth link) neglected and the mass of the load incorporated into the mass of the third link. The overall performance of the control system under different conditions, namely variation in playload, variations in coefficients of static, dynamic and viscous friction and different trajectories were studied and comparison made with an existing Neural Network Controller and two Computed Torque Controllers. The NFC was shown to be robust and is able to overcome the drawback of the existing Neural Network Controller
Auxiliary equation method for solving nonlinear partial differential equations
International Nuclear Information System (INIS)
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Maximum solid concentrations of coal water slurries predicted by neural network models
Energy Technology Data Exchange (ETDEWEB)
Cheng, Jun; Li, Yanchang; Zhou, Junhu; Liu, Jianzhong; Cen, Kefa
2010-12-15
The nonlinear back-propagation (BP) neural network models were developed to predict the maximum solid concentration of coal water slurry (CWS) which is a substitute for oil fuel, based on physicochemical properties of 37 typical Chinese coals. The Levenberg-Marquardt algorithm was used to train five BP neural network models with different input factors. The data pretreatment method, learning rate and hidden neuron number were optimized by training models. It is found that the Hardgrove grindability index (HGI), moisture and coalification degree of parent coal are 3 indispensable factors for the prediction of CWS maximum solid concentration. Each BP neural network model gives a more accurate prediction result than the traditional polynomial regression equation. The BP neural network model with 3 input factors of HGI, moisture and oxygen/carbon ratio gives the smallest mean absolute error of 0.40%, which is much lower than that of 1.15% given by the traditional polynomial regression equation. (author)
The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view
Gallouët, Thomas; Vialard, François-Xavier
2018-04-01
The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.
Efficient Neural Network Modeling for Flight and Space Dynamics Simulation
Directory of Open Access Journals (Sweden)
Ayman Hamdy Kassem
2011-01-01
Full Text Available This paper represents an efficient technique for neural network modeling of flight and space dynamics simulation. The technique will free the neural network designer from guessing the size and structure for the required neural network model and will help to minimize the number of neurons. For linear flight/space dynamics systems, the technique can find the network weights and biases directly by solving a system of linear equations without the need for training. Nonlinear flight dynamic systems can be easily modeled by training its linearized models keeping the same network structure. The training is fast, as it uses the linear system knowledge to speed up the training process. The technique is tested on different flight/space dynamic models and showed promising results.
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Bioprinting for Neural Tissue Engineering.
Knowlton, Stephanie; Anand, Shivesh; Shah, Twisha; Tasoglu, Savas
2018-01-01
Bioprinting is a method by which a cell-encapsulating bioink is patterned to create complex tissue architectures. Given the potential impact of this technology on neural research, we review the current state-of-the-art approaches for bioprinting neural tissues. While 2D neural cultures are ubiquitous for studying neural cells, 3D cultures can more accurately replicate the microenvironment of neural tissues. By bioprinting neuronal constructs, one can precisely control the microenvironment by specifically formulating the bioink for neural tissues, and by spatially patterning cell types and scaffold properties in three dimensions. We review a range of bioprinted neural tissue models and discuss how they can be used to observe how neurons behave, understand disease processes, develop new therapies and, ultimately, design replacement tissues. Copyright © 2017 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Broeckman, A. [Rijksuniversiteit Utrecht (Netherlands)
1978-12-15
In thermal ionization mass spectrometry the phenomenon of mass discrimination has led to the use of a correction factor for isotope ratio-measurements. The correction factor is defined as the measured ratio divided by the true or accepted value of this ratio. In fact this factor corrects for systematic errors of the whole procedure; however mass discrimination is often associated just with the mass spectrometer.
International Nuclear Information System (INIS)
Hammond, Richard T
2015-01-01
Some physical aspects of negative mass are examined. Several unusual properties, such as the ability of negative mass to penetrate any armor, are analysed. Other surprising effects include the bizarre system of negative mass chasing positive mass, naked singularities and the violation of cosmic censorship, wormholes, and quantum mechanical results as well. In addition, a brief look into the implications for strings is given. (paper)
dimensional Jaulent–Miodek equations
Indian Academy of Sciences (India)
(2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...
Equationally Noetherian property of Ershov algebras
Dvorzhetskiy, Yuriy
2014-01-01
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.
Appearance Matters: Neural Correlates of Food Choice and Packaging Aesthetics
Laan, van der L.N.; Ridder, de D.T.D.; Viergever, M.A.; Smeets, P.A.M.
2012-01-01
Neuro-imaging holds great potential for predicting choice behavior from brain responses. In this study we used both traditional mass-univariate and state-of-the-art multivariate pattern analysis to establish which brain regions respond to preferred packages and to what extent neural activation
Attygalle, Athula B; Pavlov, Julius
2017-08-01
The current IUPAC-recommended definition of the term "nominal mass," based on the most abundant naturally occurring stable isotope of an element, is flawed. We propose that Nominal mass should be defined as the sum of integer masses of protons and neutrons in any chemical species. In this way, all isotopes and isotopologues can be assigned a definitive identifier. Graphical Abstract ᅟ.
International Nuclear Information System (INIS)
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
International Nuclear Information System (INIS)
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Completely integrable operator evolutionary equations
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
International Nuclear Information System (INIS)
Kalinowski, M.W.; Szymanowski, L.
1982-03-01
A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)
On the Saha Ionization Equation
Indian Academy of Sciences (India)
Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...
Glueball masses in quantum chromodynamics
International Nuclear Information System (INIS)
Luo Xiangqian; Zhongshan Univ., Guangzhou, GD; Zhongshan Univ., Guangzhou; Chen Qizhou; Zhongshan Univ., Guangzhou, GD; Zhongshan Univ., Guangzhou; Guo Shuohong; Zhongshan Univ., Guangzhou, GD; Zhongshan Univ., Guangzhou; Fang Xiyan; Zhongshan Univ., Guangzhou, GD; Zhongshan Univ., Guangzhou; Liu Jinming; Zhongshan Univ., Guangzhou, GD; Zhongshan Univ., Guangzhou
1996-01-01
We review the recent glueball mass calculations using an efficient method for solving the Schroedinger equation order by order with a scheme preserving the continuum limit. The reliability of the method is further supported by new accurate results for (1+1)-dimensional σ models and (2+1)-dimensional non-abelian models. We present first and encouraging data for the glueball masses in 3+1 dimensional QCD. (orig.)
Neural multigrid for gauge theories and other disordered systems
International Nuclear Information System (INIS)
Baeker, M.; Kalkreuter, T.; Mack, G.; Speh, M.
1992-09-01
We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a 'neural computations' point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates. (orig.)
The Bethe-Salpeter equation with fermions
International Nuclear Information System (INIS)
Efimov, G.V.
2007-01-01
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K 2 = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K 0 + K I . The operator K 0 with Tr K 0 2 ∞ is of the 'fall at the center' potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K I with Tr K I 2 2 c 2 and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1 + (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schroedinger picture is made. (author)