Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

Influence of distributed delays on the dynamics of a generalized immune system cancerous cells interactions model

NASA Astrophysics Data System (ADS)

Piotrowska, M. J.; Bodnar, M.

2018-01-01

We present a generalisation of the mathematical models describing the interactions between the immune system and tumour cells which takes into account distributed time delays. For the analytical study we do not assume any particular form of the stimulus function describing the immune system reaction to presence of tumour cells but we only postulate its general properties. We analyse basic mathematical properties of the considered model such as existence and uniqueness of the solutions. Next, we discuss the existence of the stationary solutions and analytically investigate their stability depending on the forms of considered probability densities that is: Erlang, triangular and uniform probability densities separated or not from zero. Particular instability results are obtained for a general type of probability densities. Our results are compared with those for the model with discrete delays know from the literature. In addition, for each considered type of probability density, the model is fitted to the experimental data for the mice B-cell lymphoma showing mean square errors at the same comparable level. For estimated sets of parameters we discuss possibility of stabilisation of the tumour dormant steady state. Instability of this steady state results in uncontrolled tumour growth. In order to perform numerical simulation, following the idea of linear chain trick, we derive numerical procedures that allow us to solve systems with considered probability densities using standard algorithm for ordinary differential equations or differential equations with discrete delays.

Robust state estimation for uncertain fuzzy bidirectional associative memory networks with time-varying delays

NASA Astrophysics Data System (ADS)

Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Arunkumar, A.

2013-09-01

This paper addresses the issue of robust state estimation for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying delays and parameter uncertainties. By constructing the Lyapunov-Krasovskii functional, which contains the triple-integral term and using the free-weighting matrix technique, a set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to estimate the neuron states through available output measurements such that the dynamics of the estimation error system is robustly asymptotically stable. In particular, we consider a generalized activation function in which the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. More precisely, the design of the state estimator for such BAM neural networks can be obtained by solving some LMIs, which are dependent on the size of the time derivative of the time-varying delays. Finally, a numerical example with simulation result is given to illustrate the obtained theoretical results.

Market-based control strategy for long-span structures considering the multi-time delay issue

NASA Astrophysics Data System (ADS)

Li, Hongnan; Song, Jianzhu; Li, Gang

2017-01-01

To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2 N precise algorithm was selected to solve the multi-time-delay issue for long-span structures based on the market-based control (MBC) method. The concept of interval mixed energy was introduced from computational structural mechanics and optimal control research areas, and it translates the design of the MBC multi-time-delay controller into a solution for the segment matrix. This approach transforms the serial algorithm in time to parallel computing in space, greatly improving the solving efficiency and numerical stability. The designed controller is able to consider the issue of time delay with a linear controlling force combination and is especially effective for large time-delay conditions. A numerical example of a long-span structure was selected to demonstrate the effectiveness of the presented controller, and the time delay was found to have a significant impact on the results.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

PubMed

Murase, Kenya

2015-01-01

In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

PubMed

Murase, Kenya

2014-01-01

Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

Modeling nuclear processes by Simulink

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

Rashid, Nahrul Khair Alang Md, E-mail: nahrul@iium.edu.my

2015-04-29

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox softwaremore » that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples.« less

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

[Delayed reactions of active avoidance in white rats under conditions of an alternative choice].

PubMed

Ioseliani, T K; Sikharulidze, N I; Kadagishvili, A Ia; Mitashvili, E G

1995-01-01

It was shown that if the rats had been learned and then tested using conventional pain punishment of erroneous choice they were able to solve the problem of alternative choice only in the period of immediate action of conditioned stimuli. If the pain punishment for erroneously chosen compartment had not been applied in animal learning and testing, rats successfully solved the problem of alternative choice even after 5-second delay. Introduction of pain punishment led to the frustration of earlier elaborated delayed avoidance reactions. Analysis of the obtained results allows us to argue that the apparent incapability of white rats for solving the problems of delayed avoidance is caused by simultaneous action of two different mechanisms, i.e., those of the active and passive avoidance rather than short-term memory deficit.

Language, Arithmetic Word Problems, and Deaf Students: Linguistic Strategies Used To Solve Tasks.

ERIC Educational Resources Information Center

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-01-01

Examines the performance of deaf and hearing-impaired students in Queensland, Australia when solving arithmetic word problems. Subjects' solutions of word problems confirmed trends for learning students but their performance was delayed in comparison. Confirms other studies in which deaf and hearing-impaired students are delayed in their language…

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Parallel Acquisition of Awareness and Differential Delay Eyeblink Conditioning

ERIC Educational Resources Information Center

Weidemann, Gabrielle; Antees, Cassandra

2012-01-01

There is considerable debate about whether differential delay eyeblink conditioning can be acquired without awareness of the stimulus contingencies. Previous investigations of the relationship between differential-delay eyeblink conditioning and awareness of the stimulus contingencies have assessed awareness after the conditioning session was…

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-08-01

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.

Differential correction capability of the GTDS using TDRSS data

NASA Technical Reports Server (NTRS)

Liu, S. Y.; Soskey, D. G.; Jacintho, J.

1980-01-01

A differential correction (DC) capability was implemented in the Goddard Trajectory Determination System (GTDS) to process satellite tracking data acquired via the Tracking and Data Relay Satellite System (TRDRSS). Configuration of the TDRSS is reviewed, observation modeling is presented, and major features of the capability are discussed. The following types of TDRSS data can be processed by GTDS: two way relay range and Doppler measurements, hybrid relay range and Doppler measurements, one way relay Doppler measurements, and differenced one way relay Doppler measurements. These data may be combined with conventional ground based direct tracking data. By using Bayesian weighted least squares techniques, the software allows the simultaneous determination of the trajectories of up to four different satellites - one user satellite and three relay satellites. In addition to satellite trajectories, the following parameters can be optionally solved: for drag coefficient, reflectivity of a satellite for solar radiation pressure, transponder delay, station position, and biases.

Analysis of stability for stochastic delay integro-differential equations.

PubMed

Zhang, Yu; Li, Longsuo

2018-01-01

In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

24-Month-Olds Use Conceptual Similarity to Solve New Problems after a Delay

ERIC Educational Resources Information Center

Hayne, Harlene; Gross, Julien

2015-01-01

In this experiment, we used the deferred imitation paradigm to assess 24-month-olds' ability to use conceptual similarity to solve new problems after a delay. Infants in the experimental condition participated in four sessions that were each separated by 24 h. In Session 1, the experimenter modeled three target actions using one set of stimuli and…

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1988-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Estimation of time- and state-dependent delays and other parameters in functional differential equations

NASA Technical Reports Server (NTRS)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

PubMed

Banks, H Thomas; Robbins, Danielle; Sutton, Karyn L

2013-01-01

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

Distributed optimisation problem with communication delay and external disturbance

NASA Astrophysics Data System (ADS)

Tran, Ngoc-Tu; Xiao, Jiang-Wen; Wang, Yan-Wu; Yang, Wu

2017-12-01

This paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov-Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

Dynamic reduction with applications to mathematical biology and other areas.

PubMed

Sacker, Robert J; Von Bremen, Hubertus F

2007-10-01

In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping Τ of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping Τ is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions.

Emotion Discourse, Social Cognition, and Social Skills in Children with and without Developmental Delays

PubMed Central

Fenning, RM; Baker, BL; Juvonen, J

2009-01-01

This study examined parent-child emotion discourse, children’s independent social information processing, and social skills outcomes in 146 families of 8-year-olds with and without developmental delays. Children’s emergent social-cognitive understanding (internal state understanding, perspective taking, and causal reasoning/problem solving) was coded in the context of parent-child conversations about emotion, and children were interviewed separately to assess social problem solving. Mothers, fathers, and teachers reported on children’s social skills. The proposed strengths-based model partially accounted for social skills differences between typically developing children and children with delays. A multigroup analysis of the model linking emotion discourse to social skills through children’s prosocial problem solving suggested that processes operated similarly across the two groups. Implications for ecologically focused prevention and intervention are discussed. PMID:21410465

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Intuitive Tip of the Tongue Judgments Predict Subsequent Problem Solving One Day Later

ERIC Educational Resources Information Center

Collier, Azurii K.; Beeman, Mark

2012-01-01

Often when failing to solve problems, individuals report some idea of the solution, but cannot explicitly access the idea. We investigated whether such intuition would relate to improvements in solving and to the manner in which a problem was solved after a 24- hour delay. On Day 1, participants attempted to solve Compound Remote Associate…

Factors Affecting Differential Equation Problem Solving Ability of Students at Pre-University Level: A Conceptual Model

ERIC Educational Resources Information Center

Aisha, Bibi; Zamri, Sharifa NorulAkmar Syed; Abdallah, Nabeel; Abedalaziz, Mohammad; Ahmad, Mushtaq; Satti, Umbreen

2017-01-01

In this study, different factors affecting students' differential equations (DEs) solving abilities were explored at pre university level. To explore main factors affecting students' differential equations problem solving ability, articles for a 19-year period, from 1996 to 2015, were critically reviewed and analyzed. It was revealed that…

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

NASA Astrophysics Data System (ADS)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

All-optical computation system for solving differential equations based on optical intensity differentiator.

PubMed

Tan, Sisi; Wu, Zhao; Lei, Lei; Hu, Shoujin; Dong, Jianji; Zhang, Xinliang

2013-03-25

We propose and experimentally demonstrate an all-optical differentiator-based computation system used for solving constant-coefficient first-order linear ordinary differential equations. It consists of an all-optical intensity differentiator and a wavelength converter, both based on a semiconductor optical amplifier (SOA) and an optical filter (OF). The equation is solved for various values of the constant-coefficient and two considered input waveforms, namely, super-Gaussian and Gaussian signals. An excellent agreement between the numerical simulation and the experimental results is obtained.

Emotion discourse, social cognition, and social skills in children with and without developmental delays.

PubMed

Fenning, Rachel M; Baker, Bruce L; Juvonen, Jaana

2011-01-01

This study examined parent-child emotion discourse, children's independent social information processing, and social skills outcomes in 146 families of 8-year-olds with and without developmental delays. Children's emergent social-cognitive understanding (internal state understanding, perspective taking, and causal reasoning and problem solving) was coded in the context of parent-child conversations about emotion, and children were interviewed separately to assess social problem solving. Mothers, fathers, and teachers reported on children's social skills. The proposed strengths-based model partially accounted for social skills differences between typically developing children and children with delays. A multigroup analysis of the model linking emotion discourse to social skills through children's prosocial problem solving suggested that processes operated similarly for the two groups. Implications for ecologically focused prevention and intervention are discussed. © 2011 The Authors. Child Development © 2011 Society for Research in Child Development, Inc.

Improving Teaching Quality and Problem Solving Ability through Contextual Teaching and Learning in Differential Equations: A Lesson Study Approach

ERIC Educational Resources Information Center

Khotimah, Rita Pramujiyanti; Masduki

2016-01-01

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Analysis of backward differentiation formula for nonlinear differential-algebraic equations with 2 delays.

PubMed

Sun, Leping

2016-01-01

This paper is concerned with the backward differential formula or BDF methods for a class of nonlinear 2-delay differential algebraic equations. We obtain two sufficient conditions under which the methods are stable and asymptotically stable. At last, examples show that our methods are true.

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

PubMed

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

2014-08-01

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

Razumikhin-Type Stability Criteria for Differential Equations with Delayed Impulses.

PubMed

Wang, Qing; Zhu, Quanxin

2013-01-01

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

Comparison principle for impulsive functional differential equations with infinite delays and applications

NASA Astrophysics Data System (ADS)

Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.

2018-04-01

We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.

Numerical solution of a conspicuous consumption model with constant control delay☆

PubMed Central

Huschto, Tony; Feichtinger, Gustav; Hartl, Richard F.; Kort, Peter M.; Sager, Sebastian; Seidl, Andrea

2011-01-01

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account. This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions. Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case. PMID:22267871

Solving constant-coefficient differential equations with dielectric metamaterials

NASA Astrophysics Data System (ADS)

Zhang, Weixuan; Qu, Che; Zhang, Xiangdong

2016-07-01

Recently, the concept of metamaterial analog computing has been proposed (Silva et al 2014 Science 343 160-3). Some mathematical operations such as spatial differentiation, integration, and convolution, have been performed by using designed metamaterial blocks. Motivated by this work, we propose a practical approach based on dielectric metamaterial to solve differential equations. The ordinary differential equation can be solved accurately by the correctly designed metamaterial system. The numerical simulations using well-established numerical routines have been performed to successfully verify all theoretical analyses.

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

NASA Astrophysics Data System (ADS)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

Mean, covariance, and effective dimension of stochastic distributed delay dynamics

NASA Astrophysics Data System (ADS)

René, Alexandre; Longtin, André

2017-11-01

Dynamical models are often required to incorporate both delays and noise. However, the inherently infinite-dimensional nature of delay equations makes formal solutions to stochastic delay differential equations (SDDEs) challenging. Here, we present an approach, similar in spirit to the analysis of functional differential equations, but based on finite-dimensional matrix operators. This results in a method for obtaining both transient and stationary solutions that is directly amenable to computation, and applicable to first order differential systems with either discrete or distributed delays. With fewer assumptions on the system's parameters than other current solution methods and no need to be near a bifurcation, we decompose the solution to a linear SDDE with arbitrary distributed delays into natural modes, in effect the eigenfunctions of the differential operator, and show that relatively few modes can suffice to approximate the probability density of solutions. Thus, we are led to conclude that noise makes these SDDEs effectively low dimensional, which opens the possibility of practical definitions of probability densities over their solution space.

Singular Hopf bifurcation in a differential equation with large state-dependent delay

PubMed Central

Kozyreff, G.; Erneux, T.

2014-01-01

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol’s equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays. PMID:24511255

Singular Hopf bifurcation in a differential equation with large state-dependent delay.

PubMed

Kozyreff, G; Erneux, T

2014-02-08

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

Numerical modelling of multimode fibre-optic communication lines

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

Sidelnikov, O S; Fedoruk, M P; Sygletos, S

The results of numerical modelling of nonlinear propagation of an optical signal in multimode fibres with a small differential group delay are presented. It is found that the dependence of the error vector magnitude (EVM) on the differential group delay can be reduced by increasing the number of ADC samples per symbol in the numerical implementation of the differential group delay compensation algorithm in the receiver. The possibility of using multimode fibres with a small differential group delay for data transmission in modern digital communication systems is demonstrated. It is shown that with increasing number of modes the strong couplingmore » regime provides a lower EVM level than the weak coupling one. (fibre-optic communication lines)« less

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-07-01

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

On the Number of Periodic Solutions of Delay Differential Equations

NASA Astrophysics Data System (ADS)

Han, Maoan; Xu, Bing; Tian, Huanhuan; Bai, Yuzhen

In this paper, we consider the existence and number of periodic solutions for a class of delay differential equations of the form ẋ(t) = bx(t ‑ 1) + 𝜀f(x(t),x(t ‑ 1),𝜀), based on the Kaplan-Yorke method. Especially, we consider a kind of delay differential equations with f as a polynomial having parameters and find the number of periodic solutions with period 4 4k+1 or 4 4k+3.

Numerical Bifurcation Analysis of Delayed Recycle Stream in a Continuously Stirred Tank Reactor

NASA Astrophysics Data System (ADS)

Gangadhar, Nalwala Rohitbabu; Balasubramanian, Periyasamy

2010-10-01

In this paper, we present the stability analysis of delay differential equations which arise as a result of transportation lag in the CSTR-mechanical separator recycle system. A first order irreversible elementary reaction is considered to model the system and is governed by the delay differential equations. The DDE-BIFTOOL software package is used to analyze the stability of the delay system. The present analysis reveals that the system exhibits delay independent stability for isothermal operation of the CSTR. In the absence of delay, the system is dynamically unstable for non-isothermal operation of the CSTR, and as a result of delay, the system exhibits delay dependent stability.

Symbolic Solution of Linear Differential Equations

NASA Technical Reports Server (NTRS)

Feinberg, R. B.; Grooms, R. G.

1981-01-01

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Testing after Worked Example Study Does Not Enhance Delayed Problem-Solving Performance Compared to Restudy

ERIC Educational Resources Information Center

van Gog, Tamara; Kester, Liesbeth; Dirkx, Kim; Hoogerheide, Vincent; Boerboom, Joris; Verkoeijen, Peter P. J. L.

2015-01-01

Four experiments investigated whether the testing effect also applies to the acquisition of problem-solving skills from worked examples. Experiment 1 (n?=?120) showed no beneficial effects of testing consisting of "isomorphic" problem solving or "example recall" on final test performance, which consisted of isomorphic problem…

"Wait for It . . ." Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

ERIC Educational Resources Information Center

Loehr, Abbey Marie; Fyfe, Emily R.; Rittle-Johnson, Bethany

2014-01-01

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Differentiation of original and regenerated skeletal muscle fibres in mdx dystrophic muscles.

PubMed

Earnshaw, John C; Kyprianou, Phillip; Krishan, Kewal; Dhoot, Gurtej K

2002-07-01

The differentiation of both original muscle fibres and the regenerated muscle fibres following necrosis in mdx muscles was investigated using immunoblotting and immunocytochemical procedures. Before the onset of necrosis, postnatal skeletal muscles in mdx mouse differentiated well with only a slight delay in differentiation indicated by the level of developmental isoforms of troponin T. Prior to the onset of apparent myopathic change, both fast and slow skeletal muscle fibre types in mdx leg muscles also differentiated well when investigated by analysis of specific myosin heavy chain expression pattern. While the original muscle fibres in mdx leg muscles developed well, the differentiation of regenerated myotubes into both slow and distinct fast muscle fibre types, however, was markedly delayed or inhibited as indicated by several clusters of homogeneously staining fibres even at 14 weeks of age. The number of slow myosin heavy chain-positive myotubes amongst the regenerated muscle clusters was quite small even in soleus. This study thus established that while muscle fibres initially develop normally with only a slight delay in the differentiation process, the differentiation of regenerated myotubes in mdx muscles is markedly compromised and consequently delayed.

Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term.

PubMed

Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra

2016-01-01

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.

The performance of differential VLBI delay during interplanetary cruise

NASA Technical Reports Server (NTRS)

Moultrie, B.; Wolff, P. J.; Taylor, T. H.

1984-01-01

Project Voyager radio metric data are used to evaluate the orbit determination abilities of several data strategies during spacecraft interplanetary cruise. Benchmark performance is established with an operational data strategy of conventional coherent doppler, coherent range, and explicitly differenced range data from two intercontinental baselines to ameliorate the low declination singularity of the doppler data. Employing a Voyager operations trajectory as a reference, the performance of the operational data strategy is compared to the performances of data strategies using differential VLBI delay data (spacecraft delay minus quasar delay) in combinations with the aforementioned conventional data types. The comparison of strategy performances indicates that high accuracy cruise orbit determination can be achieved with a data strategy employing differential VLBI delay data, where the quantity of coherent radio metric data has been greatly reduced.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Control system estimation and design for aerospace vehicles with time delay

NASA Technical Reports Server (NTRS)

Allgaier, G. R.; Williams, T. L.

1972-01-01

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

Effect of differentiation of self on adolescent risk behavior: test of the theoretical model.

PubMed

Knauth, Donna G; Skowron, Elizabeth A; Escobar, Melicia

2006-01-01

Innovative theoretical models are needed to explain the occurrence of high-risk sexual behaviors, alcohol and other-drug (AOD) use, and academic engagement among ethnically diverse, inner-city adolescents. The aim of this study was to test the credibility of a theoretical model based on the Bowen family systems theory to explain adolescent risk behavior. Specifically tested was the relationship between the predictor variables of differentiation of self, chronic anxiety, and social problem solving and the dependent variables of high-risk sexual behaviors, AOD use, and academic engagement. An ex post facto cross-sectional design was used to test the usefulness of the theoretical model. Data were collected from 161 racially/ethnically diverse, inner-city high school students, 14 to 19 years of age. Participants completed self-report written questionnaires, including the Differentiation of Self Inventory, State-Trait Anxiety Inventory, Social Problem Solving for Adolescents, Drug Involvement Scale for Adolescents, and the Sexual Behavior Questionnaire. Consistent with the model, higher levels of differentiation of self related to lower levels of chronic anxiety (p < .001) and higher levels of social problem solving (p < .01). Higher chronic anxiety was related to lower social problem solving (p < .001). A test of mediation showed that chronic anxiety mediates the relationship between differentiation of self and social problem solving (p < .001), indicating that differentiation influences social problem solving through chronic anxiety. Higher levels of social problem solving were related to less drug use (p < .05), less high-risk sexual behaviors (p < .01), and an increase in academic engagement (p < .01). Findings support the theoretical model's credibility and provide evidence that differentiation of self is an important cognitive factor that enables adolescents to manage chronic anxiety and motivates them to use effective problem solving, resulting in less involvement in health-comprising behaviors and increased academic engagement.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Robust stability of bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Park, Ju H.

2006-01-01

Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks

NASA Astrophysics Data System (ADS)

Zevenbergen, Robyn; Hyde, Merv; Power, Des

2001-12-01

There has been limited examination of the intersection between language and arithmetic in the performance of deaf students, although some previous research has shown that deaf and hearing-impaired1 students are delayed in both their language acquisition and arithmetic performance. This paper examines the performance of deaf and hearing-impaired students in South-East Queensland, Australia, in solving arithmetic word problems. It was found that the subjects' solutions of word problems confirmed trends for hearing students, but that their performance was delayed in comparison. The results confirm other studies where deaf and hearing-impaired students are delayed in their language acquisition and this impacts on their capacity to successfully undertake the resolution of word problems.

A Distributed Algorithm for Economic Dispatch Over Time-Varying Directed Networks With Delays

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

Yang, Tao; Lu, Jie; Wu, Di

In power system operation, economic dispatch problem (EDP) is designed to minimize the total generation cost while meeting the demand and satisfying generator capacity limits. This paper proposes an algorithm based on the gradient-push method to solve the EDP in a distributed manner over communication networks potentially with time-varying topologies and communication delays. It has been shown that the proposed method is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, the proposed algorithm is also able to handle arbitrarily large but bounded time delays on communication links. Numerical simulations are usedmore » to illustrate and validate the proposed algorithm.« less

Solving Nonlinear Differential Equations in the Engineering Curriculum

ERIC Educational Resources Information Center

Auslander, David M.

1977-01-01

Described is the Dynamic System Simulation Language (SIM) mini-computer system utilized at the University of California, Los Angeles. It is used by engineering students for solving nonlinear differential equations. (SL)

A necessary and sufficient condition for well-posedness of initial value problems of retarded functional differential equations

NASA Astrophysics Data System (ADS)

Nishiguchi, Junya

2017-09-01

We introduce the retarded functional differential equations (RFDEs) with general delay structure to treat various delay differential equations (DDEs) in a unified way and to clarify the delay structure in those dynamics. We are interested in the question as to which space of histories is suitable for the dynamics of each DDE, and investigate the well-posedness of the initial value problems (IVPs) of the RFDEs. A main theorem is that the IVP is well-posed for any ;admissible; history functional if and only if the semigroup determined by the trivial RFDE x ˙ = 0 is continuous. We clarify the meaning of the Hale-Kato axiom (Hale & Kato [12]) by applying this result to RFDEs with infinite delay. We also apply the result to DDEs with unbounded time- and state-dependent delays.

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation.

PubMed

Ingalls, Brian; Mincheva, Maya; Roussel, Marc R

2017-07-01

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.

Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.

ERIC Educational Resources Information Center

Goldston, J. W.

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

Programmable Differential Delay Circuit With Fine Delay Adjustment

DOEpatents

DeRyckere, John F.; Jenkins, Philip Nord; Cornett, Frank Nolan

2002-07-09

Circuitry that provides additional delay to early arriving signals such that all data signals arrive at a receiving latch with same path delay. The delay of a forwarded clock reference is also controlled such that the capturing clock edge will be optimally positioned near quadrature (depending on latch setup/hold requirements). The circuitry continuously adapts to data and clock path delay changes and digital filtering of phase measurements reduce errors brought on by jittering data edges. The circuitry utilizes only the minimum amount of delay necessary to achieve objective thereby limiting any unintended jitter. Particularly, this programmable differential delay circuit with fine delay adjustment is designed to allow the skew between ASICS to be minimized. This includes skew between data bits, between data bits and clocks as well as minimizing the overall skew in a channel between ASICS.

The Effects of Differentiating Instruction by Learning Styles on Problem Solving in Cooperative Groups

ERIC Educational Resources Information Center

Westbrook, Amy F.

2011-01-01

It can be difficult to find adequate strategies when teaching problem solving in a standard based mathematics classroom. The purpose of this study was to improve students' problem solving skills and attitudes through differentiated instruction when working on lengthy performance tasks in cooperative groups. This action research studied for 15 days…

Speed Measurement and Motion Analysis of Chang'E-3 Rover Based on Differential Phase Delay

NASA Astrophysics Data System (ADS)

Pan, C.; Liu, Q. H.; Zheng, X.; He, Q. B.; Wu, Y. J.

2015-07-01

On 2013 December 14, the Chang'E-3 made a successful soft landing on the lunar surface, and then carried out the tasks of separating the lander and the rover, and taking the photos of each other. With the same beam VLBI (Very long baseline interferometry) technique to observe the signals transmitted by the lander and the rover simultaneously, the differential phase delay between them is calculated, which can reflect a minor change of the rover's position on a scale of a few centimeters. Based on the high sensitivity of differential phase delay, the rover's speeds during 5 movements are obtained with an average of 0.056 m/s. The relationship between the rover's shake in moving process, and lunar terrain is analyzed by using the spectrum of the residual of the differential phase delay after the first-order polynomial fitting.

Speed Measurement and Motion Analysis of Chang'E-3 Rover Based on Differential Phase Delay

NASA Astrophysics Data System (ADS)

Chao, Pan; Qing-hui, Liu; Xin, Zheng; Qing-bao, He; Ya-jun, Wu

2016-04-01

On 14th December 2013, the Chang'E-3 made a successful soft landing on the lunar surface, and then carried out the tasks of separating the lander and the rover, and taking pictures of each other. With the same beam VLBI (Very Long Baseline Interferometry) technique to observe the signals transmitted by the lander and the rover simultaneously, the differential phase delay between them is calculated, which can reflect the minor changes of the rover's position on a scale of a few centimeters. Based on the high sensitivity of differential phase delay, the rover's speeds during 5 movements are obtained with an average of 0.056 m/s. The relationship between the rover's shake in the moving process and the lunar terrain is analyzed by using the spectrum of the residual of the differential phase delay after the first-order polynomial fitting.

Optimal Integration of Departure and Arrivals in Terminal Airspace

NASA Technical Reports Server (NTRS)

Xue, Min; Zelinski, Shannon Jean

2012-01-01

Coordination of operations with spatially and temporally shared resources such as route segments, fixes, and runways improves the efficiency of terminal airspace management. Problems in this category include scheduling and routing, thus they are normally difficult to solve compared with pure scheduling problems. In order to reduce the computational time, a fast time algorithm formulation using a non-dominated sorting genetic algorithm (NSGA) was introduced in this work and applied to a test case based on existing literature. The experiment showed that new method can solve the whole problem in fast time instead of solving sub-problems sequentially with a window technique. The results showed a 60% or 406 second delay reduction was achieved by sharing departure fixes (more details on the comparison with MILP results will be presented in the final paper). Furthermore, the NSGA algorithm was applied to a problem in LAX terminal airspace, where interactions between 28% of LAX arrivals and 10% of LAX departures are resolved by spatial segregation, which may introduce unnecessary delays. In this work, spatial segregation, temporal segregation, and hybrid segregation were formulated using the new algorithm. Results showed that spatial and temporal segregation approaches achieved similar delay. Hybrid segregation introduced much less delay than the other two approaches. For a total of 9 interacting departures and arrivals, delay reduction varied from 4 minutes to 6.4 minutes corresponding flight time uncertainty from 0 to 60 seconds. Considering the amount of flights that could be affected, total annual savings with hybrid segregation would be significant.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

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

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Estimation of delays and other parameters in nonlinear functional differential equations

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lamm, P. K. D.

1983-01-01

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Solving SAT Problem Based on Hybrid Differential Evolution Algorithm

NASA Astrophysics Data System (ADS)

Liu, Kunqi; Zhang, Jingmin; Liu, Gang; Kang, Lishan

Satisfiability (SAT) problem is an NP-complete problem. Based on the analysis about it, SAT problem is translated equally into an optimization problem on the minimum of objective function. A hybrid differential evolution algorithm is proposed to solve the Satisfiability problem. It makes full use of strong local search capacity of hill-climbing algorithm and strong global search capability of differential evolution algorithm, which makes up their disadvantages, improves the efficiency of algorithm and avoids the stagnation phenomenon. The experiment results show that the hybrid algorithm is efficient in solving SAT problem.

Planning and problem-solving training for patients with schizophrenia: a randomized controlled trial

PubMed Central

2011-01-01

Background The purpose of this study was to assess whether planning and problem-solving training is more effective in improving functional capacity in patients with schizophrenia than a training program addressing basic cognitive functions. Methods Eighty-nine patients with schizophrenia were randomly assigned either to a computer assisted training of planning and problem-solving or a training of basic cognition. Outcome variables included planning and problem-solving ability as well as functional capacity, which represents a proxy measure for functional outcome. Results Planning and problem-solving training improved one measure of planning and problem-solving more strongly than basic cognition training, while two other measures of planning did not show a differential effect. Participants in both groups improved over time in functional capacity. There was no differential effect of the interventions on functional capacity. Conclusion A differential effect of targeting specific cognitive functions on functional capacity could not be established. Small differences on cognitive outcome variables indicate a potential for differential effects. This will have to be addressed in further research including longer treatment programs and other settings. Trial registration ClinicalTrials.gov NCT00507988 PMID:21527028

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

NASA Astrophysics Data System (ADS)

Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

2017-01-01

The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

Local bifurcations in differential equations with state-dependent delay.

PubMed

Sieber, Jan

2017-11-01

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.

Continuous angle steering of an optically- controlled phased array antenna based on differential true time delay constituted by micro-optical components.

PubMed

Wang, Jian; Hou, Peipei; Cai, Haiwen; Sun, Jianfeng; Wang, Shunan; Wang, Lijuan; Yang, Fei

2015-04-06

We propose an optically controlled phased array antenna (PAA) based on differential true time delay constructed optical beamforming network (OBFN). Differential true time delay is realized by stack integrated micro-optical components. Optically-controlled angle steering of radio frequency (RF) beams are realized and demonstrated by this configuration. Experimental results demonstrate that OBFN based PAA can accomplish RF-independent broadband beam steering without beam squint effect and can achieve continuous angle steering. In addition, multi-beams for different steering angles are acquired synchronously.

Delay in Apoptosome Formation Attenuates Apoptosis in Mouse Embryonic Stem Cell Differentiation

PubMed Central

Akbari-Birgani, Shiva; Hosseinkhani, Saman; Mollamohamadi, Sepideh; Baharvand, Hossein

2014-01-01

Differentiation is an inseparable process of development in multicellular organisms. Mouse embryonic stem cells (mESCs) represent a valuable research tool to conduct in vitro studies of cell differentiation. Apoptosis as a well known cell death mechanism shows some common features with cell differentiation, which has caused a number of ambiguities in the field. The research question here is how cells could differentiate these two processes from each other. We have investigated the role of the mitochondrial apoptotic pathway and cell energy level during differentiation of mESCs into the cardiomyocytes and their apoptosis. p53 expression, cytochrome c release, apoptosome formation, and caspase-3/7 activation are observed upon induction of both apoptosis and differentiation. However, remarkable differences are detected in time of cytochrome c appearance, apoptosome formation, and caspase activity upon induction of both processes. In apoptosis, apoptosome formation and caspase activity were observed rapidly following the cytochrome c release. Unlike apoptosis, the release of cytochrome c upon differentiation took more time, and the maximum caspase activity was also postponed for 24 h. This delay suggests that there is a regulatory mechanism during differentiation of mESCs into cardiomyocytes. The highest ATP content of cells was observed immediately after cytochrome c release 6 h after apoptosis induction and then decreased, but it was gradually increased up to 48 h after differentiation. These observations suggest that a delay in the release of cytochrome c or delay in ATP increase attenuate apoptosome formation, and caspase activation thereby discriminates apoptosis from differentiation in mESCs. PMID:24755221

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

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

Gupta, Chinmaya; López, José Manuel; Azencott, Robert

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemicalmore » Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.« less

Comparison of two integration methods for dynamic causal modeling of electrophysiological data.

PubMed

Lemaréchal, Jean-Didier; George, Nathalie; David, Olivier

2018-06-01

Dynamic causal modeling (DCM) is a methodological approach to study effective connectivity among brain regions. Based on a set of observations and a biophysical model of brain interactions, DCM uses a Bayesian framework to estimate the posterior distribution of the free parameters of the model (e.g. modulation of connectivity) and infer architectural properties of the most plausible model (i.e. model selection). When modeling electrophysiological event-related responses, the estimation of the model relies on the integration of the system of delay differential equations (DDEs) that describe the dynamics of the system. In this technical note, we compared two numerical schemes for the integration of DDEs. The first, and standard, scheme approximates the DDEs (more precisely, the state of the system, with respect to conduction delays among brain regions) using ordinary differential equations (ODEs) and solves it with a fixed step size. The second scheme uses a dedicated DDEs solver with adaptive step sizes to control error, making it theoretically more accurate. To highlight the effects of the approximation used by the first integration scheme in regard to parameter estimation and Bayesian model selection, we performed simulations of local field potentials using first, a simple model comprising 2 regions and second, a more complex model comprising 6 regions. In these simulations, the second integration scheme served as the standard to which the first one was compared. Then, the performances of the two integration schemes were directly compared by fitting a public mismatch negativity EEG dataset with different models. The simulations revealed that the use of the standard DCM integration scheme was acceptable for Bayesian model selection but underestimated the connectivity parameters and did not allow an accurate estimation of conduction delays. Fitting to empirical data showed that the models systematically obtained an increased accuracy when using the second integration scheme. We conclude that inference on connectivity strength and delay based on DCM for EEG/MEG requires an accurate integration scheme. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Delay-Dependent Stability Criterion for Bidirectional Associative Memory Neural Networks with Interval Time-Varying Delays

NASA Astrophysics Data System (ADS)

Park, Ju H.; Kwon, O. M.

In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

Conceptual Comparison of Population Based Metaheuristics for Engineering Problems

PubMed Central

Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes. PMID:25874265

Conceptual comparison of population based metaheuristics for engineering problems.

PubMed

Adekanmbi, Oluwole; Green, Paul

2015-01-01

Metaheuristic algorithms are well-known optimization tools which have been employed for solving a wide range of optimization problems. Several extensions of differential evolution have been adopted in solving constrained and nonconstrained multiobjective optimization problems, but in this study, the third version of generalized differential evolution (GDE) is used for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy in solving practical applications. The performance of the metaheuristic is investigated through engineering design optimization problems and the results are reported. The comparison of the numerical results with those of other metaheuristic techniques demonstrates the promising performance of the algorithm as a robust optimization tool for practical purposes.

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

NASA Astrophysics Data System (ADS)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Adaptive mapping functions to the azimuthal anisotropy of the neutral atmosphere

NASA Astrophysics Data System (ADS)

Gegout, P.; Biancale, R.; Soudarin, L.

2011-10-01

The anisotropy of propagation of radio waves used by global navigation satellite systems is investigated using high-resolution observational data assimilations produced by the European Centre for Medium-range Weather Forecast. The geometry and the refractivity of the neutral atmosphere are built introducing accurate geodetic heights and continuous formulations of the refractivity and its gradient. Hence the realistic ellipsoidal shape of the refractivity field above the topography is properly represented. Atmospheric delays are obtained by ray-tracing through the refractivity field, integrating the eikonal differential system. Ray-traced delays reveal the anisotropy of the atmosphere. With the aim to preserve the classical mapping function strategy, mapping functions can evolve to adapt to high-frequency atmospheric fluctuations and to account for the anisotropy of propagation by fitting at each site and time the zenith delays and the mapping functions coefficients. Adaptive mapping functions (AMF) are designed with coefficients of the continued fraction form which depend on azimuth. The basic idea is to expand the azimuthal dependency of the coefficients in Fourier series introducing a multi-scale azimuthal decomposition which slightly changes the elevation functions with the azimuth. AMF are used to approximate thousands of atmospheric ray-traced delays using a few tens of coefficients. Generic recursive definitions of the AMF and their partial derivatives lead to observe that the truncation of the continued fraction form at the third term and the truncation of the azimuthal Fourier series at the fourth term are sufficient in usual meteorological conditions. Delays' and elevations' mapping functions allow to store and to retrieve the ray-tracing results to solve the parallax problem at the observation level. AMF are suitable to fit the time-variable isotropic and anisotropic parts of the ray-traced delays at each site at each time step and to provide GPS range corrections at the measurement level with millimeter accuracy at low elevation. AMF to the azimuthal anisotropy of the neutral atmosphere are designed to adapt to complex weather conditions by adaptively changing their truncations.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Thermally induced delay and reversal of liquid film dewetting on chemically patterned surfaces.

PubMed

Kalpathy, Sreeram K; Francis, Lorraine F; Kumar, Satish

2013-10-15

A thin liquid film resting on a solid substrate that is heated or cooled from below experiences surface tension gradients, which lead to Marangoni flows. We explore the behavior of such a film on a chemically patterned substrate which drives film dewetting in order to determine how surface patterning and applied temperature gradients can be designed to influence the behavior of thin-film coatings. A nonlinear partial differential equation for the film height based on lubrication theory is solved numerically for a broad range of problem parameters. Uniform cooling of the substrate is found to significantly delay dewetting that is driven by wettability gradients. Uniform heating speeds up dewetting but can destroy the near-perfect templating imposed by the surface patterning. However, localized heating and cooling together can accelerate dewetting while maintaining templating quality. Localized heating and cooling can also be used to drive liquid onto areas that it would dewet from in the absence of heating. Overall, these results indicate that applied temperature gradients can significantly influence dewetting driven by surface patterning, and suggest strategies for the creation of spatially patterned thin-film coatings and flow control in microfluidic devices. Copyright © 2013 Elsevier Inc. All rights reserved.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Direct SQP-methods for solving optimal control problems with delays

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

Goellmann, L.; Bueskens, C.; Maurer, H.

The maximum principle for optimal control problems with delays leads to a boundary value problem (BVP) which is retarded in the state and advanced in the costate function. Based on shooting techniques, solution methods for this type of BVP have been proposed. In recent years, direct optimization methods have been favored for solving control problems without delays. Direct methods approximate the control and the state over a fixed mesh and solve the resulting NLP-problem with SQP-methods. These methods dispense with the costate function and have shown to be robust and efficient. In this paper, we propose a direct SQP-method formore » retarded control problems. In contrast to conventional direct methods, only the control variable is approximated by e.g. spline-functions. The state is computed via a high order Runge-Kutta type algorithm and does not enter explicitly the NLP-problem through an equation. This approach reduces the number of optimization variables considerably and is implementable even on a PC. Our method is illustrated by the numerical solution of retarded control problems with constraints. In particular, we consider the control of a continuous stirred tank reactor which has been solved by dynamic programming. This example illustrates the robustness and efficiency of the proposed method. Open questions concerning sufficient conditions and convergence of discretized NLP-problems are discussed.« less

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

Badhwar - O'Neill 2014 Galactic Cosmic Ray Flux Model Description

NASA Technical Reports Server (NTRS)

O'Neill, P. M.; Golge, S.; Slaba, T. C.

2014-01-01

The Badhwar-O'Neill (BON) Galactic Cosmic Ray (GCR) model is based on GCR measurements from particle detectors. The model has mainly been used by NASA to certify microelectronic systems and the analysis of radiation health risks to astronauts in space missions. The BON14 model numerically solves the Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration under the assumption of a spherically symmetric heliosphere. The model also incorporates an empirical time delay function to account for the lag of the solar activity to reach the boundary of the heliosphere. This technical paper describes the most recent improvements in parameter fits to the BON model (BON14). Using a comprehensive measurement database, it is shown that BON14 is significantly improved over the previous version, BON11.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

PubMed Central

Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

2013-01-01

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

Emotion Discourse, Social Cognition, and Social Skills in Children with and without Developmental Delays

ERIC Educational Resources Information Center

Fenning, Rachel M.; Baker, Bruce L.; Juvonen, Jaana

2011-01-01

This study examined parent-child emotion discourse, children's independent social information processing, and social skills outcomes in 146 families of 8-year-olds with and without developmental delays. Children's emergent social-cognitive understanding (internal state understanding, perspective taking, and causal reasoning and problem solving)…

7 CFR 1291.10 - Reporting and oversight requirements.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., identify and share the lessons learned to help expedite problem-solving. (6) Contact Person. List the... period to meet measurable outcomes for each project. (2) Problems and Delays. Note unexpected delays or... include the following: (1) Project Summary. An outline of the issue, problem, interest, or need for each...

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

Dynamics of a neutral delay equation for an insect population with long larval and short adult phases

NASA Astrophysics Data System (ADS)

Gourley, Stephen A.; Kuang, Yang

We present a global study on the stability of the equilibria in a nonlinear autonomous neutral delay differential population model formulated by Bocharov and Hadeler. This model may be suitable for describing the intriguing dynamics of an insect population with long larval and short adult phases such as the periodical cicada. We circumvent the usual difficulties associated with the study of the stability of a nonlinear neutral delay differential model by transforming it to an appropriate non-neutral nonautonomous delay differential equation with unbounded delay. In the case that no juveniles give birth, we establish the positivity and boundedness of solutions by ad hoc methods and global stability of the extinction and positive equilibria by the method of iteration. We also show that if the time adjusted instantaneous birth rate at the time of maturation is greater than 1, then the population will grow without bound, regardless of the population death process.

Delayed-enhanced cardiac MRI for differentiation of Fabry's disease from symmetric hypertrophic cardiomyopathy.

PubMed

De Cobelli, Francesco; Esposito, Antonio; Belloni, Elena; Pieroni, Maurizio; Perseghin, Gianluca; Chimenti, Cristina; Frustaci, Andrea; Del Maschio, Alessandro

2009-03-01

Fabry's disease may be difficult to differentiate from symmetric hypertrophic cardiomyopathy. Our aim was to compare the myocardial location and distribution patterns of delayed enhancement between patients with Fabry's disease who are affected by symmetric myocardial hypertrophy and patients with symmetric hypertrophic cardiomyopathy in order to identify a specific sign to best differentiate the two diseases. Patients with Fabry's disease-related hypertrophy showed left ventricular (LV) delayed enhancement with a typical and consistently found pattern characterized by the involvement of the inferolateral basal or mid basal segments and a mesocardial distribution that spared the subendocardium. This pattern seems to be specific to Fabry's disease; in fact, patients with symmetric hypertrophic cardiomyopathy had variable locations and distributions of delayed enhancement. These observations may contribute to identifying Fabry's disease as a specific cause of symmetric hypertrophy.

W-transform for exponential stability of second order delay differential equations without damping terms.

PubMed

Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid

2017-01-01

In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

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

Bi, Ping; Center for Partial Differential Equations, East China Normal University, 500 Dongchuan Rd., Shanghai 200241; Ruan, Shigui, E-mail: ruan@math.miami.edu

2014-06-15

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical valuesmore » and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.« less

Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

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

Moryakov, A. V., E-mail: sailor@orc.ru

2016-12-15

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

NASA Astrophysics Data System (ADS)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations

NASA Astrophysics Data System (ADS)

Rudmin, Joseph W.

2001-04-01

The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations Joseph W. Rudmin (Physics Dept, James Madison University) A new system of solving systems of differential equations will be presented, which has been developed by J. Edgar Parker and James Sochacki, of the James Madison University Mathematics Department. The method produces MacClaurin Series solutions to systems of differential equations, with the coefficients in either algebraic or numerical form. The method yields high-degree solutions: 20th degree is easily obtainable. It is conceptually simple, fast, and extremely general. It has been applied to over a hundred systems of differential equations, some of which were previously unsolved, and has yet to fail to solve any system for which the MacClaurin series converges. The method is non-recursive: each coefficient in the series is calculated just once, in closed form, and its accuracy is limited only by the digital accuracy of the computer. Although the original differential equations may include any mathematical functions, the computational method includes ONLY the operations of addition, subtraction, and multiplication. Furthermore, it is perfectly suited to parallel -processing computer languages. Those who learn this system will never use Runge-Kutta or predictor-corrector methods again. Examples will be presented, including the classical many-body problem.

Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay

NASA Astrophysics Data System (ADS)

Tang, Xianhua; Cao, Daomin; Zou, Xingfu

We consider a periodic Lotka-Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) x(t)=x(t)[r(t)-∑j=1na(t)x(t-τ(t))], i=1,2,…,n. We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright's 3/2 criteria for the autonomous delay logistic equation, and thereby, address the open problem proposed by both Kuang [Y. Kuang, Global stability in delayed nonautonomous Lotka-Volterra type systems without saturated equilibria, Differential Integral Equations 9 (1996) 557-567] and Teng [Z. Teng, Nonautonomous Lotka-Volterra systems with delays, J. Differential Equations 179 (2002) 538-561].

Bifurcation to large period oscillations in physical systems controlled by delay

NASA Astrophysics Data System (ADS)

Erneux, Thomas; Walther, Hans-Otto

2005-12-01

An unusual bifurcation to time-periodic oscillations of a class of delay differential equations is investigated. As we approach the bifurcation point, both the amplitude and the frequency of the oscillations go to zero. The class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations. By using asymptotic methods, we determine the bifurcation scaling laws for the amplitude and the period of the oscillations.

Delayed fission of atomic nuclei (To the 50th anniversary of the discovery)

NASA Astrophysics Data System (ADS)

Skobelev, N. K.

2017-09-01

The history of the discovery of delayed nuclear fission is presented, and the retrospective of investigations into this phenomenon that were performed at various research centers worldwide is outlined. The results obtained by measuring basic delayed-fission features, including the fission probability, the total kinetic energy of fission fragments, and their mass distributions, are analyzed. Recommendations concerning further studies in various regions of nuclear map with the aim of searches for and investigation of atomic nuclei undergoing delayed fission are given. Lines of further research into features of delayed fission with the aim of solving current problems of fission physics are discussed.

Detection of coupling delay: A problem not yet solved

NASA Astrophysics Data System (ADS)

Coufal, David; Jakubík, Jozef; Jajcay, Nikola; Hlinka, Jaroslav; Krakovská, Anna; Paluš, Milan

2017-08-01

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed—the method based on conditional mutual information—the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping—the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.

Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

ERIC Educational Resources Information Center

Tolle, John

2011-01-01

When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

Using Computer Symbolic Algebra to Solve Differential Equations.

ERIC Educational Resources Information Center

Mathews, John H.

1989-01-01

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

Stability and bifurcation analysis of a generalized scalar delay differential equation.

PubMed

Bhalekar, Sachin

2016-08-01

This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Solicited versus Unsolicited Metacognitive Prompts for Fostering Mathematical Problem Solving Using Multimedia

ERIC Educational Resources Information Center

Kramarski, Bracha; Friedman, Sheli

2014-01-01

The study examined how student control over metacognitive prompts in a multimedia environment affects students' ability to solve mathematical problems in immediate comprehension tasks using a multimedia program and a delayed-transfer test. It also examined the effect on metacognitive discourse, mental effort, and engagement with multimedia-based…

Measuring Differential Delays With Sine-Squared Pulses

NASA Technical Reports Server (NTRS)

Hurst, Robert N.

1994-01-01

Technique for measuring differential delays among red, green, and blue components of video signal transmitted on different parallel channels exploits sine-squared pulses that are parts of standard test signals transmitted during vertical blanking interval of frame period. Technique does not entail expense of test-signal generator. Also applicable to nonvideo signals including sine-squared pulses.

Speech Inconsistency in Children With Childhood Apraxia of Speech, Language Impairment, and Speech Delay: Depends on the Stimuli.

PubMed

Iuzzini-Seigel, Jenya; Hogan, Tiffany P; Green, Jordan R

2017-05-24

The current research sought to determine (a) if speech inconsistency is a core feature of childhood apraxia of speech (CAS) or if it is driven by comorbid language impairment that affects a large subset of children with CAS and (b) if speech inconsistency is a sensitive and specific diagnostic marker that can differentiate between CAS and speech delay. Participants included 48 children ranging between 4;7 to 17;8 (years;months) with CAS (n = 10), CAS + language impairment (n = 10), speech delay (n = 10), language impairment (n = 9), or typical development (n = 9). Speech inconsistency was assessed at phonemic and token-to-token levels using a variety of stimuli. Children with CAS and CAS + language impairment performed equivalently on all inconsistency assessments. Children with language impairment evidenced high levels of speech inconsistency on the phrase "buy Bobby a puppy." Token-to-token inconsistency of monosyllabic words and the phrase "buy Bobby a puppy" was sensitive and specific in differentiating children with CAS and speech delay, whereas inconsistency calculated on other stimuli (e.g., multisyllabic words) was less efficacious in differentiating between these disorders. Speech inconsistency is a core feature of CAS and is efficacious in differentiating between children with CAS and speech delay; however, sensitivity and specificity are stimuli dependent.

Radioactivity Calculations

ERIC Educational Resources Information Center

Onega, Ronald J.

1969-01-01

Three problems in radioactive buildup and decay are presented and solved. Matrix algebra is used to solve the second problem. The third problem deals with flux depression and is solved by the use of differential equations. (LC)

Enhancing the detection of edges and non-differentiable points in an NMR spectrum using delayed-acquisition.

PubMed

Gong, Zhaoyuan; Walls, Jamie D

2018-02-01

Delayed-acquisition, which is a common technique for improving spectral resolution in Fourier transform based spectroscopies, typically relies upon differences in T 2 relaxation rates that are often due to underlying differences in dynamics and/or complexities of the spin systems being studied. After an acquisition delay, the broad signals from fast T 2 -relaxing species are more suppressed relative to the sharp signals from slow T 2 -relaxing species. In this paper, an alternative source of differential "dephasing" under delayed-acquisition is demonstrated that is based solely upon the mathematical properties of the line shape and is independent of the underlying spin dynamics and/or complexity. Signals associated with frequencies where the line shape either changes sharply and/or is non-differentiable at some finite order dephase at a much slower rate than those signals associated with frequencies where the line shape is smooth. Experiments employing delayed-acquisition to study interfaces in biphasic samples, to measure spatially-dependent longitudinal relaxation, and to highlight sharp features in NMR spectra are presented. Copyright © 2017 Elsevier Inc. All rights reserved.

Enhancing the detection of edges and non-differentiable points in an NMR spectrum using delayed-acquisition

NASA Astrophysics Data System (ADS)

Gong, Zhaoyuan; Walls, Jamie D.

2018-02-01

Delayed-acquisition, which is a common technique for improving spectral resolution in Fourier transform based spectroscopies, typically relies upon differences in T2 relaxation rates that are often due to underlying differences in dynamics and/or complexities of the spin systems being studied. After an acquisition delay, the broad signals from fast T2 -relaxing species are more suppressed relative to the sharp signals from slow T2 -relaxing species. In this paper, an alternative source of differential "dephasing" under delayed-acquisition is demonstrated that is based solely upon the mathematical properties of the line shape and is independent of the underlying spin dynamics and/or complexity. Signals associated with frequencies where the line shape either changes sharply and/or is non-differentiable at some finite order dephase at a much slower rate than those signals associated with frequencies where the line shape is smooth. Experiments employing delayed-acquisition to study interfaces in biphasic samples, to measure spatially-dependent longitudinal relaxation, and to highlight sharp features in NMR spectra are presented.

A Simple Derivation of Kepler's Laws without Solving Differential Equations

ERIC Educational Resources Information Center

Provost, J.-P.; Bracco, C.

2009-01-01

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple…

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

Delay-based virtual congestion control in multi-tenant datacenters

NASA Astrophysics Data System (ADS)

Liu, Yuxin; Zhu, Danhong; Zhang, Dong

2018-03-01

With the evolution of cloud computing and virtualization, the congestion control of virtual datacenters has become the basic issue for multi-tenant datacenters transmission. Regarding to the friendly conflict of heterogeneous congestion control among multi-tenant, this paper proposes a delay-based virtual congestion control, which translates the multi-tenant heterogeneous congestion control into delay-based feedback uniformly by setting the hypervisor translation layer, modifying three-way handshake of explicit feedback and packet loss feedback and throttling receive window. The simulation results show that the delay-based virtual congestion control can effectively solve the unfairness of heterogeneous feedback congestion control algorithms.

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

PubMed

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

Differential games in economic systems with delays

NASA Astrophysics Data System (ADS)

Kim, A. V.; Kormyshev, V. M.; Novikov, M. Yu.; Nikonov, M. A.

2017-11-01

In the paper, we consider application of i-smooth analysis (A.V. Kim, 2015) to differential games with delays in economics (Dockner E.J., et all, 2000; R. Isaacs, 1999). The approach is developed in the framework of the theory of positional differential games (N.N. Krasovskii, A.I. Subbotin, 1988; A.V. Kryazhimskii, Yu.S. Osipov, 1973; Yu.S. Osipov, J. Appl. Math. Mech. Vol. 35, № 1, № 6, 1971) and is based on application of the extremal shift strategy. We consider basic notions and constructions of the approach-evasion problem for linear systems with delays. The necessary and sufficient conditions of solvability the approach-evasion problem in terms of special u-stable sets are presented in another paper.

On the Maximum Mass of Differentially Rotating Neutron Stars

NASA Astrophysics Data System (ADS)

Baumgarte, Thomas W.; Shapiro, Stuart L.; Shibata, Masaru

2000-01-01

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations that are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.

Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate

NASA Astrophysics Data System (ADS)

Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan

2017-08-01

In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

NASA Astrophysics Data System (ADS)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Adaptive Information Dissemination Control to Provide Diffdelay for the Internet of Things.

PubMed

Liu, Xiao; Liu, Anfeng; Huang, Changqin

2017-01-12

Applications running on the Internet of Things, such as the Wireless Sensor and Actuator Networks (WSANs) platform, generally have different quality of service (QoS) requirements. For urgent events, it is crucial that information be reported to the actuator quickly, and the communication cost is the second factor. However, for interesting events, communication costs, network lifetime and time all become important factors. In most situations, these different requirements cannot be satisfied simultaneously. In this paper, an adaptive communication control based on a differentiated delay (ACCDS) scheme is proposed to resolve this conflict. In an ACCDS, source nodes of events adaptively send various searching actuators routings (SARs) based on the degree of sensitivity to delay while maintaining the network lifetime. For a delay-sensitive event, the source node sends a large number of SARs to actuators to identify and inform the actuators in an extremely short time; thus, action can be taken quickly but at higher communication costs. For delay-insensitive events, the source node sends fewer SARs to reduce communication costs and improve network lifetime. Therefore, an ACCDS can meet the QoS requirements of different events using a differentiated delay framework. Theoretical analysis simulation results indicate that an ACCDS provides delay and communication costs and differentiated services; an ACCDS scheme can reduce the network delay by 11.111%-53.684% for a delay-sensitive event and reduce the communication costs by 5%-22.308% for interesting events, and reduce the network lifetime by about 28.713%.

Adaptive Information Dissemination Control to Provide Diffdelay for the Internet of Things

PubMed Central

Liu, Xiao; Liu, Anfeng; Huang, Changqin

2017-01-01

Applications running on the Internet of Things, such as the Wireless Sensor and Actuator Networks (WSANs) platform, generally have different quality of service (QoS) requirements. For urgent events, it is crucial that information be reported to the actuator quickly, and the communication cost is the second factor. However, for interesting events, communication costs, network lifetime and time all become important factors. In most situations, these different requirements cannot be satisfied simultaneously. In this paper, an adaptive communication control based on a differentiated delay (ACCDS) scheme is proposed to resolve this conflict. In an ACCDS, source nodes of events adaptively send various searching actuators routings (SARs) based on the degree of sensitivity to delay while maintaining the network lifetime. For a delay-sensitive event, the source node sends a large number of SARs to actuators to identify and inform the actuators in an extremely short time; thus, action can be taken quickly but at higher communication costs. For delay-insensitive events, the source node sends fewer SARs to reduce communication costs and improve network lifetime. Therefore, an ACCDS can meet the QoS requirements of different events using a differentiated delay framework. Theoretical analysis simulation results indicate that an ACCDS provides delay and communication costs and differentiated services; an ACCDS scheme can reduce the network delay by 11.111%–53.684% for a delay-sensitive event and reduce the communication costs by 5%–22.308% for interesting events, and reduce the network lifetime by about 28.713%. PMID:28085097

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

A flatness-based control approach to drug infusion for cardiac function regulation

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Zervos, Nikolaos; Melkikh, Alexey

2016-12-01

A new control method based on differential flatness theory is developed in this article, aiming at solving the problem of regulation of haemodynamic parameters, Actually control of the cardiac output (volume of blood pumped out by heart per unit of time) and of the arterial blood pressure is achieved through the administered infusion of cardiovascular drugs, such as dopamine and sodium nitroprusside. Time delays between the control inputs and the system's outputs are taken into account. Using the principle of dynamic extension, which means that by considering certain control inputs and their derivatives as additional state variables, a state-space description for the heart's function is obtained. It is proven that the dynamic model of the heart is a differentially flat one. This enables its transformation into a linear canonical and decoupled form, for which the design of a stabilizing feedback controller becomes possible. The proposed feedback controller is of proven stability and assures fast and accurate tracking of the reference setpoints by the outputs of the heart's dynamic model. Moreover, by using a Kalman Filter-based disturbances' estimator, it becomes possible to estimate in real-time and compensate for the model uncertainty and external perturbation inputs that affect the heart's model.

Effects of Delay Duration on the WMS Logical Memory Performance of Older Adults with Probable Alzheimer's Disease, Probable Vascular Dementia, and Normal Cognition.

PubMed

Montgomery, Valencia; Harris, Katie; Stabler, Anthony; Lu, Lisa H

2017-05-01

To examine how the duration of time delay between Wechsler Memory Scale (WMS) Logical Memory I and Logical Memory II (LM) affected participants' recall performance. There are 46,146 total Logical Memory administrations to participants diagnosed with either Alzheimer's disease (AD), vascular dementia (VaD), or normal cognition in the National Alzheimer's Disease Coordinating Center's Uniform Data Set. Only 50% of the sample was administered the standard 20-35 min of delay as specified by WMS-R and WMS-III. We found a significant effect of delay time duration on proportion of information retained for the VaD group compared to its control group, which remained after adding LMI raw score as a covariate. There was poorer retention of information with longer delay for this group. This association was not as strong for the AD and cognitively normal groups. A 24.5-min delay was most optimal for differentiating AD from VaD participants (47.7% classification accuracy), an 18.5-min delay was most optimal for differentiating AD versus normal participants (51.7% classification accuracy), and a 22.5-min delay was most optimal for differentiating VaD versus normal participants (52.9% classification accuracy). Considering diagnostic implications, our findings suggest that test administration should incorporate precise tracking of delay periods. We recommend a 20-min delay with 18-25-min range. Poor classification accuracy based on LM data alone is a reminder that story memory performance is only one piece of data that contributes to complex clinical decisions. However, strict adherence to the recommended range yields optimal data for diagnostic decisions. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

NASA Astrophysics Data System (ADS)

Torabi, H.; Pariz, N.; Karimpour, A.

2016-02-01

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems.

Stability Switches, Hopf Bifurcations, and Spatio-temporal Patterns in a Delayed Neural Model with Bidirectional Coupling

NASA Astrophysics Data System (ADS)

Song, Yongli; Zhang, Tonghua; Tadé, Moses O.

2009-12-01

The dynamical behavior of a delayed neural network with bi-directional coupling is investigated by taking the delay as the bifurcating parameter. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. As the propagation time delay in the coupling varies, stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. In particular, we obtain that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural activities. Numerical simulations are given to illustrate the obtained results and show the existence of bursts in some interval of the time for large enough delay.

Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays

NASA Astrophysics Data System (ADS)

Nguimdo, Romain Modeste

2018-03-01

Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.

Discussion summary: Fictitious domain methods

NASA Technical Reports Server (NTRS)

Glowinski, Rowland; Rodrigue, Garry

1991-01-01

Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations.

Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane-Emden type differential equations (LETDEs).

PubMed

Tripathi, Rajnee; Mishra, Hradyesh Kumar

2016-01-01

In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.

To Solve or Not to Solve, that Is the Problem

ERIC Educational Resources Information Center

Braiden, Doug

2011-01-01

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

An electric-analog simulation of elliptic partial differential equations using finite element theory

USGS Publications Warehouse

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

Reaction-diffusion systems in natural sciences and new technology transfer

NASA Astrophysics Data System (ADS)

Keller, André A.

2012-12-01

Diffusion mechanisms in natural sciences and innovation management involve partial differential equations (PDEs). This is due to their spatio-temporal dimensions. Functional semi-discretized PDEs (with lattice spatial structures or time delays) may be even more adapted to real world problems. In the modeling process, PDEs can also formalize behaviors, such as the logistic growth of populations with migration, and the adopters’ dynamics of new products in innovation models. In biology, these events are related to variations in the environment, population densities and overcrowding, migration and spreading of humans, animals, plants and other cells and organisms. In chemical reactions, molecules of different species interact locally and diffuse. In the management of new technologies, the diffusion processes of innovations in the marketplace (e.g., the mobile phone) are a major subject. These innovation diffusion models refer mainly to epidemic models. This contribution introduces that modeling process by using PDEs and reviews the essential features of the dynamics and control in biological, chemical and new technology transfer. This paper is essentially user-oriented with basic nonlinear evolution equations, delay PDEs, several analytical and numerical methods for solving, different solutions, and with the use of mathematical packages, notebooks and codes. The computations are carried out by using the software Wolfram Mathematica®7, and C++ codes.

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1987-01-01

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay.

Global exponential stability of inertial memristor-based neural networks with time-varying delays and impulses.

PubMed

Zhang, Wei; Huang, Tingwen; He, Xing; Li, Chuandong

2017-11-01

In this study, we investigate the global exponential stability of inertial memristor-based neural networks with impulses and time-varying delays. We construct inertial memristor-based neural networks based on the characteristics of the inertial neural networks and memristor. Impulses with and without delays are considered when modeling the inertial neural networks simultaneously, which are of great practical significance in the current study. Some sufficient conditions are derived under the framework of the Lyapunov stability method, as well as an extended Halanay differential inequality and a new delay impulsive differential inequality, which depend on impulses with and without delays, in order to guarantee the global exponential stability of the inertial memristor-based neural networks. Finally, two numerical examples are provided to illustrate the efficiency of the proposed methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Predicting flight delay based on multiple linear regression

NASA Astrophysics Data System (ADS)

Ding, Yi

2017-08-01

Delay of flight has been regarded as one of the toughest difficulties in aviation control. How to establish an effective model to handle the delay prediction problem is a significant work. To solve the problem that the flight delay is difficult to predict, this study proposes a method to model the arriving flights and a multiple linear regression algorithm to predict delay, comparing with Naive-Bayes and C4.5 approach. Experiments based on a realistic dataset of domestic airports show that the accuracy of the proposed model approximates 80%, which is further improved than the Naive-Bayes and C4.5 approach approaches. The result testing shows that this method is convenient for calculation, and also can predict the flight delays effectively. It can provide decision basis for airport authorities.

Robustness analysis of an air heating plant and control law by using polynomial chaos

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

Colón, Diego; Ferreira, Murillo A. S.; Bueno, Átila M.

2014-12-10

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputsmore » (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.« less

Delayed Feedback Disrupts the Procedural-Learning System but Not the Hypothesis-Testing System in Perceptual Category Learning

ERIC Educational Resources Information Center

Maddox, W. Todd; Ing, A. David

2005-01-01

W. T. Maddox, F. G. Ashby, and C. J. Bohil (2003) found that delayed feedback adversely affects information-integration but not rule-based category learning in support of a multiple-systems approach to category learning. However, differences in the number of stimulus dimensions relevant to solving the task and perceptual similarity failed to rule…

Episodic foresight beyond the very next event in 3- and 4-year-old children.

PubMed

Boden, Hannah; Labuschagne, Lisa G; Hinten, Ashley E; Scarf, Damian

2017-11-01

Testing episodic foresight in children generally involves presenting them with a problem in one location (e.g., Room A) and, after a spending a delay in a different location, telling them they will be returning to Room A. Before they go, children are presented with a number of items, one of which will allow them to solve the problem in Room A. At around 3 to 4 years of age children display episodic foresight, selecting the item that will allow them to solve the problem. To date, however, no study has assessed whether 3- and 4-year-old children can plan beyond the very next event, selecting the correct item when there is a delay before returning to Room A. Here, we show that 3- and 4-year-old children can pass when a delay is imposed but that their performance is significantly worse than when they are planning for an immediate event. © 2017 Wiley Periodicals, Inc.

[Action-oriented versus state-oriented reactions to experimenter-induced failures].

PubMed

Brunstein, J C

1989-01-01

The present study assessed different effects of action-oriented versus state-oriented styles of coping with failure on achievement-related performance and cognition. In a learned helplessness experiment, students were exposed to an academic failure situation and were then tested on a series of problem-solving tasks, either immediately after the pretreatment or after a delay of 24 hours. Performance and cognitive concomitants were measured during both experimental periods. Results demonstrated that action orientation was associated with self-immunizing cognitions during helplessness training. Action-oriented participants improved their performance level even after repeated failure feedbacks. Moreover, action-oriented students assigned to the delayed test condition responded with increased striving for success and showed performance increments, even in comparison with control subjects. In contrast, state-oriented participants developed symptoms of helplessness and showed impaired performance during failure inductions. In later tests on problem-solving tasks, state-oriented groups responded with increased fear of failure. Independent of immediate or delayed test conditions, they soon lapsed into new performance decrements.

Self-Regulatory Speech during Planning and Problem-Solving in Children with SLI and Their Typically Developing Peers

ERIC Educational Resources Information Center

Abdul Aziz, Safiyyah; Fletcher, Janet; Bayliss, Donna M.

2017-01-01

Background: Past research with children with specific language impairment (SLI) has shown them to have poorer planning and problem-solving ability, and delayed self-regulatory speech (SRS) relative to their typically developing (TD) peers. However, the studies are few in number and are restricted in terms of the number and age range of…

Low Latency MAC Protocol in Wireless Sensor Networks Using Timing Offset

NASA Astrophysics Data System (ADS)

Choi, Seung Sik

This paper proposes a low latency MAC protocol that can be used in sensor networks. To extend the lifetime of sensor nodes, the conventional solution is to synchronize active/sleep periods of all sensor nodes. However, due to these synchronized sensor nodes, packets in the intermediate nodes must wait until the next node wakes up before it can forward a packet. This induces a large delay in sensor nodes. To solve this latency problem, a clustered sensor network which uses two types of sensor nodes and layered architecture is considered. Clustered heads in each cluster are synchronized with different timing offsets to reduce the sleep delay. Using this concept, the latency problem can be solved and more efficient power usage can be obtained.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

PubMed

Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

2009-02-01

Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

ERIC Educational Resources Information Center

Kougias, Ioannis E.

2009-01-01

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

Theory and practice of solving ordinary differential equations (ODEs). [Runge-Kutta method; lectures in Spanish

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

Shampine, L.F.

1978-04-01

Between January 23 and 27, 1978, several lectures were presented at the Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, National University of Mexico, Mexico City. The author concentrated on the Runge--Kutta method of solving differential equations because its details are simple and it is illustrative of classical perturbation and asymptotic methods.

Give Me a Hand: Differential Effects of Gesture Type in Guiding Young Children's Problem-Solving

ERIC Educational Resources Information Center

Vallotton, Claire; Fusaro, Maria; Hayden, Julia; Decker, Kalli; Gutowski, Elizabeth

2015-01-01

Adults' gestures support children's learning in problem-solving tasks, but gestures may be differentially useful to children of different ages, and different features of gestures may make them more or less useful to children. The current study investigated parents' use of gestures to support their young children (1.5-6 years) in a block puzzle…

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Who Solved the Bernoulli Differential Equation and How Did They Do It?

ERIC Educational Resources Information Center

Parker, Adam E.

2013-01-01

The Bernoulli brothers, Jacob and Johann, and Leibniz: Any of these might have been first to solve what is called the Bernoulli differential equation. We explore their ideas and the chronology of their work, finding out, among other things, that variation of parameters was used in 1697, 78 years before 1775, when Lagrange introduced it in general.

Spectral characterization of differential group delay in uniform fiber Bragg gratings.

PubMed

Bette, S; Caucheteur, C; Wuilpart, M; Mégret, P; Garcia-Olcina, R; Sales, S; Capmany, J

2005-12-12

In this paper, we completely study the wavelength dependency of differential group delay (DGD) in uniform fiber Bragg gratings (FBG) exhibiting birefringence. An analytical expression of DGD is established. We analyze the impact of grating parameters (physical length, index modulation and apodization profile) on the wavelength dependency of DGD. Experimental results complete the paper. A very good agreement between theory and experience is reported.

Effects of Training in Problem Solving on the Problem-Solving Abilities of Gifted Fourth Graders: A Comparison of the Future Problem Solving and Instrumental Enrichment Programs.

ERIC Educational Resources Information Center

Dufner, Hillrey A.; Alexander, Patricia A.

The differential effects of two different types of problem-solving training on the problem-solving abilities of gifted fourth graders were studied. Two successive classes of gifted fourth graders from Weslaco Independent School District (Texas) were pretested with the Coloured Progressive Matrices (CPM) and Thinking Creatively With Pictures…

Coded acoustic wave sensors and system using time diversity

NASA Technical Reports Server (NTRS)

Solie, Leland P. (Inventor); Hines, Jacqueline H. (Inventor)

2012-01-01

An apparatus and method for distinguishing between sensors that are to be wirelessly detected is provided. An interrogator device uses different, distinct time delays in the sensing signals when interrogating the sensors. The sensors are provided with different distinct pedestal delays. Sensors that have the same pedestal delay as the delay selected by the interrogator are detected by the interrogator whereas other sensors with different pedestal delays are not sensed. Multiple sensors with a given pedestal delay are provided with different codes so as to be distinguished from one another by the interrogator. The interrogator uses a signal that is transmitted to the sensor and returned by the sensor for combination and integration with the reference signal that has been processed by a function. The sensor may be a surface acoustic wave device having a differential impulse response with a power spectral density consisting of lobes. The power spectral density of the differential response is used to determine the value of the sensed parameter or parameters.

A neuro approach to solve fuzzy Riccati differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Kumaresan, N.; Kamali, M. Z. M.; Ratnavelu, Kurunathan

2015-10-01

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.

A neuro approach to solve fuzzy Riccati differential equations

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

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com; Telekom Malaysia, R&D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor; Kumaresan, N., E-mail: drnk2008@gmail.com

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.

Preliminary Evaluation of BIM-based Approaches for Schedule Delay Analysis

NASA Astrophysics Data System (ADS)

Chou, Hui-Yu; Yang, Jyh-Bin

2017-10-01

The problem of schedule delay commonly occurs in construction projects. The quality of delay analysis depends on the availability of schedule-related information and delay evidence. More information used in delay analysis usually produces more accurate and fair analytical results. How to use innovative techniques to improve the quality of schedule delay analysis results have received much attention recently. As Building Information Modeling (BIM) technique has been quickly developed, using BIM and 4D simulation techniques have been proposed and implemented. Obvious benefits have been achieved especially in identifying and solving construction consequence problems in advance of construction. This study preforms an intensive literature review to discuss the problems encountered in schedule delay analysis and the possibility of using BIM as a tool in developing a BIM-based approach for schedule delay analysis. This study believes that most of the identified problems can be dealt with by BIM technique. Research results could be a fundamental of developing new approaches for resolving schedule delay disputes.

Time-delayed feedback control of diffusion in random walkers.

PubMed

Ando, Hiroyasu; Takehara, Kohta; Kobayashi, Miki U

2017-07-01

Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.

SIRT1 deficiency compromises mouse embryonic stem cell hematopoietic differentiation, and embryonic and adult hematopoiesis in the mouse

PubMed Central

Ou, Xuan; Chae, Hee-Don; Wang, Rui-Hong; Shelley, William C.; Cooper, Scott; Taylor, Tammi; Kim, Young-June; Deng, Chu-Xia; Yoder, Mervin C.

2011-01-01

SIRT1 is a founding member of a sirtuin family of 7 proteins and histone deacetylases. It is involved in cellular resistance to stress, metabolism, differentiation, aging, and tumor suppression. SIRT1−/− mice demonstrate embryonic and postnatal development defects. We examined hematopoietic and endothelial cell differentiation of SIRT1−/− mouse embryonic stem cells (ESCs) in vitro, and hematopoietic progenitors in SIRT1+/++/−, and −/− mice. SIRT1−/− ESCs formed fewer mature blast cell colonies. Replated SIRT1−/− blast colony-forming cells demonstrated defective hematopoietic potential. Endothelial cell production was unaltered, but there were defects in formation of a primitive vascular network from SIRT1−/−-derived embryoid bodies. Development of primitive and definitive progenitors derived from SIRT1−/− ESCs were also delayed and/or defective. Differentiation delay/defects were associated with delayed capacity to switch off Oct4, Nanog and Fgf5 expression, decreased β-H1 globin, β-major globin, and Scl gene expression, and reduced activation of Erk1/2. Ectopic expression of SIRT1 rescued SIRT1−/− ESC differentiation deficiencies. SIRT1−/− yolk sacs manifested fewer primitive erythroid precursors. SIRT1−/− and SIRT1+/− adult marrow had decreased numbers and cycling of hematopoietic progenitors, effects more apparent at 5%, than at 20%, oxygen tension, and these progenitors survived less well in vitro under conditions of delayed growth factor addition. This suggests a role for SIRT1 in ESC differentiation and mouse hematopoiesis. PMID:20966168

An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

NASA Astrophysics Data System (ADS)

Alam Khan, Najeeb; Razzaq, Oyoon Abdul

2016-03-01

In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

The 2010 Eyjafjallajökull and 2011 Grimsvötn ash plumes as seen by GPS

NASA Astrophysics Data System (ADS)

Grapenthin, R.; Hreinsdottir, S.; Gudmundsson, M. T.

2015-12-01

The injection of a volcanic plume introduces a dynamic, localized, short-term heterogeneity in the atmosphere. Satellite-imagery based remote sensing techniques provide good spatial coverage for the detection of such plumes, but slow satellite repeat times (>30 minutes) and cloud cover can delay, if not entirely prevent, the detection. GPS, in turn, provides excellent temporal coverage, but requires favorable satellite-station-geometry such that the signal propagates through the plume if it is to be used for plume detection and analysis. Two methods exist to detect / analyze ash plumes with GPS: (a) Ash-heavy plumes result in signal dispersion and hence a lowered signal-to-noise ratio (SNR). A lowered SNR, recorded by some receivers, can provide useful information about the plume, such as location and velocity of ascent. These data can be evaluated directly as they are recorded by the receiver; without the need of solving for a receiver's position. (b) Wet plumes refract the GPS signals piercing the plume and hence induce a propagation delay. When solving for a receiver position GPS analysis tools do not model this localized phase delay effect and solutions for plume-piercing satellites do not fit the data well. This can be exploited for plume analysis such as the estimation of changes to the atmospheric refractivity index. We analyze GPS data of the ~2 month 2010 Eyafjallajökull erption and the week-long 2011 Grímsvötn eruption to infer a first order estimate of plume geometry and its progression. Using SNR and phase delay information, we evaluate the evolution of the partitioning of wet versus dry parts of the plume. During the GPS processing we iteratively solve for phase-delay and position and fix other parameters, hence reducing the mapping of least-squares misfit into position estimates and other parameters. Nearly continuous webcam imagery provides independent observations of first-order plume characteristics for the Eyafjallajökull event.

Nonlinear interaction in differential mode delay managed mode-division multiplexed transmission systems.

PubMed

Rademacher, Georg; Warm, Stefan; Petermann, Klaus

2015-01-12

We analyze the impact of Differential Mode Delay (DMD) Management on the nonlinear impairments in mode-division multiplexed transmission systems. It is found out that DMD Management can lead to a degraded performance, due to enhanced intermodal nonlinear interaction. This can be attributed to an increased correlation of co-propagating channels, similar to the effects that show up in dispersion managed single-mode systems.

Differentiation of Speech Delay and Global Developmental Delay in Children Using DTI Tractography-Based Connectome.

PubMed

Jeong, J-W; Sundaram, S; Behen, M E; Chugani, H T

2016-06-01

Pure speech delay is a common developmental disorder which, according to some estimates, affects 5%-8% of the population. Speech delay may not only be an isolated condition but also can be part of a broader condition such as global developmental delay. The present study investigated whether diffusion tensor imaging tractography-based connectome can differentiate global developmental delay from speech delay in young children. Twelve children with pure speech delay (39.1 ± 20.9 months of age, 9 boys), 14 children with global developmental delay (39.3 ± 18.2 months of age, 12 boys), and 10 children with typical development (38.5 ± 20.5 months of age, 7 boys) underwent 3T DTI. For each subject, whole-brain connectome analysis was performed by using 116 cortical ROIs. The following network metrics were measured at individual regions: strength (number of the shortest paths), efficiency (measures of global and local integration), cluster coefficient (a measure of local aggregation), and betweeness (a measure of centrality). Compared with typical development, global and local efficiency were significantly reduced in both global developmental delay and speech delay (P < .0001). The nodal strength of the cognitive network is reduced in global developmental delay, whereas the nodal strength of the language network is reduced in speech delay. This finding resulted in a high accuracy of >83% ± 4% to discriminate global developmental delay from speech delay. The network abnormalities identified in the present study may underlie the neurocognitive and behavioral consequences commonly identified in children with global developmental delay and speech delay. Further validation studies in larger samples are required. © 2016 by American Journal of Neuroradiology.

Sea Ice Detection Based on Differential Delay-Doppler Maps from UK TechDemoSat-1

PubMed Central

Zhu, Yongchao; Yu, Kegen; Zou, Jingui; Wickert, Jens

2017-01-01

Global Navigation Satellite System (GNSS) signals can be exploited to remotely sense atmosphere and land and ocean surface to retrieve a range of geophysical parameters. This paper proposes two new methods, termed as power-summation of differential Delay-Doppler Maps (PS-D) and pixel-number of differential Delay-Doppler Maps (PN-D), to distinguish between sea ice and sea water using differential Delay-Doppler Maps (dDDMs). PS-D and PN-D make use of power-summation and pixel-number of dDDMs, respectively, to measure the degree of difference between two DDMs so as to determine the transition state (water-water, water-ice, ice-ice and ice-water) and hence ice and water are detected. Moreover, an adaptive incoherent averaging of DDMs is employed to improve the computational efficiency. A large number of DDMs recorded by UK TechDemoSat-1 (TDS-1) over the Arctic region are used to test the proposed sea ice detection methods. Through evaluating against ground-truth measurements from the Ocean Sea Ice SAF, the proposed PS-D and PN-D methods achieve a probability of detection of 99.72% and 99.69% respectively, while the probability of false detection is 0.28% and 0.31% respectively. PMID:28704948

Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

NASA Astrophysics Data System (ADS)

Ansmann, Gerrit

2018-04-01

We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large systems of differential equations such as those used to describe dynamics on complex networks. Through the selected method of input, the presented modules also allow almost complete automatization of the process of estimating regular as well as transversal Lyapunov exponents for ordinary and delay differential equations. We conceptually discuss the modules' design, analyze their performance, and demonstrate their capabilities by application to timely problems.

Application of differential evolution algorithm on self-potential data.

PubMed

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods.

Application of Differential Evolution Algorithm on Self-Potential Data

PubMed Central

Li, Xiangtao; Yin, Minghao

2012-01-01

Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces, and has been successfully used to solve several kinds of problems. In this paper, differential evolution is used for quantitative interpretation of self-potential data in geophysics. Six parameters are estimated including the electrical dipole moment, the depth of the source, the distance from the origin, the polarization angle and the regional coefficients. This study considers three kinds of data from Turkey: noise-free data, contaminated synthetic data, and Field example. The differential evolution and the corresponding model parameters are constructed as regards the number of the generations. Then, we show the vibration of the parameters at the vicinity of the low misfit area. Moreover, we show how the frequency distribution of each parameter is related to the number of the DE iteration. Experimental results show the DE can be used for solving the quantitative interpretation of self-potential data efficiently compared with previous methods. PMID:23240004

Composite transcriptome assembly of RNA-seq data in a sheep model for delayed bone healing.

PubMed

Jäger, Marten; Ott, Claus-Eric; Grünhagen, Johannes; Hecht, Jochen; Schell, Hanna; Mundlos, Stefan; Duda, Georg N; Robinson, Peter N; Lienau, Jasmin

2011-03-24

The sheep is an important model organism for many types of medically relevant research, but molecular genetic experiments in the sheep have been limited by the lack of knowledge about ovine gene sequences. Prior to our study, mRNA sequences for only 1,556 partial or complete ovine genes were publicly available. Therefore, we developed a composite de novo transcriptome assembly method for next-generation sequence data to combine known ovine mRNA and EST sequences, mRNA sequences from mouse and cow, and sequences assembled de novo from short read RNA-Seq data into a composite reference transcriptome, and identified transcripts from over 12 thousand previously undescribed ovine genes. Gene expression analysis based on these data revealed substantially different expression profiles in standard versus delayed bone healing in an ovine tibial osteotomy model. Hundreds of transcripts were differentially expressed between standard and delayed healing and between the time points of the standard and delayed healing groups. We used the sheep sequences to design quantitative RT-PCR assays with which we validated the differential expression of 26 genes that had been identified by RNA-seq analysis. A number of clusters of characteristic expression profiles could be identified, some of which showed striking differences between the standard and delayed healing groups. Gene Ontology (GO) analysis showed that the differentially expressed genes were enriched in terms including extracellular matrix, cartilage development, contractile fiber, and chemokine activity. Our results provide a first atlas of gene expression profiles and differentially expressed genes in standard and delayed bone healing in a large-animal model and provide a number of clues as to the shifts in gene expression that underlie delayed bone healing. In the course of our study, we identified transcripts of 13,987 ovine genes, including 12,431 genes for which no sequence information was previously available. This information will provide a basis for future molecular research involving the sheep as a model organism.

Composite transcriptome assembly of RNA-seq data in a sheep model for delayed bone healing

PubMed Central

2011-01-01

Background The sheep is an important model organism for many types of medically relevant research, but molecular genetic experiments in the sheep have been limited by the lack of knowledge about ovine gene sequences. Results Prior to our study, mRNA sequences for only 1,556 partial or complete ovine genes were publicly available. Therefore, we developed a composite de novo transcriptome assembly method for next-generation sequence data to combine known ovine mRNA and EST sequences, mRNA sequences from mouse and cow, and sequences assembled de novo from short read RNA-Seq data into a composite reference transcriptome, and identified transcripts from over 12 thousand previously undescribed ovine genes. Gene expression analysis based on these data revealed substantially different expression profiles in standard versus delayed bone healing in an ovine tibial osteotomy model. Hundreds of transcripts were differentially expressed between standard and delayed healing and between the time points of the standard and delayed healing groups. We used the sheep sequences to design quantitative RT-PCR assays with which we validated the differential expression of 26 genes that had been identified by RNA-seq analysis. A number of clusters of characteristic expression profiles could be identified, some of which showed striking differences between the standard and delayed healing groups. Gene Ontology (GO) analysis showed that the differentially expressed genes were enriched in terms including extracellular matrix, cartilage development, contractile fiber, and chemokine activity. Conclusions Our results provide a first atlas of gene expression profiles and differentially expressed genes in standard and delayed bone healing in a large-animal model and provide a number of clues as to the shifts in gene expression that underlie delayed bone healing. In the course of our study, we identified transcripts of 13,987 ovine genes, including 12,431 genes for which no sequence information was previously available. This information will provide a basis for future molecular research involving the sheep as a model organism. PMID:21435219

Delay differential analysis of time series.

PubMed

Lainscsek, Claudia; Sejnowski, Terrence J

2015-03-01

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

Fractional Order Spatiotemporal Chaos with Delay in Spatial Nonlinear Coupling

NASA Astrophysics Data System (ADS)

Zhang, Yingqian; Wang, Xingyuan; Liu, Liyan; Liu, Jia

We investigate the spatiotemporal dynamics with fractional order differential logistic map with delay under nonlinear chaotic maps for spatial coupling connections. Here, the coupling methods between lattices are the nonlinear chaotic map coupling of lattices. The fractional order differential logistic map with delay breaks the limits of the range of parameter μ ∈ [3.75, 4] in the classical logistic map for chaotic states. The Kolmogorov-Sinai entropy density and universality, and bifurcation diagrams are employed to investigate the chaotic behaviors of the proposed model in this paper. The proposed model can also be applied for cryptography, which is verified in a color image encryption scheme in this paper.

Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

PubMed

He, Wangli; Qian, Feng; Han, Qing-Long; Cao, Jinde

2012-10-01

This paper investigates the problem of master-slave synchronization of two delayed Lur'e systems in the presence of parameter mismatches. First, by analyzing the corresponding synchronization error system, synchronization with an error level, which is referred to as quasi-synchronization, is established. Some delay-dependent quasi-synchronization criteria are derived. An estimation of the synchronization error bound is given, and an explicit expression of error levels is obtained. Second, sufficient conditions on the existence of feedback controllers under a predetermined error level are provided. The controller gains are obtained by solving a set of linear matrix inequalities. Finally, a delayed Chua's circuit is chosen to illustrate the effectiveness of the derived results.

Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems.

PubMed

Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai

2014-10-20

We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Do Right- and Left-Handed Monkeys Differ on Cognitive Measures?

NASA Technical Reports Server (NTRS)

Hopkins, William D.; Washburn, David A.

1994-01-01

Twelve left- and 14 right-handed monkeys were compared on 6 measures of cognitive performance (2 maze-solving tasks, matching-to-sample, delayed matching-to-sample, delayed response using spatial cues, and delayed response using form cues). The dependent variable was trials-to-training criterion for each of the 6 tasks. Significant differences were found between left- and right-handed monkeys on the 2 versions of the delayed response task. Right-handed monkeys reached criterion significantly faster on the form cue version of the task, whereas left-handed monkeys reached criterion significantly faster on delayed response for spatial position (p less than .05). The results suggest that sensitive hand preference measures of laterality can reveal differences in cognitive performance, which in turn may reflect underlying laterality in functional organization of the nervous system.

LORENE: Spectral methods differential equations solver

NASA Astrophysics Data System (ADS)

Gourgoulhon, Eric; Grandclément, Philippe; Marck, Jean-Alain; Novak, Jérôme; Taniguchi, Keisuke

2016-08-01

LORENE (Langage Objet pour la RElativité NumériquE) solves various problems arising in numerical relativity, and more generally in computational astrophysics. It is a set of C++ classes and provides tools to solve partial differential equations by means of multi-domain spectral methods. LORENE classes implement basic structures such as arrays and matrices, but also abstract mathematical objects, such as tensors, and astrophysical objects, such as stars and black holes.

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

A differential delay equation arising from the sieve of Eratosthenes

NASA Technical Reports Server (NTRS)

Cheer, A. Y.; Goldston, D. A.

1990-01-01

Consideration is given to the differential delay equation introduced by Buchstab (1937) in connection with an asymptotic formula for the uncanceled terms in the sieve of Eratosthenes. Maier (1985) used this result to show there is unexpected irreqularity in the distribution of primes in short intervals. The function omega(u) is studied in this paper using numerical and analytical techniques. The results are applied to give some numerical constants in Maier's theorem.

Delayed nonlinear cournot and bertrand dynamics with product differentiation.

PubMed

Matsumoto, Akio; Szidarovszky, Ferenc

2007-07-01

Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

Alternans promotion in cardiac electrophysiology models by delay differential equations.

PubMed

Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M

2017-09-01

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Cognitive functioning and employment among people with schizophrenia in vocational rehabilitation.

PubMed

Lexén, Annika; Hofgren, Caisa; Stenmark, Richard; Bejerholm, Ulrika

2016-06-16

Employment is central to recovery in schizophrenia, but little attention has been paid to its relationship with cognitive functioning. This cross-sectional study adds to the knowledge base of relationships between cognitive functioning and gaining competitive employment, work hours per week, and monthly income among people with schizophrenia in vocational rehabilitation. It also examines which area of cognitive function may be decisive for gaining employment. Thirty-nine vocational rehabilitation participants were administered a cognitive battery based on MATRICS Consensus Cognitive Battery. Socio-demographic, clinical, and vocational data were gathered and analyzed with nonparametric statistics. Individuals with competitive employment differed from those without competitive employment in attention and psychomotor speed, delayed verbal recall, immediate visual recall, and planning, reasoning, and problem-solving. Higher scores in immediate and delayed verbal recall and planning, reasoning, and problem-solving correlated with more work hours per week and higher income. Immediate visual recall was related to higher income. Higher scores in planning, reasoning, and problem-solving was an indicator of competitive employment (OR = 1.48). Higher order cognitive functioning of planning, reasoning, and problem-solving may have a central role in gaining employment. The findings should be considered in compensation for or improving cognitive functions for vocational rehabilitation participants.

High-precision GNSS ocean positioning with BeiDou short-message communication

NASA Astrophysics Data System (ADS)

Li, Bofeng; Zhang, Zhiteng; Zang, Nan; Wang, Siyao

2018-04-01

The current popular GNSS RTK technique would be not applicable on ocean due to the limited communication access for transmitting differential corrections. A new technique is proposed for high-precision ocean RTK, referred to as ORTK, where the corrections are transmitted by employing the function of BeiDou satellite short-message communication (SMC). To overcome the limitation of narrow bandwidth of BeiDou SMC, a new strategy of simplifying and encoding corrections is proposed instead of standard differential corrections, which reduces the single-epoch corrections from more than 1000 to less than 300 bytes. To solve the problems of correction delays, cycle slips, blunders and abnormal epochs over ultra-long baseline ORTK, a series of powerful algorithms were designed at the user-end software for achieving the stable and precise kinematic solutions on far ocean applications. The results from two long baselines of 240 and 420 km and real ocean experiments reveal that the kinematic solutions with horizontal accuracy of 5 cm and vertical accuracy of better than 15 cm are achievable by convergence time of 3-10 min. Compared to commercial ocean PPP with satellite telecommunication, ORTK is of much cheaper expense, higher accuracy and shorter convergence. It will be very prospective in many location-based ocean services.

Decentralized control

NASA Technical Reports Server (NTRS)

Steffen, Chris

1990-01-01

An overview of the time-delay problem and the reliability problem which arise in trying to perform robotic construction operations at a remote space location are presented. The effects of the time-delay upon the control system design will be itemized. A high level overview of a decentralized method of control which is expected to perform better than the centralized approach in solving the time-delay problem is given. The lower level, decentralized, autonomous, Troter Move-Bar algorithm is also presented (Troters are coordinated independent robots). The solution of the reliability problem is connected to adding redundancy to the system. One method of adding redundancy is given.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

NASA Astrophysics Data System (ADS)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Neural correlates of sample-coding and reward-coding in the delay activity of neurons in the entopallium and nidopallium caudolaterale of pigeons (Columba livia).

PubMed

Johnston, Melissa; Anderson, Catrona; Colombo, Michael

2017-01-15

We recorded neuronal activity from the nidopallium caudolaterale, the avian equivalent of mammalian prefrontal cortex, and the entopallium, the avian equivalent of the mammalian visual cortex, in four birds trained on a differential outcomes delayed matching-to-sample procedure in which one sample stimulus was followed by reward and the other was not. Despite similar incidence of reward-specific and reward-unspecific delay cell types across the two areas, overall entopallium delay activity occurred following both rewarded and non-rewarded stimuli, whereas nidopallium caudolaterale delay activity tended to occur following the rewarded stimulus but not the non-rewarded stimulus. These findings are consistent with the view that delay activity in entopallium represents a code of the sample stimulus whereas delay activity in nidopallium caudolaterale represents a code of the possibility of an upcoming reward. However, based on the types of delay cells encountered, cells in NCL also code the sample stimulus and cells in ENTO are influenced by reward. We conclude that both areas support the retention of information, but that the activity in each area is differentially modulated by factors such as reward and attentional mechanisms. Copyright © 2016 Elsevier B.V. All rights reserved.

Persistent Language Delay Versus Late Language Emergence in Children With Early Cochlear Implantation

PubMed Central

Nicholas, Johanna; Tobey, Emily; Davidson, Lisa

2016-01-01

Purpose The purpose of the present investigation is to differentiate children using cochlear implants (CIs) who did or did not achieve age-appropriate language scores by midelementary grades and to identify risk factors for persistent language delay following early cochlear implantation. Materials and Method Children receiving unilateral CIs at young ages (12–38 months) were tested longitudinally and classified with normal language emergence (n = 19), late language emergence (n = 22), or persistent language delay (n = 19) on the basis of their test scores at 4.5 and 10.5 years of age. Relative effects of demographic, audiological, linguistic, and academic characteristics on language emergence were determined. Results Age at CI was associated with normal language emergence but did not differentiate late emergence from persistent delay. Children with persistent delay were more likely to use left-ear implants and older speech processor technology. They experienced higher aided thresholds and lower speech perception scores. Persistent delay was foreshadowed by low morphosyntactic and phonological diversity in preschool. Logistic regression analysis predicted normal language emergence with 84% accuracy and persistent language delay with 74% accuracy. Conclusion CI characteristics had a strong effect on persistent versus resolving language delay, suggesting that right-ear (or bilateral) devices, technology upgrades, and improved audibility may positively influence long-term language outcomes. PMID:26501740

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

NASA Astrophysics Data System (ADS)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

Teaching Differentials in Thermodynamics Using Spatial Visualization

ERIC Educational Resources Information Center

Wang, Chih-Yueh; Hou, Ching-Han

2012-01-01

The greatest difficulty that is encountered by students in thermodynamics classes is to find relationships between variables and to solve a total differential equation that relates one thermodynamic state variable to two mutually independent state variables. Rules of differentiation, including the total differential and the cyclic rule, are…

Optimal Control for Stochastic Delay Evolution Equations

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

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

Increased proliferation of late-born retinal progenitor cells by gestational lead exposure delays rod and bipolar cell differentiation.

PubMed

Chaney, Shawnta Y; Mukherjee, Shradha; Giddabasappa, Anand; Rueda, Elda M; Hamilton, W Ryan; Johnson, Jerry E; Fox, Donald A

2016-01-01

Studies of neuronal development in the retina often examine the stages of proliferation, differentiation, and synaptic development, albeit independently. Our goal was to determine if a known neurotoxicant insult to a population of retinal progenitor cells (RPCs) would affect their eventual differentiation and synaptic development. To that end, we used our previously published human equivalent murine model of low-level gestational lead exposure (GLE). Children and animals with GLE exhibit increased scotopic electroretinogram a- and b-waves. Adult mice with GLE exhibit an increased number of late-born RPCs, a prolonged period of RPC proliferation, and an increased number of late-born rod photoreceptors and rod and cone bipolar cells (BCs), with no change in the number of late-born Müller glial cells or early-born neurons. The specific aims of this study were to determine whether increased and prolonged RPC proliferation alters the spatiotemporal differentiation and synaptic development of rods and BCs in early postnatal GLE retinas compared to control retinas. C57BL/6N mouse pups were exposed to lead acetate via drinking water throughout gestation and until postnatal day 10, which is equivalent to the human gestation period for retinal neurogenesis. RT-qPCR, immunohistochemical analysis, and western blots of well-characterized, cell-specific genes and proteins were performed at embryonic and early postnatal ages to assess rod and cone photoreceptor differentiation, rod and BC differentiation and synaptic development, and Müller glial cell differentiation. Real-time quantitative PCR (RT-qPCR) with the rod-specific transcription factors Nrl , Nr2e3 , and Crx and the rod-specific functional gene Rho , along with central retinal confocal studies with anti-recoverin and anti-rhodopsin antibodies, revealed a two-day delay in the differentiation of rod photoreceptors in GLE retinas. Rhodopsin immunoblots supported this conclusion. No changes in glutamine synthetase gene or protein expression, a marker for late-born Müller glial cells, were observed in the developing retinas. In the retinas from the GLE mice, anti-PKCα, - Chx10 (Vsx2) and -secretagogin antibodies revealed a two- to three-day delay in the differentiation of rod and cone BCs, whereas the expression of the proneural and BC genes Otx2 and Chx10 , respectively, increased. In addition, confocal studies of proteins associated with functional synapses (e.g., vesicular glutamate transporter 1 [VGluT1], plasma membrane calcium ATPase [PMCA], transient receptor potential channel M1 [TRPM1], and synaptic vesicle glycoprotein 2B [SV2B]) revealed a two-day delay in the formation of the outer and inner plexiform layers of the GLE retinas. Moreover, several markers revealed that the initiation of the differentiation and intensity of the labeling of early-born cells in the retinal ganglion cell and inner plexiform layers were not different in the control retinas. Our combined gene, confocal, and immunoblot findings revealed that the onset of rod and BC differentiation and their subsequent synaptic development is delayed by two to three days in GLE retinas. These results suggest that perturbations during the early proliferative stages of late-born RPCs fated to be rods and BCs ultimately alter the coordinated time-dependent progression of rod and BC differentiation and synaptic development. These GLE effects were selective for late-born neurons. Although the molecular mechanisms are unknown, alterations in soluble neurotrophic factors and/or their receptors are likely to play a role. Since neurodevelopmental delays and altered synaptic connectivity are associated with neuropsychiatric and behavioral disorders as well as cognitive deficits, future work is needed to determine if similar effects occur in the brains of GLE mice and whether children with GLE experience similar delays in retinal and brain neuronal differentiation and synaptic development.

PLATFORM DEFORMATION PHASE CORRECTION FOR THE AMiBA-13 COPLANAR INTERFEROMETER

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

Liao, Yu-Wei; Lin, Kai-Yang; Huang, Yau-De

2013-05-20

We present a new way to solve the platform deformation problem of coplanar interferometers. The platform of a coplanar interferometer can be deformed due to driving forces and gravity. A deformed platform will induce extra components into the geometric delay of each baseline and change the phases of observed visibilities. The reconstructed images will also be diluted due to the errors of the phases. The platform deformations of The Yuan-Tseh Lee Array for Microwave Background Anisotropy (AMiBA) were modeled based on photogrammetry data with about 20 mount pointing positions. We then used the differential optical pointing error between two opticalmore » telescopes to fit the model parameters in the entire horizontal coordinate space. With the platform deformation model, we can predict the errors of the geometric phase delays due to platform deformation with a given azimuth and elevation of the targets and calibrators. After correcting the phases of the radio point sources in the AMiBA interferometric data, we recover 50%-70% flux loss due to phase errors. This allows us to restore more than 90% of a source flux. The method outlined in this work is not only applicable to the correction of deformation for other coplanar telescopes but also to single-dish telescopes with deformation problems. This work also forms the basis of the upcoming science results of AMiBA-13.« less

Application of InSAR and GIS techniques to ground subsidence assessment in the Nobi Plain, Central Japan.

PubMed

Zheng, Minxue; Fukuyama, Kaoru; Sanga-Ngoie, Kazadi

2013-12-31

Spatial variation and temporal changes in ground subsidence over the Nobi Plain, Central Japan, are assessed using GIS techniques and ground level measurements data taken over this area since the 1970s. Notwithstanding the general slowing trend observed in ground subsidence over the plains, we have detected ground rise at some locations, more likely due to the ground expansion because of recovering groundwater levels and the tilting of the Nobi land mass. The problem of non-availability of upper-air meteorological information, especially the 3-dimensional water vapor distribution, during the JERS-1 observational period (1992-1998) was solved by applying the AWC (analog weather charts) method onto the high-precision GPV-MSM (Grid Point Value of Meso-Scale Model) water-vapor data to find the latter's matching meteorological data. From the selected JERS-1 interferometry pair and the matching GPV-MSM meteorological data, the atmospheric path delay generated by water vapor inhomogeneity was then quantitatively evaluated. A highly uniform spatial distribution of the atmospheric delay, with a maximum deviation of approximately 38 mm in its horizontal distribution was found over the Plain. This confirms the effectiveness of using GPV-MSM data for SAR differential interferometric analysis, and sheds thus some new light on the possibility of improving InSAR analysis results for land subsidence applications.

Application of InSAR and GIS Techniques to Ground Subsidence Assessment in the Nobi Plain, Central Japan

PubMed Central

Zheng, Minxue; Fukuyama, Kaoru; Sanga-Ngoie, Kazadi

2014-01-01

Spatial variation and temporal changes in ground subsidence over the Nobi Plain, Central Japan, are assessed using GIS techniques and ground level measurements data taken over this area since the 1970s. Notwithstanding the general slowing trend observed in ground subsidence over the plains, we have detected ground rise at some locations, more likely due to the ground expansion because of recovering groundwater levels and the tilting of the Nobi land mass. The problem of non-availability of upper-air meteorological information, especially the 3-dimensional water vapor distribution, during the JERS-1 observational period (1992–1998) was solved by applying the AWC (analog weather charts) method onto the high-precision GPV-MSM (Grid Point Value of Meso-Scale Model) water-vapor data to find the latter's matching meteorological data. From the selected JERS-1 interferometry pair and the matching GPV-MSM meteorological data, the atmospheric path delay generated by water vapor inhomogeneity was then quantitatively evaluated. A highly uniform spatial distribution of the atmospheric delay, with a maximum deviation of approximately 38 mm in its horizontal distribution was found over the Plain. This confirms the effectiveness of using GPV-MSM data for SAR differential interferometric analysis, and sheds thus some new light on the possibility of improving InSAR analysis results for land subsidence applications. PMID:24385028

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

PubMed

Bai, Shirong; Skodje, Rex T

2017-08-17

A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

Limitations to Dual Frequency Ionosphere Corrections for Frequency Switched K-Q-Band Observations with the VLBA

NASA Technical Reports Server (NTRS)

Lanyi, Gabor; Gordon, David; Sovers, Ojars J.

2004-01-01

A series of VLBA experiments were carried out at K and Q bands for astrometry and imaging within the KQ VLBI Survey Collaboration. The paired K and Q observations of each source are separated by approximately 3 minutes of time. We investigate the delay effect of the ionosphere between K and Q bands involving the interscan separation. This differential delay effect is intermixed with the differential fluctuation effect of the troposphere.

Genetic differential susceptibility in literacy-delayed children: a randomized controlled trial on emergent literacy in kindergarten.

PubMed

Plak, Rachel D; Kegel, Cornelia A T; Bus, Adriana G

2015-02-01

In this randomized controlled trial, 508 5-year-old kindergarten children participated, of whom 257 were delayed in literacy skills because they belonged to the lowest quartile of a national standard literacy test. We tested the hypothesis that some children are more susceptible to school-entry educational interventions than their peers due to their genetic makeup, and thus whether the dopamine receptor D4 gene moderated intervention effects. Children were randomly assigned to a control condition or one of two interventions involving computer programs tailored to the literacy needs of delayed pupils: Living Letters for alphabetic knowledge and Living Books for text comprehension. Effects of Living Books met the criteria of differential susceptibility. For carriers of the dopamine receptor D4 gene seven-repeat allele (about one-third of the delayed group), the Living Books program was an important addition to the common core curriculum in kindergarten (effect size d = 0.56), whereas the program did not affect the other children (d = -0.09). The same seven-repeat carriers benefited more from Living Letters than did the noncarriers, as reflected in effect sizes of 0.63 and 0.34, respectively, although such differences did not fulfill the statistical criteria for differential susceptibility. The implications of differential susceptibility for education and regarding the crucial question "what works for whom?" are discussed.

Delay time in a single barrier for a movable quantum shutter

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

Hernandez, Alberto

2010-05-15

The transient solution and delay time for a {delta} potential scatterer with a movable quantum shutter is calculated by solving analytically the time-dependent Schroedinger equation. The delay time is analyzed as a function of the distance between the shutter and the potential barrier and also as a function of the distance between the potential barrier and the detector. In both cases, it is found that the delay time exhibits a dynamical behavior and that it tends to a saturation value {Delta}t{sub sat} in the limit of very short distances, which represents the maximum delay produced by the potential barrier nearmore » the interaction region. The phase time {tau}{sub {theta},} on the other hand, is not an appropriate time scale for measuring the time delay near the interaction region, except if the shutter is moved far away from the potential. The role played by the antibound state of the system on the behavior of the delay time is also discussed.« less

Quality of service routing in the differentiated services framework

NASA Astrophysics Data System (ADS)

Oliveira, Marilia C.; Melo, Bruno; Quadros, Goncalo; Monteiro, Edmundo

2001-02-01

In this paper we present a quality of service routing strategy for network where traffic differentiation follows the class-based paradigm, as in the Differentiated Services framework. This routing strategy is based on a metric of quality of service. This metric represents the impact that delay and losses verified at each router in the network have in application performance. Based on this metric, it is selected a path for each class according to the class sensitivity to delay and losses. The distribution of the metric is triggered by a relative criterion with two thresholds, and the values advertised are the moving average of the last values measured.

New stability conditions for mixed linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Dung, Nguyen Tien

2013-08-01

For the mixed Levin-Nohel integro-differential equation, we obtain new necessary and sufficient conditions of asymptotic stability. These results improve those obtained by Becker and Burton ["Stability, fixed points and inverse of delays," Proc. - R. Soc. Edinburgh, Sect. A 136, 245-275 (2006)], 10.1017/S0308210500004546 and Jin and Luo ["Stability of an integro-differential equation," Comput. Math. Appl. 57(7), 1080-1088 (2009)], 10.1016/j.camwa.2009.01.006 when b(t) = 0 and supplement the 3/2-stability theorem when a(t, s) = 0. In addition, the case of the equations with several delays is discussed as well.

Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Cao, Jinde; Song, Qiankun

2006-07-01

In this paper, the exponential stability problem is investigated for a class of Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. By using the analysis method, inequality technique and the properties of an M-matrix, several novel sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. Moreover, the exponential convergence rate is estimated. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions and differentiability of the time-varying delays are removed. Two examples with their simulations are given to show the effectiveness of the obtained results.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

NASA Astrophysics Data System (ADS)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Pulmonary MRA: differentiation of pulmonary embolism from truncation artefact.

PubMed

Bannas, Peter; Schiebler, Mark L; Motosugi, Utaroh; François, Christopher J; Reeder, Scott B; Nagle, Scott K

2014-08-01

Truncation artefact (Gibbs ringing) causes central signal drop within vessels in pulmonary magnetic resonance angiography (MRA) that can be mistaken for emboli, reducing diagnostic accuracy for pulmonary embolism (PE). We propose a quantitative approach to differentiate truncation artefact from PE. Twenty-eight patients who underwent pulmonary computed tomography angiography (CTA) for suspected PE were recruited for pulmonary MRA. Signal intensity drops within pulmonary arteries that persisted on both arterial-phase and delayed-phase MRA were identified. The percent signal loss between the vessel lumen and central drop was measured. CTA served as the reference standard for presence of pulmonary emboli. A total of 65 signal intensity drops were identified on MRA. Of these, 48 (74%) were artefacts and 17 (26%) were PE, as confirmed by CTA. Truncation artefacts had a significantly lower median signal drop than PE on both arterial-phase (26% [range 12-58%] vs. 85% [range 53-91%]) and delayed-phase MRA (26% [range 11-55%] vs. 77% [range 47-89%]), p < 0.0001 for both. Receiver operating characteristic (ROC) analyses revealed a threshold value of 51% (arterial phase) and 47% signal drop (delayed phase) to differentiate between truncation artefact and PE with 100% sensitivity and greater than 90% specificity. Quantitative signal drop is an objective tool to help differentiate truncation artefact and pulmonary embolism in pulmonary MRA. • Inexperienced readers may mistake truncation artefacts for emboli on pulmonary MRA • Pulmonary emboli have non-uniform signal drop • 51% (arterial phase) and 47% (delayed phase) cut-off differentiates truncation artefact from PE • Quantitative signal drop measurement enables more accurate pulmonary embolism diagnosis with MRA.

Dynamics of the mean signal amplitude of a crystal oscillator with a nonlinear resonator and low drives

NASA Astrophysics Data System (ADS)

Shmaliy, Yuriy S.; Rosales, Juan

2004-09-01

Dynamics of the mean amplitude of oscillations of a crystal oscillator with a linear feedback is outlined for low drives when the losses (friction) of a resonator become large and nonlinear after a long storage. The drive-level-dependence (DLD) of the crystal resonator losses is assumed to change inversely to the piezoelectric current. A stochastic differential equation for the mean amplitude is derived and solved in a sense of Ito. The development and attenuation processes are learned and it is shown that attenuation finishes at some non-zero level associated with the effect termed "sleeping sickness." The critical value of the friction is calculated and the conditions are discussed to avoid attenuation. Based upon, we show in that (1) if the value of the DLD coefficient of the resonator losses ranges below the critical point, the effect occurs primarilly in a delay of self-excitation; (2) contrary, noise drives the crystal oscillator.

Robust output feedback H∞ control for networked control systems based on the occurrence probabilities of time delays

NASA Astrophysics Data System (ADS)

Guo, Chenyu; Zhang, Weidong; Bao, Jie

2012-02-01

This article is concerned with the problem of robust H ∞ output feedback control for a kind of networked control systems with time-varying network-induced delays. Instead of using boundaries of time delays to represent all time delays, the occurrence probability of each time delay is considered in H∞ stability analysis and stabilisation. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is stochastically stable for the zero disturbance input and also simultaneously achieves a prescribed H∞ performance level. It is shown that less conservativeness is obtained. A set of linear matrix inequalities is given to solve the corresponding controller design problem. An example is provided to show the effectiveness and applicability of the proposed method.

The Effect of Strategy on Problem Solving: An FMRI Study

ERIC Educational Resources Information Center

Newman, Sharlene D.; Pruce, Benjamin; Rusia, Akash; Burns, Thomas, Jr.

2010-01-01

fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

Differential contributions of executive and episodic memory functions to problem solving in younger and older adults.

PubMed

Vandermorris, Susan; Sheldon, Signy; Winocur, Gordon; Moscovitch, Morris

2013-11-01

The relationship of higher order problem solving to basic neuropsychological processes likely depends on the type of problems to be solved. Well-defined problems (e.g., completing a series of errands) may rely primarily on executive functions. Conversely, ill-defined problems (e.g., navigating socially awkward situations) may, in addition, rely on medial temporal lobe (MTL) mediated episodic memory processes. Healthy young (N = 18; M = 19; SD = 1.3) and old (N = 18; M = 73; SD = 5.0) adults completed a battery of neuropsychological tests of executive and episodic memory function, and experimental tests of problem solving. Correlation analyses and age group comparisons demonstrated differential contributions of executive and autobiographical episodic memory function to well-defined and ill-defined problem solving and evidence for an episodic simulation mechanism underlying ill-defined problem solving efficacy. Findings are consistent with the emerging idea that MTL-mediated episodic simulation processes support the effective solution of ill-defined problems, over and above the contribution of frontally mediated executive functions. Implications for the development of intervention strategies that target preservation of functional independence in older adults are discussed.

Direct measurement of group delay with joint time-frequency analysis of a white-light spectral interferogram.

PubMed

Deng, Yuqiang; Yang, Weijian; Zhou, Chun; Wang, Xi; Tao, Jun; Kong, Weipeng; Zhang, Zhigang

2008-12-01

We propose and demonstrate an analysis method to directly extract the group delay rather than the phase from the white-light spectral interferogram. By the joint time-frequency analysis technique, group delay is directly read from the ridge of wavelet transform, and group-delay dispersion is easily obtained by additional differentiation. The technique shows reasonable potential for the characterization of ultra-broadband chirped mirrors.

Lateral Orbitofrontal Cortical Modulation on the Medial Prefrontal Cortex-Amygdala Pathway: Differential Regulation of Intra-Amygdala GABAA and GABAB Receptors.

PubMed

Chang, Chun-Hui

2017-07-01

The basolateral complex of the amygdala receives inputs from neocortical areas, including the medial prefrontal cortex and lateral orbitofrontal cortex. Earlier studies have shown that lateral orbitofrontal cortex activation exerts an inhibitory gating on medial prefrontal cortex-amygdala information flow. Here we examined the individual role of GABAA and GABAB receptors in this process. In vivo extracellular single-unit recordings were done in anesthetized rats. We searched amygdala neurons that fire in response to medial prefrontal cortex activation, tested lateral orbitofrontal cortex gating at different delays (lateral orbitofrontal cortex-medial prefrontal cortex delays: 25, 50, 100, 250, 500, and 1000 milliseconds), and examined differential contribution of GABAA and GABAB receptors with iontophoresis. Relative to baseline, lateral orbitofrontal cortex stimulation exerted an inhibitory modulatory gating on the medial prefrontal cortex-amygdala pathway and was effective up to a long delay of 500 ms (long-delay latencies at 100, 250, and 500 milliseconds). Moreover, blockade of intra-amygdala GABAA receptors with bicuculline abolished the lateral orbitofrontal cortex inhibitory gating at both short- (25 milliseconds) and long-delay (100 milliseconds) intervals, while blockade of GABAB receptors with saclofen reversed the inhibitory gating at long delay (100 milliseconds) only. Among the majority of the neurons examined (8 of 9), inactivation of either GABAA or GABAB receptors during baseline did not change evoked probability per se, suggesting that local feed-forward inhibitory mechanism is pathway specific. Our results suggest that the effect of lateral orbitofrontal cortex inhibitory modulatory gating was effective up to 500 milliseconds and that intra-amygdala GABAA and GABAB receptors differentially modulate the short- and long-delay lateral orbitofrontal cortex inhibitory gating on the medial prefrontal cortex-amygdala pathway. © The Author 2017. Published by Oxford University Press on behalf of CINP.

The politics of insight

PubMed Central

Salvi, Carola; Cristofori, Irene; Grafman, Jordan; Beeman, Mark

2016-01-01

Previous studies showed that liberals and conservatives differ in cognitive style. Liberals are more flexible, and tolerant of complexity and novelty, whereas conservatives are more rigid, are more resistant to change, and prefer clear answers. We administered a set of compound remote associate problems, a task extensively used to differentiate problem-solving styles (via insight or analysis). Using this task, several researches have proven that self-reports, which differentiate between insight and analytic problem-solving, are reliable and are associated with two different neural circuits. In our research we found that participants self-identifying with distinct political orientations demonstrated differences in problem-solving strategy. Liberals solved significantly more problems via insight instead of in a step-by-step analytic fashion. Our findings extend previous observations that self-identified political orientations reflect differences in cognitive styles. More specifically, we show that type of political orientation is associated with problem-solving strategy. The data converge with previous neurobehavioural and cognitive studies indicating a link between cognitive style and the psychological mechanisms that mediate political beliefs. PMID:26810954

The politics of insight.

PubMed

Salvi, Carola; Cristofori, Irene; Grafman, Jordan; Beeman, Mark

2016-01-01

Previous studies showed that liberals and conservatives differ in cognitive style. Liberals are more flexible, and tolerant of complexity and novelty, whereas conservatives are more rigid, are more resistant to change, and prefer clear answers. We administered a set of compound remote associate problems, a task extensively used to differentiate problem-solving styles (via insight or analysis). Using this task, several researches have proven that self-reports, which differentiate between insight and analytic problem-solving, are reliable and are associated with two different neural circuits. In our research we found that participants self-identifying with distinct political orientations demonstrated differences in problem-solving strategy. Liberals solved significantly more problems via insight instead of in a step-by-step analytic fashion. Our findings extend previous observations that self-identified political orientations reflect differences in cognitive styles. More specifically, we show that type of political orientation is associated with problem-solving strategy. The data converge with previous neurobehavioural and cognitive studies indicating a link between cognitive style and the psychological mechanisms that mediate political beliefs.

Recovery after Work: The Role of Work Beliefs in the Unwinding Process

PubMed Central

Zoupanou, Zoe; Cropley, Mark; Rydstedt, Leif W.

2013-01-01

According to the Effort-Recovery model, mental or physical detachment from work is an important mechanism of work related recovery, as delayed recovery has been associated with range of negative health symptoms. In this paper, we examine whether recovery from work (in the form of mentally disengagement from work) is affected by the concept of ‘work ethic’, which refers to beliefs workers hold about their work and leisure and the effects of experiencing interruptions at work. Two indices of post-work recovery were utilized: problem solving pondering and psychological detachment. The study was conducted with 310 participants employed from diverse occupational sectors. Main effects of positive and negative appraisal of work interruption and beliefs were analysed using mediated and moderated regression analysis on problem-solving pondering and detachment. Weakened belief in wasted time as a partial mediator, reduced problem-solving pondering post work when interruptions were appraised as positive, and a high evaluation of leisure partially mediated problem-solving pondering when interruptions were appraised as positive. The results also showed that a high evaluation of centrality of work and leisure moderated the effect of negative appraisal of work interruption on elevated problem-solving pondering. Positive appraisal of work interruption was related to problem-solving pondering, and the strength of this association was further moderated by a strong belief in delay of gratification. In addition, employees' positive appraisal of work interruption was related to work detachment, and the strength of this association was further moderated by strong beliefs in hard work and self-reliance. These findings are discussed in terms of their theoretical and practical implications for employees who are strongly influenced by such work beliefs. PMID:24349060

Recovery after work: the role of work beliefs in the unwinding process.

PubMed

Zoupanou, Zoe; Cropley, Mark; Rydstedt, Leif W

2013-01-01

According to the Effort-Recovery model, mental or physical detachment from work is an important mechanism of work related recovery, as delayed recovery has been associated with range of negative health symptoms. In this paper, we examine whether recovery from work (in the form of mentally disengagement from work) is affected by the concept of 'work ethic', which refers to beliefs workers hold about their work and leisure and the effects of experiencing interruptions at work. Two indices of post-work recovery were utilized: problem solving pondering and psychological detachment. The study was conducted with 310 participants employed from diverse occupational sectors. Main effects of positive and negative appraisal of work interruption and beliefs were analysed using mediated and moderated regression analysis on problem-solving pondering and detachment. Weakened belief in wasted time as a partial mediator, reduced problem-solving pondering post work when interruptions were appraised as positive, and a high evaluation of leisure partially mediated problem-solving pondering when interruptions were appraised as positive. The results also showed that a high evaluation of centrality of work and leisure moderated the effect of negative appraisal of work interruption on elevated problem-solving pondering. Positive appraisal of work interruption was related to problem-solving pondering, and the strength of this association was further moderated by a strong belief in delay of gratification. In addition, employees' positive appraisal of work interruption was related to work detachment, and the strength of this association was further moderated by strong beliefs in hard work and self-reliance. These findings are discussed in terms of their theoretical and practical implications for employees who are strongly influenced by such work beliefs.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays.

PubMed

Wan, Peng; Jian, Jigui

2018-03-01

This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

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

PubMed

Benhammouda, Brahim

2016-01-01

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

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Response of an oscillatory differential delay equation to a single stimulus.

PubMed

Mackey, Michael C; Tyran-Kamińska, Marta; Walther, Hans-Otto

2017-04-01

Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case.

New optical frequency domain differential mode delay measurement method for a multimode optical fiber.

PubMed

Ahn, T; Moon, S; Youk, Y; Jung, Y; Oh, K; Kim, D

2005-05-30

A novel mode analysis method and differential mode delay (DMD) measurement technique for a multimode optical fiber based on optical frequency domain reflectometry has been proposed for the first time. We have used a conventional OFDR with a tunable external cavity laser and a Michelson interferometer. A few-mode optical multimode fiber was prepared to test our proposed measurement technique. We have also compared the OFDR measurement results with those obtained using a traditional time-domain measurement method.

LiDAR-IMU Time Delay Calibration Based on Iterative Closest Point and Iterated Sigma Point Kalman Filter.

PubMed

Liu, Wanli

2017-03-08

The time delay calibration between Light Detection and Ranging (LiDAR) and Inertial Measurement Units (IMUs) is an essential prerequisite for its applications. However, the correspondences between LiDAR and IMU measurements are usually unknown, and thus cannot be computed directly for the time delay calibration. In order to solve the problem of LiDAR-IMU time delay calibration, this paper presents a fusion method based on iterative closest point (ICP) and iterated sigma point Kalman filter (ISPKF), which combines the advantages of ICP and ISPKF. The ICP algorithm can precisely determine the unknown transformation between LiDAR-IMU; and the ISPKF algorithm can optimally estimate the time delay calibration parameters. First of all, the coordinate transformation from the LiDAR frame to the IMU frame is realized. Second, the measurement model and time delay error model of LiDAR and IMU are established. Third, the methodology of the ICP and ISPKF procedure is presented for LiDAR-IMU time delay calibration. Experimental results are presented that validate the proposed method and demonstrate the time delay error can be accurately calibrated.

New algorithms for solving high even-order differential equations using third and fourth Chebyshev-Galerkin methods

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.; Bassuony, M. A.

2013-03-01

This paper is concerned with spectral Galerkin algorithms for solving high even-order two point boundary value problems in one dimension subject to homogeneous and nonhomogeneous boundary conditions. The proposed algorithms are extended to solve two-dimensional high even-order differential equations. The key to the efficiency of these algorithms is to construct compact combinations of Chebyshev polynomials of the third and fourth kinds as basis functions. The algorithms lead to linear systems with specially structured matrices that can be efficiently inverted. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithms, and some comparisons with some other methods are made.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

PubMed

Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad

2014-11-01

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Differential Effects of Methylphenidate on Problem Solving in Adults with ADHD

ERIC Educational Resources Information Center

Tucha, Lara; Tucha, Oliver; Sontag, Thomas A.; Stasik, Dorota; Laufkotter, Rainer; Lange, Klaus W.

2011-01-01

Objective: Two studies were performed to assess both divergent and convergent thinking in adults with ADHD. Method: The first study compared the problem-solving abilities of healthy participants (N = 144) and unmedicated adults with ADHD (N = 144). In the second study, problem-solving abilities of adults with diagnosed ADHD (N = 22) were examined…

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

NASA Astrophysics Data System (ADS)

Wan, Li; Zhou, Qinghua

2007-10-01

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.

Global Hopf bifurcation analysis on a BAM neural network with delays

NASA Astrophysics Data System (ADS)

Sun, Chengjun; Han, Maoan; Pang, Xiaoming

2007-01-01

A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.

Super-Latent Inhibition of Conditioned Taste Preference with a Long Retention Interval

ERIC Educational Resources Information Center

De la Casa, L. G.; Marquez, R.; Lubow, R. E.

2009-01-01

A long delay inserted between conditioning and test phases of a 3-stage Latent Inhibition (LI) procedure produces differential effects on LI depending on the delay context. Thus, enhanced LI has been obtained when the delay is spent in a context that is different from the remaining experimental contexts, but not when it is the same. The present…

Comment on “Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems”

NASA Astrophysics Data System (ADS)

Pan, Yongping; Huang, Daoping

2011-03-01

In this comment, we point out the inappropriateness of Theorem 1 in the article [Tsung-Chih Lin, Mehdi Roopaei. Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems. Commun Nonlinear Sci Numer Simulat 2010;15:4065-75]. For solving this problem, some formular mistakes are corrected and novel parameter adaptive laws of interval type-2 fuzzy neural network system are given.

Optimal Time Advance In Terminal Area Arrivals: Throughput vs. Fuel Savings

NASA Technical Reports Server (NTRS)

Sadovsky, Alexander V .; Swenson, Harry N.; Haskell, William B.; Rakas, Jasenka

2011-01-01

The current operational practice in scheduling air traffic arriving at an airport is to adjust flight schedules by delay, i.e. a postponement of an aircrafts arrival at a scheduled location, to manage safely the FAA-mandated separation constraints between aircraft. To meet the observed and forecast growth in traffic demand, however, the practice of time advance (speeding up an aircraft toward a scheduled location) is envisioned for future operations as a practice additional to delay. Time advance has two potential advantages. The first is the capability to minimize, or at least reduce, the excess separation (the distances between pairs of aircraft immediately in-trail) and thereby to increase the throughput of the arriving traffic. The second is to reduce the total traffic delay when the traffic sample is below saturation density. A cost associated with time advance is the fuel expenditure required by an aircraft to speed up. We present an optimal control model of air traffic arriving in a terminal area and solve it using the Pontryagin Maximum Principle. The admissible controls allow time advance, as well as delay, some of the way. The cost function reflects the trade-off between minimizing two competing objectives: excess separation (negatively correlated with throughput) and fuel burn. A number of instances are solved using three different methods, to demonstrate consistency of solutions.

Self-regulatory speech during planning and problem-solving in children with SLI and their typically developing peers.

PubMed

Abdul Aziz, Safiyyah; Fletcher, Janet; Bayliss, Donna M

2017-05-01

Past research with children with specific language impairment (SLI) has shown them to have poorer planning and problem-solving ability, and delayed self-regulatory speech (SRS) relative to their typically developing (TD) peers. However, the studies are few in number and are restricted in terms of the number and age range of participants, which limits our understanding of the nature and extent of any delays. Moreover, no study has examined the performance of a significant subset of children with SLI, those who have hyperactive and inattentive behaviours. This cross-sectional study aimed to compare the performance of young children with SLI (aged 4-7 years) with that of their TD peers on a planning and problem-solving task and to examine the use of SRS while performing the task. Within each language group, the performance of children with and without hyperactive and inattentive behaviours was further examined. Children with SLI (n = 91) and TD children (n = 81), with and without hyperactive and inattentive behaviours across the three earliest school years (Kindergarten, Preprimary and Year 1) were video-taped while they completed the Tower of London (TOL), a planning and problem-solving task. Their recorded speech was coded and analysed to look at differences in SRS and its relation to TOL performance across the groups. Children with SLI scored lower on the TOL than TD children. Additionally, children with hyperactive and inattentive behaviours performed worse than those without hyperactive and inattentive behaviours, but only in the SLI group. This suggests that children with SLI with hyperactive and inattentive behaviours experience a double deficit. Children with SLI produced less inaudible muttering than TD children, and showed no reduction in social speech across the first three years of school. Finally, for children with SLI, a higher percentage performed better on the TOL when they used SRS than when they did not. The results point towards a significant delay in the development and internalization of SRS in the SLI group, which should be taken into account when considering the planning and problem-solving of young children with SLI. © 2016 Royal College of Speech and Language Therapists.

Batch Scheduling for Hybrid Assembly Differentiation Flow Shop to Minimize Total Actual Flow Time

NASA Astrophysics Data System (ADS)

Maulidya, R.; Suprayogi; Wangsaputra, R.; Halim, A. H.

2018-03-01

A hybrid assembly differentiation flow shop is a three-stage flow shop consisting of Machining, Assembly and Differentiation Stages and producing different types of products. In the machining stage, parts are processed in batches on different (unrelated) machines. In the assembly stage, each part of the different parts is assembled into an assembly product. Finally, the assembled products will further be processed into different types of final products in the differentiation stage. In this paper, we develop a batch scheduling model for a hybrid assembly differentiation flow shop to minimize the total actual flow time defined as the total times part spent in the shop floor from the arrival times until its due date. We also proposed a heuristic algorithm for solving the problems. The proposed algorithm is tested using a set of hypothetic data. The solution shows that the algorithm can solve the problems effectively.

Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation. © 2011 American Institute of Physics

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval

NASA Astrophysics Data System (ADS)

Shi, Xiangyun; Kuang, Yang; Makroglou, Athena; Mokshagundam, Sriprakash; Li, Jiaxu

2017-11-01

Type 2 diabetes mellitus (T2DM) has become prevalent pandemic disease in view of the modern life style. Both diabetic population and health expenses grow rapidly according to American Diabetes Association. Detecting the potential onset of T2DM is an essential focal point in the research of diabetes mellitus. The intravenous glucose tolerance test (IVGTT) is an effective protocol to determine the insulin sensitivity, glucose effectiveness, and pancreatic β-cell functionality, through the analysis and parameter estimation of a proper differential equation model. Delay differential equations have been used to study the complex physiological phenomena including the glucose and insulin regulations. In this paper, we propose a novel approach to model the time delay in IVGTT modeling. This novel approach uses two parameters to simulate not only both discrete time delay and distributed time delay in the past interval, but also the time delay distributed in a past sub-interval. Normally, larger time delay, either a discrete or a distributed delay, will destabilize the system. However, we find that time delay over a sub-interval might not. We present analytically some basic model properties, which are desirable biologically and mathematically. We show that this relatively simple model provides good fit to fluctuating patient data sets and reveals some intriguing dynamics. Moreover, our numerical simulation results indicate that our model may remove the defect in well known Minimal Model, which often overestimates the glucose effectiveness index.

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This 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 Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

Optimization of MLS receivers for multipath environments

NASA Technical Reports Server (NTRS)

Mcalpine, G. A.; Irwin, S. H.; NELSON; Roleyni, G.

1977-01-01

Optimal design studies of MLS angle-receivers and a theoretical design-study of MLS DME-receivers are reported. The angle-receiver results include an integration of the scan data processor and tracking filter components of the optimal receiver into a unified structure. An extensive simulation study comparing the performance of the optimal and threshold receivers in a wide variety of representative dynamical interference environments was made. The optimal receiver was generally superior. A simulation of the performance of the threshold and delay-and-compare receivers in various signal environments was performed. An analysis of combined errors due to lateral reflections from vertical structures with small differential path delays, specular ground reflections with neglible differential path delays, and thermal noise in the receivers is provided.

Two Different Approaches to Nonzero-Sum Stochastic Differential Games

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

Rainer, Catherine

2007-06-15

We make the link between two approaches to Nash equilibria for nonzero-sum stochastic differential games: the first one using backward stochastic differential equations and the second one using strategies with delay. We prove that, when both exist, the two notions of Nash equilibria coincide.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks

NASA Astrophysics Data System (ADS)

Shirvany, Yazdan; Hayati, Mohsen; Moradian, Rostam

2008-12-01

We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems.

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1994-01-01

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

An Efficient Offloading Scheme For MEC System Considering Delay and Energy Consumption

NASA Astrophysics Data System (ADS)

Sun, Yanhua; Hao, Zhe; Zhang, Yanhua

2018-01-01

With the increasing numbers of mobile devices, mobile edge computing (MEC) which provides cloud computing capabilities proximate to mobile devices in 5G networks has been envisioned as a promising paradigm to enhance users experience. In this paper, we investigate a joint consideration of delay and energy consumption offloading scheme (JCDE) for MEC system in 5G heterogeneous networks. An optimization is formulated to minimize the delay as well as energy consumption of the offloading system, which the delay and energy consumption of transmitting and calculating tasks are taken into account. We adopt an iterative greedy algorithm to solve the optimization problem. Furthermore, simulations were carried out to validate the utility and effectiveness of our proposed scheme. The effect of parameter variations on the system is analysed as well. Numerical results demonstrate delay and energy efficiency promotion of our proposed scheme compared with another paper’s scheme.

Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication.

PubMed

Song, Qiang; Liu, Fang; Wen, Guanghui; Cao, Jinde; Yang, Xinsong

2017-04-24

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

Delayed Accumulation of H3K27me3 on Nascent DNA Is Essential for Recruitment of Transcription Factors at Early Stages of Stem Cell Differentiation.

PubMed

Petruk, Svetlana; Cai, Jingli; Sussman, Robyn; Sun, Guizhi; Kovermann, Sina K; Mariani, Samanta A; Calabretta, Bruno; McMahon, Steven B; Brock, Hugh W; Iacovitti, Lorraine; Mazo, Alexander

2017-04-20

Recruitment of transcription factors (TFs) to repressed genes in euchromatin is essential to activate new transcriptional programs during cell differentiation. However, recruitment of all TFs, including pioneer factors, is impeded by condensed H3K27me3-containing chromatin. Single-cell and gene-specific analyses revealed that, during the first hours of induction of differentiation of mammalian embryonic stem cells (ESCs), accumulation of the repressive histone mark H3K27me3 is delayed after DNA replication, indicative of a decondensed chromatin structure in all regions of the replicating genome. This delay provides a critical "window of opportunity" for recruitment of lineage-specific TFs to DNA. Increasing the levels of post-replicative H3K27me3 or preventing S phase entry inhibited recruitment of new TFs to DNA and significantly blocked cell differentiation. These findings suggest that recruitment of lineage-specifying TFs occurs soon after replication and is facilitated by a decondensed chromatin structure. This insight may explain the developmental plasticity of stem cells and facilitate their exploitation for therapeutic purposes. Copyright © 2017 Elsevier Inc. All rights reserved.

Anti-synchronization control of BAM memristive neural networks with multiple proportional delays and stochastic perturbations

NASA Astrophysics Data System (ADS)

Wang, Weiping; Yuan, Manman; Luo, Xiong; Liu, Linlin; Zhang, Yao

2018-01-01

Proportional delay is a class of unbounded time-varying delay. A class of bidirectional associative memory (BAM) memristive neural networks with multiple proportional delays is concerned in this paper. First, we propose the model of BAM memristive neural networks with multiple proportional delays and stochastic perturbations. Furthermore, by choosing suitable nonlinear variable transformations, the BAM memristive neural networks with multiple proportional delays can be transformed into the BAM memristive neural networks with constant delays. Based on the drive-response system concept, differential inclusions theory and Lyapunov stability theory, some anti-synchronization criteria are obtained. Finally, the effectiveness of proposed criteria are demonstrated through numerical examples.

Building Flexible User Interfaces for Solving PDEs

NASA Astrophysics Data System (ADS)

Logg, Anders; Wells, Garth N.

2010-09-01

FEniCS is a collection of software tools for the automated solution of differential equations by finite element methods. In this note, we describe how FEniCS can be used to solve a simple nonlinear model problem with varying levels of automation. At one extreme, FEniCS provides tools for the fully automated and adaptive solution of nonlinear partial differential equations. At the other extreme, FEniCS provides a range of tools that allow the computational scientist to experiment with novel solution algorithms.

The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

NASA Technical Reports Server (NTRS)

Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

1988-01-01

This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

Variational estimate method for solving autonomous ordinary differential equations

NASA Astrophysics Data System (ADS)

Mungkasi, Sudi

2018-04-01

In this paper, we propose a method for solving first-order autonomous ordinary differential equation problems using a variational estimate formulation. The variational estimate is constructed with a Lagrange multiplier which is chosen optimally, so that the formulation leads to an accurate solution to the problem. The variational estimate is an integral form, which can be computed using a computer software. As the variational estimate is an explicit formula, the solution is easy to compute. This is a great advantage of the variational estimate formulation.

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Synchronization in networks with heterogeneous coupling delays

NASA Astrophysics Data System (ADS)

Otto, Andreas; Radons, Günter; Bachrathy, Dániel; Orosz, Gábor

2018-01-01

Synchronization in networks of identical oscillators with heterogeneous coupling delays is studied. A decomposition of the network dynamics is obtained by block diagonalizing a newly introduced adjacency lag operator which contains the topology of the network as well as the corresponding coupling delays. This generalizes the master stability function approach, which was developed for homogenous delays. As a result the network dynamics can be analyzed by delay differential equations with distributed delay, where different delay distributions emerge for different network modes. Frequency domain methods are used for the stability analysis of synchronized equilibria and synchronized periodic orbits. As an example, the synchronization behavior in a system of delay-coupled Hodgkin-Huxley neurons is investigated. It is shown that the parameter regions where synchronized periodic spiking is unstable expand when increasing the delay heterogeneity.

Stuck in the moment: cognitive inflexibility in preschoolers following an extended time period

PubMed Central

Garcia, Carolina; Dick, Anthony Steven

2013-01-01

Preschoolers display surprising inflexibility in problem solving, but seem to approach new challenges with a fresh slate. We provide evidence that while the former is true the latter is not. Here, we examined whether brief exposure to stimuli can influence children’s problem solving following several weeks after first exposure to the stimuli. We administered a common executive function task, the Dimensional Change Card Sort, which requires children to sort picture cards by one dimension (e.g., color) and then switch to sort the same cards by a conflicting dimension (e.g., shape). After a week or after a month delay, we administered the second rule again. We found that 70% of preschoolers continued to sort by the initial sorting rule, even after a month delay, and even though they are explicitly told what to do. We discuss implications for theories of executive function development, and for classroom learning. PMID:24399978

Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach.

PubMed

Dharani, S; Rakkiyappan, R; Cao, Jinde; Alsaedi, Ahmed

2017-08-01

This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.

Intrinsic delay of permeable base transistor

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

Chen, Wenchao; Guo, Jing; So, Franky

2014-07-28

Permeable base transistors (PBTs) fabricated by vacuum deposition or solution process have the advantages of easy fabrication and low power operation and are a promising device structure for flexible electronics. Intrinsic delay of PBT, which characterizes the speed of the transistor, is investigated by solving the three-dimensional Poisson equation and drift-diffusion equation self-consistently using finite element method. Decreasing the emitter thickness lowers the intrinsic delay by improving on-current, and a thinner base is also preferred for low intrinsic delay because of fewer carriers in the base region at off-state. The intrinsic delay exponentially decreases as the emitter contact Schottky barriermore » height decreases, and it linearly depends on the carrier mobility. With an optimized emitter contact barrier height and device geometry, a sub-nano-second intrinsic delay can be achieved with a carrier mobility of ∼10 cm{sup 2}/V/s obtainable in solution processed indium gallium zinc oxide, which indicates the potential of solution processed PBTs for GHz operations.« less

Timing group delay and differential code bias corrections for BeiDou positioning

NASA Astrophysics Data System (ADS)

Guo, Fei; Zhang, Xiaohong; Wang, Jinling

2015-05-01

This article first clearly figures out the relationship between parameters of timing group delay (TGD) and differential code bias (DCB) for BDS, and demonstrates the equivalence of TGD and DCB correction models combining theory with practice. The TGD/DCB correction models have been extended to various occasions for BDS positioning, and such models have been evaluated by real triple-frequency datasets. To test the effectiveness of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both standard point positioning (SPP) and precise point positioning (PPP) tests are carried out for BDS signals with different schemes. Furthermore, the influence of differential code biases on BDS positioning estimates such as coordinates, receiver clock biases, tropospheric delays and carrier phase ambiguities is investigated comprehensively. Comparative analysis show that the unmodeled differential code biases degrade the performance of BDS SPP by a factor of two or more, whereas the estimates of PPP are subject to varying degrees of influences. For SPP, the accuracy of dual-frequency combinations is slightly worse than that of single-frequency, and they are much more sensitive to the differential code biases, particularly for the B2B3 combination. For PPP, the uncorrected differential code biases are mostly absorbed into the receiver clock bias and carrier phase ambiguities and thus resulting in a much longer convergence time. Even though the influence of the differential code biases could be mitigated over time and comparable positioning accuracy could be achieved after convergence, it is suggested to properly handle with the differential code biases since it is vital for PPP convergence and integer ambiguity resolution.

Estimation of coupling between time-delay systems from time series

NASA Astrophysics Data System (ADS)

Prokhorov, M. D.; Ponomarenko, V. I.

2005-07-01

We propose a method for estimation of coupling between the systems governed by scalar time-delay differential equations of the Mackey-Glass type from the observed time series data. The method allows one to detect the presence of certain types of linear coupling between two time-delay systems, to define the type, strength, and direction of coupling, and to recover the model equations of coupled time-delay systems from chaotic time series corrupted by noise. We verify our method using both numerical and experimental data.

HAM2D: 2D Shearing Box Model

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; Guan, Xiaoyue

2012-10-01

HAM solves non-relativistic hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HAM has been configured to solve the magnetohydrodynamic equations of motion in axisymmetry to evolve a shearing box model.

Social Problem-Solving Skills of Children in Terms of Maternal Acceptance-Rejection Levels

ERIC Educational Resources Information Center

Tepeli, Kezban; Yilmaz, Elif

2013-01-01

This study was conducted to find an answer to the question of "Do social problem-solving skills of 5-6 years old children differentiate depending on the levels of maternal acceptance rejection?" The participants of the study included 359 5-6 years old children and their mothers. Wally Social Problem-Solving Test and PARQ (Parental…

The use of spectral methods in bidomain studies.

PubMed

Trayanova, N; Pilkington, T

1992-01-01

A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

Solving Differential Equations Using Modified Picard Iteration

ERIC Educational Resources Information Center

Robin, W. A.

2010-01-01

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

A Randomized Trial of the Effects of Schema-Based Instruction on Proportional Problem-Solving for Students With Mathematics Problem-Solving Difficulties.

PubMed

Jitendra, Asha K; Harwell, Michael R; Dupuis, Danielle N; Karl, Stacy R

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.

Radar wideband digital beamforming based on time delay and phase compensation

NASA Astrophysics Data System (ADS)

Fu, Wei; Jiang, Defu

2018-07-01

In conventional phased array radars, analogue time delay devices and phase shifters have been used for wideband beamforming. These methods suffer from insertion losses, gain mismatches and delay variations, and they occupy a large chip area. To solve these problems, a compact architecture of digital array antennas based on subarrays was considered. In this study, the receiving beam patterns of wideband linear frequency modulation (LFM) signals were constructed by applying analogue stretch processing via mixing with delayed reference signals at the subarray level. Subsequently, narrowband digital time delaying and phase compensation of the tone signals were implemented with reduced arithmetic complexity. Due to the differences in amplitudes, phases and time delays between channels, severe performance degradation of the beam patterns occurred without corrections. To achieve good beamforming performance, array calibration was performed in each channel to adjust the amplitude, frequency and phase of the tone signal. Using a field-programmable gate array, wideband LFM signals and finite impulse response filters with continuously adjustable time delays were implemented in a polyphase structure. Simulations and experiments verified the feasibility and effectiveness of the proposed digital beamformer.

Genetic network inference as a series of discrimination tasks.

PubMed

Kimura, Shuhei; Nakayama, Satoshi; Hatakeyama, Mariko

2009-04-01

Genetic network inference methods based on sets of differential equations generally require a great deal of time, as the equations must be solved many times. To reduce the computational cost, researchers have proposed other methods for inferring genetic networks by solving sets of differential equations only a few times, or even without solving them at all. When we try to obtain reasonable network models using these methods, however, we must estimate the time derivatives of the gene expression levels with great precision. In this study, we propose a new method to overcome the drawbacks of inference methods based on sets of differential equations. Our method infers genetic networks by obtaining classifiers capable of predicting the signs of the derivatives of the gene expression levels. For this purpose, we defined a genetic network inference problem as a series of discrimination tasks, then solved the defined series of discrimination tasks with a linear programming machine. Our experimental results demonstrated that the proposed method is capable of correctly inferring genetic networks, and doing so more than 500 times faster than the other inference methods based on sets of differential equations. Next, we applied our method to actual expression data of the bacterial SOS DNA repair system. And finally, we demonstrated that our approach relates to the inference method based on the S-system model. Though our method provides no estimation of the kinetic parameters, it should be useful for researchers interested only in the network structure of a target system. Supplementary data are available at Bioinformatics online.

International and domestic mobile satellite regulatory proceedings: A comparison of outcomes and discussion of implications

NASA Technical Reports Server (NTRS)

Freibaum, Jerry

1988-01-01

It is argued that we are on the threshold of a new multibillion dollar industry that can enhance economic development, dramatically improve disaster assessment and relief operations, improve rural health care and solve many safety and security concerns of the transportation industry. Further delays in resolving conflicts between vested interests will be extremely costly to users, providers and equipment manufacturers. Conference participants are urged to move quickly and decisively towards solving outstanding problems.

Transmission ultrasonography. [time delay spectrometry for soft tissue transmission imaging

NASA Technical Reports Server (NTRS)

Heyser, R. C.; Le Croissette, D. H.

1973-01-01

Review of the results of the application of an advanced signal-processing technique, called time delay spectrometry, in obtaining soft tissue transmission images by transmission ultrasonography, both in vivo and in vitro. The presented results include amplitude ultrasound pictures and phase ultrasound pictures obtained by this technique. While amplitude ultrasonographs of tissue are closely analogous to X-ray pictures in that differential absorption is imaged, phase ultrasonographs represent an entirely new source of information based on differential time of propagation. Thus, a new source of information is made available for detailed analysis.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

Stabilisation of time-varying linear systems via Lyapunov differential equations

NASA Astrophysics Data System (ADS)

Zhou, Bin; Cai, Guang-Bin; Duan, Guang-Ren

2013-02-01

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches.

Clinical Implications of Cardiac-MIBG SPECT in the Differentiation of Parkinsonian Syndromes

PubMed Central

Shin, Dong Hoon; Bang, Oh Young; Joo, In Soo; Huh, Kyoon

2006-01-01

Background and Purpose 123I cardiac meta-iodobenzylguanidine (MIBG), an analogue of norepinephrine, has been used to estimate myocardial sympathetic nerve function. We investigate whether cardiac-MIBG SPECT is clinically applicable in the differentiation of Parkinson's disease (PD) from parkinsonian syndromes. Methods Cardiac-MIBG scintigraphy was performed in 27 controls, in 40 patients with PD and in 52 patients with other parkinsonian syndromes comprising 23 with multiple system atrophy (MSA), 26 with drug-induced parkinsonism (DIP), and 3 with corticobasal degeneration (CBD). The heart to mediastinum (H/M) uptake ratio was calculated for each subjects. Patients who either had medical conditions that confused the MIBG SPECT results or who took medications that interfere with MIBG accumulation were excluded from the study. Results Both early and delayed H/M ratios were in patients with PD significantly lower than in controls (early, 1.34±0.15 vs 1.79±0.19; delayed, 1.29±0.15 vs 2.06±0.29, p<0.001). In patients with PD, both early and delayed H/M ratios were significantly lower than those in patients with MSA (early, 1.68±0.23; delayed, 1.80±0.34, p<0.001), DIP (early, 1.83±0.24; delayed, 2.07±0.4, p<0.001), or CBD (early, 1.85±0.01; delayed, 1.99±0.19, p<0.001). Two patients with DIP, who were within the range of patients with PD, showed clinically similar courses of PD. Conclusions This study demonstrates that cardiac-MIBG is a clinically powerful tools to differentiate PD from other parkinsonian syndromes. PMID:20396485

A note on the generation of phase plane plots on a digital computer. [for solution of nonlinear differential equations

NASA Technical Reports Server (NTRS)

Simon, M. K.

1980-01-01

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated.

Variable-mesh method of solving differential equations

NASA Technical Reports Server (NTRS)

Van Wyk, R.

1969-01-01

Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.

Achievement motivation and memory: achievement goals differentially influence immediate and delayed remember-know recognition memory.

PubMed

Murayama, Kou; Elliot, Andrew J

2011-10-01

Little research has been conducted on achievement motivation and memory and, more specifically, on achievement goals and memory. In the present research, the authors conducted two experiments designed to examine the influence of mastery-approach and performance-approach goals on immediate and delayed remember-know recognition memory. The experiments revealed differential effects for achievement goals over time: Performance-approach goals showed higher correct remember responding on an immediate recognition test, whereas mastery-approach goals showed higher correct remember responding on a delayed recognition test. Achievement goals had no influence on overall recognition memory and no consistent influence on know responding across experiments. These findings indicate that it is important to consider quality, not just quantity, in both motivation and memory, when studying relations between these constructs.

Control-based method to identify underlying delays of a nonlinear dynamical system.

PubMed

Yu, Dongchuan; Frasca, Mattia; Liu, Fang

2008-10-01

We suggest several stationary state control-based delay identification methods which do not require any structural information about the controlled systems and are applicable to systems described by delayed ordinary differential equations. This proposed technique includes three steps: (i) driving a system to a steady state; (ii) perturbing the control signal for shifting the steady state; and (iii) identifying all delays by detecting the time that the system is abruptly drawn out of stationarity. Some aspects especially important for applications are discussed as well, including interaction delay identification, stationary state convergence speed, performance comparison, and the influence of noise on delay identification. Several examples are presented to illustrate the reliability and robustness of all delay identification methods suggested.

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

NASA Technical Reports Server (NTRS)

Milman, Mark M.; Scheid, Robert E.

1987-01-01

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

LiDAR-IMU Time Delay Calibration Based on Iterative Closest Point and Iterated Sigma Point Kalman Filter

PubMed Central

Liu, Wanli

2017-01-01

The time delay calibration between Light Detection and Ranging (LiDAR) and Inertial Measurement Units (IMUs) is an essential prerequisite for its applications. However, the correspondences between LiDAR and IMU measurements are usually unknown, and thus cannot be computed directly for the time delay calibration. In order to solve the problem of LiDAR-IMU time delay calibration, this paper presents a fusion method based on iterative closest point (ICP) and iterated sigma point Kalman filter (ISPKF), which combines the advantages of ICP and ISPKF. The ICP algorithm can precisely determine the unknown transformation between LiDAR-IMU; and the ISPKF algorithm can optimally estimate the time delay calibration parameters. First of all, the coordinate transformation from the LiDAR frame to the IMU frame is realized. Second, the measurement model and time delay error model of LiDAR and IMU are established. Third, the methodology of the ICP and ISPKF procedure is presented for LiDAR-IMU time delay calibration. Experimental results are presented that validate the proposed method and demonstrate the time delay error can be accurately calibrated. PMID:28282897

Optimal control of LQR for discrete time-varying systems with input delays

NASA Astrophysics Data System (ADS)

Yin, Yue-Zhu; Yang, Zhong-Lian; Yin, Zhi-Xiang; Xu, Feng

2018-04-01

In this work, we consider the optimal control problem of linear quadratic regulation for discrete time-variant systems with single input and multiple input delays. An innovative and simple method to derive the optimal controller is given. The studied problem is first equivalently converted into a problem subject to a constraint condition. Last, with the established duality, the problem is transformed into a static mathematical optimisation problem without input delays. The optimal control input solution to minimise performance index function is derived by solving this optimisation problem with two methods. A numerical simulation example is carried out and its results show that our two approaches are both feasible and very effective.

Movement of Landslide Triggered by Bedrock Exfiltration with Nonuniform Pore Pressure Distribution

NASA Astrophysics Data System (ADS)

Jan, C. D.; Jian, Z. K.

2014-12-01

Landslides are common phenomena of sediment movement in mountain areas and usually pose severe risks to people and infrastructure around those areas. The occurrence of landslides is influenced by groundwater dynamics and bedrock characteristics as well as by rainfall and soil-mass properties. The bedrock may drain or contribute to groundwater in the overlying soil mass, depending on the hydraulic conductivity, degree of fracturing, saturation, and hydraulic head. Our study here is based on the model proposed by Iverson (2005). The model describes the relation between landslide displacement and the shear-zone dilation/contraction of pore water pressure. To study landslide initiation and movement, a block soil mass sliding down an inclined beck-rock plane is governed by Newton's equation of motion, while both the bedrock exfiltration and excess pore pressure induced by dilatation or contraction of basal shear zone are described by diffusion equations. The Chebyshev collocation method was used to transform the governing equations to a system of first-order ordinary differential equations, without the need of iteration. Then a fourth-order Runge-Kutta scheme was used to solve these ordinary differential equations. The effects of nonuniform bedrock exfiltration pressure distributions, such as the delayed peak, central peak, and advanced peak distributions, on the time of landslide initiation and the speed of landslide movement were compared and discussed.

Robotic reactions: delay-induced patterns in autonomous vehicle systems.

PubMed

Orosz, Gábor; Moehlis, Jeff; Bullo, Francesco

2010-02-01

Fundamental design principles are presented for vehicle systems governed by autonomous cruise control devices. By analyzing the corresponding delay differential equations, it is shown that for any car-following model short-wavelength oscillations can appear due to robotic reaction times, and that there are tradeoffs between the time delay and the control gains. The analytical findings are demonstrated on an optimal velocity model using numerical continuation and numerical simulation.

Robotic reactions: Delay-induced patterns in autonomous vehicle systems

NASA Astrophysics Data System (ADS)

Orosz, Gábor; Moehlis, Jeff; Bullo, Francesco

2010-02-01

Fundamental design principles are presented for vehicle systems governed by autonomous cruise control devices. By analyzing the corresponding delay differential equations, it is shown that for any car-following model short-wavelength oscillations can appear due to robotic reaction times, and that there are tradeoffs between the time delay and the control gains. The analytical findings are demonstrated on an optimal velocity model using numerical continuation and numerical simulation.

Lead exposure delays the differentiation of oligodendroglial progenitors in vitro.

PubMed

Deng, W; McKinnon, R D; Poretz, R D

2001-08-01

Lead (Pb) is an environmental neurotoxicant that can cause hypo- and demyelination. Oligodendrocytes (OLs), the myelin-forming cells in the central nervous system, may be a possible target for Pb toxicity. The present study describes the effect of Pb on the maturation of rat OL progenitor (OP) cells and the developmental expression of myelin-specific galactolipids. Dose-response studies showed that OP cultures were more sensitive to Pb than mature OLs. Pb delayed the differentiation of OL progenitors, as demonstrated by cell morphology and immunostaining with a panel of stage-specific differentiation markers. Pb given prior to and during differentiation caused a decrease in the biosynthesis of galactolipids in both undifferentiated and differentiated OLs, as detected by metabolic radiolabeling with 3H-D-galactose. While the ratios of galacto/gluco-cerebrosides, hydroxy fatty acid/nonhydroxy fatty acid galactolipids, and galactocerebrosides/sulfatides increased in control cultures during cell differentiation, Pb treatment prevented these changes. The results suggest that chronic Pb exposure may impact brain development by interfering with the timely developmental maturation of OL progenitors. Copyright 2001 Academic Press.

Ionospheric corrections to precise time transfer using GPS

NASA Technical Reports Server (NTRS)

Snow, Robert W.; Osborne, Allen W., III; Klobuchar, John A.; Doherty, Patricia H.

1994-01-01

The free electrons in the earth's ionosphere can retard the time of reception of GPS signals received at a ground station, compared to their time in free space, by many tens of nanoseconds, thus limiting the accuracy of time transfer by GPS. The amount of the ionospheric time delay is proportional to the total number of electrons encountered by the wave on its path from each GPS satellite to a receiver. This integrated number of electrons is called Total Electron Content, or TEC. Dual frequency GPS receivers designed by Allen Osborne Associates, Inc. (AOA) directly measure both the ionospheric differential group delay and the differential carrier phase advance for the two GPS frequencies and derive from this the TEC between the receiver and each GPS satellite in track. The group delay information is mainly used to provide an absolute calibration to the relative differential carrier phase, which is an extremely precise measure of relative TEC. The AOA Mini-Rogue ICS-4Z and the AOA TurboRogue ICS-4000Z receivers normally operate using the GPS P code, when available, and switch to cross-correlation signal processing when the GPS satellites are in the Anti-Spoofing (A-S) mode and the P code is encrypted. An AOA ICS-Z receiver has been operated continuously for over a year at Hanscom AFB, MA to determine the statistics of the variability of the TEC parameter using signals from up to four different directions simultaneously. The 4-channel ICS-4Z and the 8-channel ICS-4000Z, have proven capabilities to make precise, well calibrated, measurements of the ionosphere in several directions simultaneously. In addition to providing ionospheric corrections for precise time transfer via satellite, this dual frequency design allows full code and automatic codeless operation of both the differential group delay and differential carrier phase for numerous ionospheric experiments being conducted. Statistical results of the data collected from the ICS-4Z during the initial year of ionospheric time delay in the northeastern U.S., and initial results with the ICS-4000Z, will be presented.

Analysis of a dc bus system with a nonlinear constant power load and its delayed feedback control.

PubMed

Konishi, Keiji; Sugitani, Yoshiki; Hara, Naoyuki

2014-02-01

This paper tackles a destabilizing problem of a direct-current (dc) bus system with constant power loads, which can be considered a fundamental problem of dc power grid networks. The present paper clarifies scenarios of the destabilization and applies the well-known delayed-feedback control to the stabilization of the destabilized bus system on the basis of nonlinear science. Further, we propose a systematic procedure for designing the delayed feedback controller. This controller can converge the bus voltage exactly on an unstable operating point without accurate information and can track it using tiny control energy even when a system parameter, such as the power consumption of the load, is slowly varied. These features demonstrate that delayed feedback control can be considered a strong candidate for solving the destabilizing problem.

Neural network error correction for solving coupled ordinary differential equations

NASA Technical Reports Server (NTRS)

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.

Strategies for Hard Times in Higher Education.

ERIC Educational Resources Information Center

Desfosses, Louis R.

1996-01-01

Planning and management strategies used in the private sector have practical applications for higher education in a period of systemic and organizational stress. Promising strategies include organizational delayering; employee empowerment; boundless thinking, problem-solving teams; accelerated processes; quality management and improvement; and…

Monte Carlo Simulations for VLBI2010

NASA Astrophysics Data System (ADS)

Wresnik, J.; Böhm, J.; Schuh, H.

2007-07-01

Monte Carlo simulations are carried out at the Institute of Geodesy and Geophysics (IGG), Vienna, and at Goddard Space Flight Center (GSFC), Greenbelt (USA), with the goal to design a new geodetic Very Long Baseline Interferometry (VLBI) system. Influences of the schedule, the network geometry and the main stochastic processes on the geodetic results are investigated. Therefore schedules are prepared with the software package SKED (Vandenberg 1999), and different strategies are applied to produce temporally very dense schedules which are compared in terms of baseline length repeatabilities. For the simulation of VLBI observations a Monte Carlo Simulator was set up which creates artificial observations by randomly simulating wet zenith delay and clock values as well as additive white noise representing the antenna errors. For the simulation at IGG the VLBI analysis software OCCAM (Titov et al. 2004) was adapted. Random walk processes with power spectrum densities of 0.7 and 0.1 psec2/sec are used for the simulation of wet zenith delays. The clocks are simulated with Allan Standard Deviations of 1*10^-14 @ 50 min and 2*10^-15 @ 15 min and three levels of white noise, 4 psec, 8 psec and, 16 psec, are added to the artificial observations. The variations of the power spectrum densities of the clocks and wet zenith delays, and the application of different white noise levels show clearly that the wet delay is the critical factor for the improvement of the geodetic VLBI system. At GSFC the software CalcSolve is used for the VLBI analysis, therefore a comparison between the software packages OCCAM and CalcSolve was done with simulated data. For further simulations the wet zenith delay was modeled by a turbulence model. This data was provided by Nilsson T. and was added to the simulation work. Different schedules have been run.

On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

NASA Astrophysics Data System (ADS)

Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

2018-04-01

We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

Pulmonary MRA: Differentiation of pulmonary embolism from truncation artifact

PubMed Central

Bannas, Peter; Schiebler, Mark L; Motosugi, Utaroh; François, Christopher J; Reeder, Scott B; Nagle, Scott K

2015-01-01

Purpose Truncation artifact (Gibbs ringing) causes central signal drop within vessels in pulmonary MRA that can be mistaken for emboli, reducing the diagnostic accuracy for pulmonary embolism (PE). We propose a quantitative approach to differentiate truncation artifact from PE. Methods Twenty-eight patients who underwent pulmonary CTA for suspected PE were recruited for pulmonary MRA. Signal intensity drops within pulmonary arteries that persisted on both arterial-phase and delayed-phase MRA were identified. The percent signal loss between the vessel lumen and central drop was measured. CTA served as the reference standard for presence of pulmonary emboli. Results A total of 65 signal intensity drops were identified on MRA. 48 (74%) of these were artifact and 17 (26%) were PE, as confirmed by CTA. Truncation artifacts had a significantly lower median signal drop than PE at both arterial-phase (26% [range 12–58%] vs. 85% [range 53–91%]) and at delayed-phase MRA (26% [range 11–55%] vs. 77% [range 47–89%]), p<0.0001 for both. ROC analyses revealed a threshold value of 51% (arterial-phase) and 47%-signal drop (delayed-phase) to differentiate between truncation artifact and PE with 100% sensitivity and >90% specificity. Conclusion Quantitative signal drop is an objective tool to help differentiate truncation artifact and pulmonary embolism in pulmonary MRA. PMID:24863886

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

A new numerical approximation of the fractal ordinary differential equation

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Context-dependent dynamic processes in attention deficit/hyperactivity disorder: differentiating common and unique effects of state regulation deficits and delay aversion.

PubMed

Sonuga-Barke, Edmund J S; Wiersema, Jan R; van der Meere, Jacob J; Roeyers, Herbert

2010-03-01

The ability to specify differential predictions is a mark of a scientific models' value. State regulation deficits (SRD) and delay aversion (DAv) have both been hypothesized as context-dependent dynamic dysfunctions in ADHD. However, to date there has been no systematic comparison of their common and unique elements. Here we review these hypotheses-and describe the core and secondary manifestations of the two constructs and review evidence in support of them. Second, we focus on what are seen as the hallmark indicators of the two deficits-preference of small immediate over large delayed rewards for DAv and the slow event rate effect for SRD. We describe the overlap between these two manifestations and then explore how experimental manipulations and the analysis of neuropsychological and physiological mediators of effects can allow us to differentiate these two patterns of neuropsychological dysfunction on the basis of specific predictions. Finally, we highlight the implications of neuropsychological heterogeneity for the practical implementation of tests of DAv and SRD.

Differential geometric methods in system theory.

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

Operator Factorization and the Solution of Second-Order Linear Ordinary Differential Equations

ERIC Educational Resources Information Center

Robin, W.

2007-01-01

The theory and application of second-order linear ordinary differential equations is reviewed from the standpoint of the operator factorization approach to the solution of ordinary differential equations (ODE). Using the operator factorization approach, the general second-order linear ODE is solved, exactly, in quadratures and the resulting…

Understanding Student Use of Differentials in Physics Integration Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2013-01-01

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

The Local Brewery: A Project for Use in Differential Equations Courses

ERIC Educational Resources Information Center

Starling, James K.; Povich, Timothy J.; Findlay, Michael

2016-01-01

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Reconstruction of ensembles of coupled time-delay systems from time series.

PubMed

Sysoev, I V; Prokhorov, M D; Ponomarenko, V I; Bezruchko, B P

2014-06-01

We propose a method to recover from time series the parameters of coupled time-delay systems and the architecture of couplings between them. The method is based on a reconstruction of model delay-differential equations and estimation of statistical significance of couplings. It can be applied to networks composed of nonidentical nodes with an arbitrary number of unidirectional and bidirectional couplings. We test our method on chaotic and periodic time series produced by model equations of ensembles of diffusively coupled time-delay systems in the presence of noise, and apply it to experimental time series obtained from electronic oscillators with delayed feedback coupled by resistors.

Solving Differential Equations in R

EPA Science Inventory

Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

Trajectory controllability of semilinear systems with multiple variable delays in control

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

Klamka, Jerzy, E-mail: Jerzy.Klamka@polsl.pl, E-mail: Michal.Niezabitowski@polsl.pl; Niezabitowski, Michał, E-mail: Jerzy.Klamka@polsl.pl, E-mail: Michal.Niezabitowski@polsl.pl

In this paper, finite-dimensional dynamical control system described by semilinear differential state equation with multiple variable delays in control are considered. The concept of controllability we extend on trajectory controllability for systems with multiple point delays in control. Moreover, remarks and comments on the relationships between different concepts of controllability are presented. Finally, simple numerical example, which illustrates theoretical considerations is also given. The possible extensions are also proposed.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Stability and global Hopf bifurcation in a delayed food web consisting of a prey and two predators

NASA Astrophysics Data System (ADS)

Meng, Xin-You; Huo, Hai-Feng; Zhang, Xiao-Bing

2011-11-01

This paper is concerned with a predator-prey system with Holling II functional response and hunting delay and gestation. By regarding the sum of delays as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. We obtained explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation. Using a global Hopf bifurcation result of Wu [Wu JH. Symmetric functional differential equations and neural networks with memory, Trans Amer Math Soc 1998;350:4799-4838] for functional differential equations, we may show the global existence of the periodic solutions. Finally, several numerical simulations illustrating the theoretical analysis are also given.

Toward Diagnostic and Phenotype Markers for Genetically Transmitted Speech Delay

ERIC Educational Resources Information Center

Shriberg, Lawrence D.; Lewis, Barbara A.; Tomblin, J. Bruce; McSweeny, Jane L.; Karlsson, Heather B.; Scheer, Alison R.

2005-01-01

Converging evidence supports the hypothesis that the most common subtype of childhood speech sound disorder (SSD) of currently unknown origin is genetically transmitted. We report the first findings toward a set of diagnostic markers to differentiate this proposed etiological subtype (provisionally termed "speech delay-genetic") from other…

Motivational Control of Impulsive Behavior Interacts with Choice Opportunities

ERIC Educational Resources Information Center

Tanno, Takayuki; Kurashima, Ryo; Watanabe, Shigeru

2011-01-01

Impulsive behavior has been investigated through choice between a smaller/immediate reinforcer and a larger/delayed reinforcer, or through performance on a differential reinforcement of low rate (DRL) schedule. In the present study, we investigated a methodological divergence between these two procedures: in the former procedure, delay is a…

Local Stability of AIDS Epidemic Model Through Treatment and Vertical Transmission with Time Delay

NASA Astrophysics Data System (ADS)

Novi W, Cascarilla; Lestari, Dwi

2016-02-01

This study aims to explain stability of the spread of AIDS through treatment and vertical transmission model. Human with HIV need a time to positively suffer AIDS. The existence of a time, human with HIV until positively suffer AIDS can be delayed for a time so that the model acquired is the model with time delay. The model form is a nonlinear differential equation with time delay, SIPTA (susceptible-infected-pre AIDS-treatment-AIDS). Based on SIPTA model analysis results the disease free equilibrium point and the endemic equilibrium point. The disease free equilibrium point with and without time delay are local asymptotically stable if the basic reproduction number is less than one. The endemic equilibrium point will be local asymptotically stable if the time delay is less than the critical value of delay, unstable if the time delay is more than the critical value of delay, and bifurcation occurs if the time delay is equal to the critical value of delay.

Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

PubMed

Liu, Meiqin

2009-09-01

This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

A differential delay equation arising from the sieve of Eratosthenes

NASA Astrophysics Data System (ADS)

Cheer, A. Y.; Goldston, D. A.

1990-07-01

The differential delay equation defined by ω (u) = 1/u for 1 ≤ u ≤ 2 and (uω (u))' = ω (u - 1) for u ≥ 2 was introduced by Buchstab in connection with an asymptotic formula for the number of uncanceled terms in the sieve of Eratosthenes. Maier has recently used this result to show there is unexpected irregularity in the distribution of primes in short intervals. The function ω (u) is studied in this paper using numerical and analytical techniques. The results are applied to give some numerical constants in Maier's theorem.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

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

Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Robust stability bounds for multi-delay networked control systems

NASA Astrophysics Data System (ADS)

Seitz, Timothy; Yedavalli, Rama K.; Behbahani, Alireza

2018-04-01

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.

The Senior Experience: Applied, Team Problem Solving in Business Education.

ERIC Educational Resources Information Center

Jessup, Leonard M.

1995-01-01

A yearlong senior experience course requires teams of business students to solve real problems for organizations in the community. Students enhanced responsibility, confidence, and organizational skills. Problems centered on differentiating the course from internships and improving staffing. Students had problems with group dynamics, team…

Assessing Design Activity in Complex CMOS Circuit Design.

ERIC Educational Resources Information Center

Biswas, Gautam; And Others

This report characterizes human problem solving in digital circuit design. Protocols of 11 different designers with varying degrees of training were analyzed by identifying the designers' problem solving strategies and discussing activity patterns that differentiate the designers. These methods are proposed as a tentative basis for assessing…

On a numerical method for solving integro-differential equations with variable coefficients with applications in finance

NASA Astrophysics Data System (ADS)

Kudryavtsev, O.; Rodochenko, V.

2018-03-01

We propose a new general numerical method aimed to solve integro-differential equations with variable coefficients. The problem under consideration arises in finance where in the context of pricing barrier options in a wide class of stochastic volatility models with jumps. To handle the effect of the correlation between the price and the variance, we use a suitable substitution for processes. Then we construct a Markov-chain approximation for the variation process on small time intervals and apply a maturity randomization technique. The result is a system of boundary problems for integro-differential equations with constant coefficients on the line in each vertex of the chain. We solve the arising problems using a numerical Wiener-Hopf factorization method. The approximate formulae for the factors are efficiently implemented by means of the Fast Fourier Transform. Finally, we use a recurrent procedure that moves backwards in time on the variance tree. We demonstrate the convergence of the method using Monte-Carlo simulations and compare our results with the results obtained by the Wiener-Hopf method with closed-form expressions of the factors.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

A pertinent approach to solve nonlinear fuzzy integro-differential equations.

PubMed

Narayanamoorthy, S; Sathiyapriya, S P

2016-01-01

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations using homotopy perturbation method. A clear and detailed description of the proposed method is provided. Our main objective is to illustrate that the construction of appropriate convex homotopy in a proper way leads to highly accurate solutions with less computational work. The efficiency of the approximation technique is expressed via stability and convergence analysis so as to guarantee the efficiency and performance of the methodology. Numerical examples are demonstrated to verify the convergence and it reveals the validity of the presented numerical technique. Numerical results are tabulated and examined by comparing the obtained approximate solutions with the known exact solutions. Graphical representations of the exact and acquired approximate fuzzy solutions clarify the accuracy of the approach.

Super-Resolution Algorithm in Cumulative Virtual Blanking

NASA Astrophysics Data System (ADS)

Montillet, J. P.; Meng, X.; Roberts, G. W.; Woolfson, M. S.

2008-11-01

The proliferation of mobile devices and the emergence of wireless location-based services have generated consumer demand for precise location. In this paper, the MUSIC super-resolution algorithm is applied to time delay estimation for positioning purposes in cellular networks. The goal is to position a Mobile Station with UMTS technology. The problem of Base-Stations herability is solved using Cumulative Virtual Blanking. A simple simulator is presented using DS-SS signal. The results show that MUSIC algorithm improves the time delay estimation in both the cases whether or not Cumulative Virtual Blanking was carried out.

Automated Measurement of P- and S-Wave Differential Times for Imaging Spatial Distributions of Vp/Vs Ratio, with Moving-Window Cross-Correlation Technique

NASA Astrophysics Data System (ADS)

Taira, T.; Kato, A.

2013-12-01

A high-resolution Vp/Vs ratio estimate is one of the key parameters to understand spatial variations of composition and physical state within the Earth. Lin and Shearer (2007, BSSA) recently developed a methodology to obtain local Vp/Vs ratios in individual similar earthquake clusters, based on P- and S-wave differential times. A waveform cross-correlation approach is typically employed to measure those differential times for pairs of seismograms from similar earthquakes clusters, at narrow time windows around the direct P and S waves. This approach effectively collects P- and S-wave differential times and however requires the robust P- and S-wave time windows that are extracted based on either manually or automatically picked P- and S-phases. We present another technique to estimate P- and S-wave differential times by exploiting temporal properties of delayed time as a function of elapsed time on the seismograms with a moving-window cross-correlation analysis (e.g., Snieder, 2002, Phys. Rev. E; Niu et al. 2003, Nature). Our approach is based on the principle that the delayed time for the direct S wave differs from that for the direct P wave. Two seismograms aligned by the direct P waves from a pair of similar earthquakes yield that delayed times become zero around the direct P wave. In contrast, delayed times obtained from time windows including the direct S wave have non-zero value. Our approach, in principle, is capable of measuring both P- and S-wave differential times from single-component seismograms. In an ideal case, the temporal evolution of delayed time becomes a step function with its discontinuity at the onset of the direct S wave. The offset in the resulting step function would be the S-wave differential time, relative to the P-wave differential time as the two waveforms are aligned by the direct P wave. We apply our moving-window cross-correlation technique to the two different data sets collected at: 1) the Wakayama district, Japan and 2) the Geysers geothermal field, California. The both target areas are characterized by earthquake swarms that provide a number of similar events clusters. We use the following automated procedure to systematically analyze the two data sets: 1) the identification of the direct P arrivals by using an Akaike Information Criterion based phase picking algorithm introduced by Zhang and Thurber (2003, BSSA), 2) the waveform alignment by the P-wave with a waveform cross-correlation to obtain P-wave differential time, 3) the moving-time window analysis to estimate the S-differential time. Kato et al. (2010, GRL) have estimated the Vp/Vs ratios for a few similar earthquake clusters from the Wakayama data set, by a conventional approach to obtain differential times. We find that the resulting Vp/Vs ratios from our approach for the same earthquake clusters are comparable with those obtained from Kato et al. (2010, GRL). We show that the moving-window cross-correlation technique effectively measures both P- and S-wave differential times for the seismograms in which the clear P and S phases are not observed. We will show spatial distributions in Vp/Vs ratios in our two target areas.

VLBI observations to the APOD satellite

NASA Astrophysics Data System (ADS)

Sun, Jing; Tang, Geshi; Shu, Fengchun; Li, Xie; Liu, Shushi; Cao, Jianfeng; Hellerschmied, Andreas; Böhm, Johannes; McCallum, Lucia; McCallum, Jamie; Lovell, Jim; Haas, Rüdiger; Neidhardt, Alexander; Lu, Weitao; Han, Songtao; Ren, Tianpeng; Chen, Lue; Wang, Mei; Ping, Jinsong

2018-02-01

The APOD (Atmospheric density detection and Precise Orbit Determination) is the first LEO (Low Earth Orbit) satellite in orbit co-located with a dual-frequency GNSS (GPS/BD) receiver, an SLR reflector, and a VLBI X/S dual band beacon. From the overlap statistics between consecutive solution arcs and the independent validation by SLR measurements, the orbit position deviation was below 10 cm before the on-board GNSS receiver got partially operational. In this paper, the focus is on the VLBI observations to the LEO satellite from multiple geodetic VLBI radio telescopes, since this is the first implementation of a dedicated VLBI transmitter in low Earth orbit. The practical problems of tracking a fast moving spacecraft with current VLBI ground infrastructure were solved and strong interferometric fringes were obtained by cross-correlation of APOD carrier and DOR (Differential One-way Ranging) signals. The precision in X-band time delay derived from 0.1 s integration time of the correlator output is on the level of 0.1 ns. The APOD observations demonstrate encouraging prospects of co-location of multiple space geodetic techniques in space, as a first prototype.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

A knowledge-based system with learning for computer communication network design

NASA Technical Reports Server (NTRS)

Pierre, Samuel; Hoang, Hai Hoc; Tropper-Hausen, Evelyne

1990-01-01

Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay.

Experimental problem solving: An instructional improvement field experiment

NASA Astrophysics Data System (ADS)

Ross, John A.; Maynes, Florence J.

An instructional program based on expert-novice differences in experimental problem-solving performance was taught to grade 6 students (N = 265). Classes of students were randomly assigned to conditions in a delayed treatment design. Performance was assessed with multiple-choice and open-ended measures of specific transfer. Between group comparisons using pretest scores as a covariate showed that treatment condition students consistently outperformed controls; similar results were revealed in the within group comparisons. The achievement of the early treatment group did not decline in tests administered one month after the posttest.

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

New Passivity Criteria for Fuzzy Bam Neural Networks with Markovian Jumping Parameters and Time-Varying Delays

NASA Astrophysics Data System (ADS)

Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Thangaraj, P.

2013-02-01

This paper addresses the problem of passivity analysis issue for a class of fuzzy bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time varying delays. A set of sufficient conditions for the passiveness of the considered fuzzy BAM neural network model is derived in terms of linear matrix inequalities by using the delay fractioning technique together with the Lyapunov function approach. In addition, the uncertainties are inevitable in neural networks because of the existence of modeling errors and external disturbance. Further, this result is extended to study the robust passivity criteria for uncertain fuzzy BAM neural networks with time varying delays and uncertainties. These criteria are expressed in the form of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Two numerical examples are provided to demonstrate the effectiveness of the obtained results.

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Differentiation of Self, Personal Adjustment, Problem Solving, and Ethnic Group Belonging among Persons of Color.

ERIC Educational Resources Information Center

Skowron, Elizabeth A.

2004-01-01

This study focused on examining the cross-cultural validity of Bowen family systems theory (M. Bowen, 1978), namely differentiation of self for individuals of color. Ethnic minority men and women completed measures of differentiation of self, ethnic group belonging, and 3 indices of personal adjustment. Initial support for the cross-cultural…

Integrated corridor management and advanced technologies for Florida : [summary].

DOT National Transportation Integrated Search

2012-11-01

The U.S. Department of Transportation (USDOT) has estimated the costs of congestion at $200 billion a year in delayed shipments and wasted fuel and 4 billion hours lost by drivers in traffic. New roads alone cannot solve the problem because travel de...

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Nonlinear Fourier algorithm applied to solving equations of gravitational gas dynamics

NASA Technical Reports Server (NTRS)

Kolosov, B. I.

1979-01-01

Two dimensional gas flow problems were reduced to an approximating system of common differential equations, which were solved by a standard procedure of the Runge-Kutta type. A theorem of the existence of stationary conical shock waves with the cone vertex in the gravitating center was proved.

Intergenerational Family Conflict and Coping Among Hmong American College Students

ERIC Educational Resources Information Center

Su, Jenny; Lee, Richard M.; Vang, Shary

2005-01-01

Problem solving and social support, as different styles of coping with intergenerational family conflict, were examined among 86 Hmong American college students. Problem solving and social support were hypothesized to differentially moderate the effects of family conflict on psychological adjustment. Furthermore, the effects of attributions of…

Problem-Solving Test: The Mechanism of Protein Synthesis

ERIC Educational Resources Information Center

Szeberenyi, Jozsef

2009-01-01

Terms to be familiar with before you start to solve the test: protein synthesis, ribosomes, amino acids, peptides, peptide bond, polypeptide chain, N- and C-terminus, hemoglobin, [alpha]- and [beta]-globin chains, radioactive labeling, [[to the third power]H] and [[to the fourteenth power]C]leucine, cytosol, differential centrifugation, density…

A framework for qualitative reasoning about solid objects

NASA Technical Reports Server (NTRS)

Davis, E.

1987-01-01

Predicting the behavior of a qualitatively described system of solid objects requires a combination of geometrical, temporal, and physical reasoning. Methods based upon formulating and solving differential equations are not adequate for robust prediction, since the behavior of a system over extended time may be much simpler than its behavior over local time. A first-order logic, in which one can state simple physical problems and derive their solution deductively, without recourse to solving the differential equations, is discussed. This logic is substantially more expressive and powerful than any previous AI representational system in this domain.

Mathematical model of one-man air revitalization system

NASA Technical Reports Server (NTRS)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Differentiation of Recurrent Glioblastoma from Delayed Radiation Necrosis by Using Voxel-based Multiparametric Analysis of MR Imaging Data.

PubMed

Yoon, Ra Gyoung; Kim, Ho Sung; Koh, Myeong Ju; Shim, Woo Hyun; Jung, Seung Chai; Kim, Sang Joon; Kim, Jeong Hoon

2017-10-01

Purpose To assess a volume-weighted voxel-based multiparametric (MP) clustering method as an imaging biomarker to differentiate recurrent glioblastoma from delayed radiation necrosis. Materials and Methods The institutional review board approved this retrospective study and waived the informed consent requirement. Seventy-five patients with pathologic analysis-confirmed recurrent glioblastoma (n = 42) or radiation necrosis (n = 33) who presented with enlarged contrast material-enhanced lesions at magnetic resonance (MR) imaging after they completed concurrent chemotherapy and radiation therapy were enrolled. The diagnostic performance of the total MP cluster score was determined by using the area under the receiver operating characteristic curve (AUC) with cross-validation and compared with those of single parameter measurements (10% histogram cutoffs of apparent diffusion coefficient [ADC10] or 90% histogram cutoffs of normalized cerebral blood volume and initial time-signal intensity AUC). Results Receiver operating characteristic curve analysis showed that an AUC for differentiating recurrent glioblastoma from delayed radiation necrosis was highest in the total MP cluster score and lowest for ADC10 for both readers. The total MP cluster score had significantly better diagnostic accuracy than any single parameter (corrected P = .001-.039 for reader 1; corrected P = .005-.041 for reader 2). The total MP cluster score was the best predictor of recurrent glioblastoma (cross-validated AUCs, 0.942-0.946 for both readers), with a sensitivity of 95.2% for reader 1 and 97.6% for reader 2. Conclusion Quantitative analysis with volume-weighted voxel-based MP clustering appears to be superior to the use of single imaging parameters to differentiate recurrent glioblastoma from delayed radiation necrosis. © RSNA, 2017 Online supplemental material is available for this article.

Hopf-Pitchfork Bifurcation in a Symmetrically Conservative Two-Mass System with Delay

NASA Astrophysics Data System (ADS)

Sun, Ye; Zhang, Chunrui; Cai, Yuting

2018-06-01

A symmetrically conservative two-mass system with time delay is considered here. We analyse the influence of interaction coefficient and time delay on the Hopf-pitchfork bifurcation. The bifurcation diagrams and phase portraits are then obtained by computing the normal forms for the system in which, particularly, the unfolding form for case III is seldom given in delayed differential equations. Furthermore, we also find some interesting dynamical behaviours of the original system, such as the coexistence of two stable non-trivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically.

Light and melatonin schedule neuronal differentiation in the habenular nuclei

PubMed Central

de Borsetti, Nancy Hernandez; Dean, Benjamin J.; Bain, Emily J.; Clanton, Joshua A.; Taylor, Robert W.; Gamse, Joshua T.

2011-01-01

The formation of the embryonic brain requires the production, migration, and differentiation of neurons to be timely and coordinated. Coupling to the photoperiod could synchronize the development of neurons in the embryo. Here, we consider the effect of light and melatonin on the differentiation of embryonic neurons in zebrafish. We examine the formation of neurons in the habenular nuclei, a paired structure found near the dorsal surface of the brain adjacent to the pineal organ. Keeping embryos in constant darkness causes a temporary accumulation of habenular precursor cells, resulting in late differentiation and a long-lasting reduction in neuronal processes (neuropil). Because constant darkness delays the accumulation of the neurendocrine hormone melatonin in embryos, we looked for a link between melatonin signaling and habenular neurogenesis. A pharmacological block of melatonin receptors delays neurogenesis and reduces neuropil similarly to constant darkness, while addition of melatonin to embryos in constant darkness restores timely neurogenesis and neuropil. We conclude that light and melatonin schedule the differentiation of neurons and the formation of neural processes in the habenular nuclei. PMID:21840306

Method to control artifacts of microstructural fabrication

DOEpatents

Shul, Randy J.; Willison, Christi G.; Schubert, W. Kent; Manginell, Ronald P.; Mitchell, Mary-Anne; Galambos, Paul C.

2006-09-12

New methods for fabrication of silicon microstructures have been developed. In these methods, an etching delay layer is deposited and patterned so as to provide differential control on the depth of features being etched into a substrate material. Compensation for etching-related structural artifacts can be accomplished by proper use of such an etching delay layer.

Wavefronts for a global reaction-diffusion population model with infinite distributed delay

NASA Astrophysics Data System (ADS)

Weng, Peixuan; Xu, Zhiting

2008-09-01

We consider a global reaction-diffusion population model with infinite distributed delay which includes models of Nicholson's blowflies and hematopoiesis derived by Gurney, Mackey and Glass, respectively. The existence of monotone wavefronts is derived by using the abstract settings of functional differential equations and Schauder fixed point theory.

Stability Criteria for Differential Equations with Variable Time Delays

ERIC Educational Resources Information Center

Schley, D.; Shail, R.; Gourley, S. A.

2002-01-01

Time delays are an important aspect of mathematical modelling, but often result in highly complicated equations which are difficult to treat analytically. In this paper it is shown how careful application of certain undergraduate tools such as the Method of Steps and the Principle of the Argument can yield significant results. Certain delay…

Persistent Language Delay versus Late Language Emergence in Children with Early Cochlear Implantation

ERIC Educational Resources Information Center

Geers, Ann E.; Nicholas, Johanna; Tobey, Emily; Davidson, Lisa

2016-01-01

Purpose: The purpose of the present investigation is to differentiate children using cochlear implants (CIs) who did or did not achieve age-appropriate language scores by mid-elementary grades and to identify risk factors for persistent language delay following early cochlear implantation. Materials and Method: Children receiving unilateral CIs at…

Ectopic expression of Capsicum-specific cell wall protein Capsicum annuum senescence-delaying 1 (CaSD1) delays senescence and induces trichome formation in Nicotiana benthamiana.

PubMed

Seo, Eunyoung; Yeom, Seon-In; Jo, Sunghwan; Jeong, Heejin; Kang, Byoung-Cheorl; Choi, Doil

2012-04-01

Secreted proteins are known to have multiple roles in plant development, metabolism, and stress response. In a previous study to understand the roles of secreted proteins, Capsicum annuum secreted proteins (CaS) were isolated by yeast secretion trap. Among the secreted proteins, we further characterized Capsicum annuum senescence-delaying 1 (CaSD1), a gene encoding a novel secreted protein that is present only in the genus Capsicum. The deduced CaSD1 contains multiple repeats of the amino acid sequence KPPIHNHKPTDYDRS. Interestingly, the number of repeats varied among cultivars and species in the Capsicum genus. CaSD1 is constitutively expressed in roots, and Agrobacterium-mediated transient overexpression of CaSD1 in Nicotiana benthamiana leaves resulted in delayed senescence with a dramatically increased number of trichomes and enlarged epidermal cells. Furthermore, senescence- and cell division-related genes were differentially regulated by CaSD1-overexpressing plants. These observations imply that the pepper-specific cell wall protein CaSD1 plays roles in plant growth and development by regulating cell division and differentiation.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations.

PubMed

Chen, Jiejie; Chen, Boshan; Zeng, Zhigang

2018-04-01

This paper investigates O(t -α )-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t -α )-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays. Copyright © 2018 Elsevier Ltd. All rights reserved.

Transit and lifespan in neutrophil production: implications for drug intervention.

PubMed

Câmara De Souza, Daniel; Craig, Morgan; Cassidy, Tyler; Li, Jun; Nekka, Fahima; Bélair, Jacques; Humphries, Antony R

2018-02-01

A comparison of the transit compartment ordinary differential equation modelling approach to distributed and discrete delay differential equation models is studied by focusing on Quartino's extension to the Friberg transit compartment model of myelosuppression, widely relied upon in the pharmaceutical sciences to predict the neutrophil response after chemotherapy, and on a QSP delay differential equation model of granulopoiesis. An extension to the Quartino model is provided by considering a general number of transit compartments and introducing an extra parameter that allows for the decoupling of the maturation time from the production rate of cells. An overview of the well established linear chain technique, used to reformulate transit compartment models with constant transit rates as distributed delay differential equations (DDEs), is then given. A state-dependent time rescaling of the Quartino model is performed to apply the linear chain technique and rewrite the Quartino model as a distributed DDE, yielding a discrete DDE model in a certain parameter limit. Next, stability and bifurcation analyses are undertaken in an effort to situate such studies in a mathematical pharmacology context. We show that both the original Friberg and the Quartino extension models incorrectly define the mean maturation time, essentially treating the proliferative pool as an additional maturation compartment. This misspecification can have far reaching consequences on the development of future models of myelosuppression in PK/PD.

Benefits of Incubation on Divergent Thinking

ERIC Educational Resources Information Center

Chiang, Noelle C.; Chen, Meng-Liang

2017-01-01

Studies on whether fixation cues provided in the first episode of divergent thinking tasks influence creative outcomes after incubation, as they do for convergent problem-solving tasks, remain limited. This research examined the beneficial effects of incubation using the delayed- and immediate-incubation paradigms. Participants in Experiment 1…

On the role of differenced phase-delays in high-precision wide-field multi-source astrometry

NASA Astrophysics Data System (ADS)

Martí-Vidal, I.; Marcaide, J. M.; Guirado, J. C.

2007-07-01

Phase-delay is, by far, the most precise observable used in interferometry. In typical very-long-baseline-interferometry (VLBI) observations, the uncertainties of the phase-delays can be about 100 times smaller than those of the group delays. However, the phase-delays have an important handicap: they are ambiguous, since they are computed from the relative phases of the signals of the different antennas, and an indeterminate number of complete 2¶- cycles can be added to those phases leaving them unchanged. There are different approaches to solve the ambiguity problem of the phase delays (Shapiro et al., 1979; Beasley & Conway, 1995), but none of them has been ever used in observations involving more than 2.3 sources. In this contribution, we will report for the first-time wide-field multi-source astrometric analysis that has been performed on a complete set of radio sources using the phase-delay observable. The target of our analysis is the S5 polar cap sample, consisting on 13 bright ICRF sources near the North Celestial Pole. We have developed new algorithms and updated existing software to correct, in an automatic way, the ambiguities of the phase-delay and, therefore, perform a phasedelay astrometric analysis of all the sources in the sample. We will also discuss on the impact of the use of phase-delays in the astrometric precision.

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Ultimate boundedness stability and controllability of hereditary systems

NASA Technical Reports Server (NTRS)

Chukwu, E. N.

1979-01-01

By generalizing the Liapunov-Yoshizawa techniques, necessary and sufficient conditions are given for uniform boundedness and uniform ultimate boundedness of a rather general class of nonlinear differential equations of neutral type. Among the applications treated by the methods are the Lienard equation of neutral type and hereditary systems of Lurie type. The absolute stability of this later equation is also investigated. A certain existence result of a solution of a neutral functional differential inclusion with two point boundary values is applied to study the exact function space controllability of a nonlinear neutral functional differential control system. A geometric growth condition is used to characterize both the function space and Euclidean controllability of another nonlinear delay system which has a compact and convex control set. This yields conditions under which perturbed nonlinear delay controllable systems are controllable.

Galileo radio science investigations

NASA Technical Reports Server (NTRS)

Howard, H. T.; Eshleman, V. R.; Hinson, D. P.; Kliore, A. J.; Lindal, G. F.; Woo, R.; Bird, M. K.; Volland, H.; Edenhoffer, P.; Paetzold, M.

1992-01-01

Galileo radio-propagation experiments are based on measurements of absolute and differential propagation time delay, differential phase delay, Doppler shift, signal strength, and polarization. These measurements can be used to study: the atmospheric and ionospheric structure, constituents, and dynamics of Jupiter; the magnetic field of Jupiter; the diameter of Io, its ionospheric structure, and the distribution of plasma in the Io torus; the diameters of the other Galilean satellites, certain properties of their surfaces, and possibly their atmospheres and ionospheres; and the plasma dynamics and magnetic field of the solar corona. The spacecraft system provides linear rather than circular polarization on the S-band downlink signal, the capability to receive X-band uplink signals, and a differential downlink ranging mode. A highly-stable, dual-frequency, spacecraft radio system is developed that is suitable for simultaneous measurements of all the parameters normally attributed to radio waves.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

Delayed fungal endophthalmitis secondary to Curvularia.

PubMed

Xu, Kunyong; Almeida, David R P; Chin, Eric K; Mahajan, Vinit B

2016-10-01

To describe a case of fungal endophthalmitis secondary to Curvularia after cataract surgery. This case showed delayed and recalcitrant fungal endophthalmitis secondary to Curvularia despite treatment with pars plana vitrectomy, intravitreal antifungal therapy, and systemic antifungals. Curvularia -associated endophthalmitis should be considered in the differential diagnosis of delayed post-cataract endophthalmitis, especially in tropical or subtropical geographical areas. Awareness and early identification, timely removal of the nidi of sequestration, and prolonged antifungal treatments are important for the eradication of Curvularia -associated endophthalmitis.

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Incorporating time-delays in S-System model for reverse engineering genetic networks.

PubMed

Chowdhury, Ahsan Raja; Chetty, Madhu; Vinh, Nguyen Xuan

2013-06-18

In any gene regulatory network (GRN), the complex interactions occurring amongst transcription factors and target genes can be either instantaneous or time-delayed. However, many existing modeling approaches currently applied for inferring GRNs are unable to represent both these interactions simultaneously. As a result, all these approaches cannot detect important interactions of the other type. S-System model, a differential equation based approach which has been increasingly applied for modeling GRNs, also suffers from this limitation. In fact, all S-System based existing modeling approaches have been designed to capture only instantaneous interactions, and are unable to infer time-delayed interactions. In this paper, we propose a novel Time-Delayed S-System (TDSS) model which uses a set of delay differential equations to represent the system dynamics. The ability to incorporate time-delay parameters in the proposed S-System model enables simultaneous modeling of both instantaneous and time-delayed interactions. Furthermore, the delay parameters are not limited to just positive integer values (corresponding to time stamps in the data), but can also take fractional values. Moreover, we also propose a new criterion for model evaluation exploiting the sparse and scale-free nature of GRNs to effectively narrow down the search space, which not only reduces the computation time significantly but also improves model accuracy. The evaluation criterion systematically adapts the max-min in-degrees and also systematically balances the effect of network accuracy and complexity during optimization. The four well-known performance measures applied to the experimental studies on synthetic networks with various time-delayed regulations clearly demonstrate that the proposed method can capture both instantaneous and delayed interactions correctly with high precision. The experiments carried out on two well-known real-life networks, namely IRMA and SOS DNA repair network in Escherichia coli show a significant improvement compared with other state-of-the-art approaches for GRN modeling.

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

NASA Astrophysics Data System (ADS)

Liu, Lidan; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

Bistability and State Transition of a Delay Differential Equation Model of Neutrophil Dynamics

NASA Astrophysics Data System (ADS)

Ma, Suqi; Zhu, Kaiyi; Lei, Jinzhi

This paper studies the existence of bistable states and control strategies to induce state transitions of a delay differential equation model of neutrophil dynamics. We seek the conditions that a stable steady state and an oscillatory state coexist in the neutrophil dynamical system. Physiologically, stable steady state represents the healthy state, while oscillatory state is usually associated with diseases such as cyclical neutropenia. We study the control strategies to induce the transitions from the disease state to the healthy state by introducing temporal perturbations to system parameters. This study is valuable in designing clinical protocols for the treatment of cyclical neutropenia.

Psychometric characteristics of the Rivermead Behavioural Memory Test (RBMT) as an early detection instrument for dementia and mild cognitive impairment in Brazil.

PubMed

Yassuda, Mônica Sanches; Flaks, Mariana Kneese; Viola, Luciane Fátima; Pereira, Fernanda Speggiorin; Memória, Claudia Maia; Nunes, Paula Villela; Forlenza, Orestes Vicente

2010-09-01

The Rivermead Behavioural Memory Test (RBMT) assesses everyday memory by means of tasks which mimic daily challenges. The objective was to examine the validity of the Brazilian version of the RBMT to detect cognitive decline. 195 older adults were diagnosed as normal controls (NC) or with mild cognitive impairment (MCI) or Alzheimer's disease (AD) by a multidisciplinary team, after participants completed clinical and neuropsychological protocols. Cronbach's alpha was high for the total sample for the RBMT profile (PS) and screening scores (SS) (PS = 0.91, SS = 0.87) and for the AD group (PS = 0.84, SS = 0.85), and moderate for the MCI (PS = 0.62, SS = 0.55) and NC (PS = 0.62, SS = 0.60) groups. RBMT total scores, Appointment, Pictures, Immediate and Delayed Story, Immediate and Delayed Route, Delayed Message and Date contributed to differentiate NC from MCI. ROC curve analyses indicated high accuracy to differentiate NC from AD patients, and, moderate accuracy to differentiate NC from MCI. The Brazilian version of the RBMT seems to be an appropriate instrument to identify memory decline in Brazilian older adults.

Differential short-term memorisation for vocal and instrumental rhythms.

PubMed

Klyn, Niall A M; Will, Udo; Cheong, Yong-Jeon; Allen, Erin T

2016-07-01

This study explores differential processing of vocal and instrumental rhythms in short-term memory with three decision (same/different judgments) and one reproduction experiment. In the first experiment, memory performance declined for delayed versus immediate recall, with accuracy for the two rhythms being affected differently: Musicians performed better than non-musicians on clapstick but not on vocal rhythms, and musicians were better on vocal rhythms in the same than in the different condition. Results for the second experiment showed that concurrent sub-vocal articulation and finger-tapping differentially affected the two rhythms and same/different decisions, but produced no evidence for articulatory loop involvement in delayed decision tasks. In a third experiment, which tested rhythm reproduction, concurrent sub-vocal articulation decreased memory performance, with a stronger deleterious effect on the reproduction of vocal than of clapstick rhythms. This suggests that the articulatory loop may only be involved in delayed reproduction not in decision tasks. The fourth experiment tested whether differences between filled and empty rhythms (continuous vs. discontinuous sounds) can explain the different memorisation of vocal and clapstick rhythms. Though significant differences were found for empty and filled instrumental rhythms, the differences between vocal and clapstick can only be explained by considering additional voice specific features.

Increased dosage of DYRK1A and DSCR1 delays neuronal differentiation in neocortical progenitor cells

PubMed Central

Kurabayashi, Nobuhiro; Sanada, Kamon

2013-01-01

Down's syndrome (DS), a major genetic cause of mental retardation, arises from triplication of genes on human chromosome 21. Here we show that DYRK1A (dual-specificity tyrosine-phosphorylated and -regulated kinase 1A) and DSCR1 (DS critical region 1), two genes lying within human chromosome 21 and encoding for a serine/threonine kinase and calcineurin regulator, respectively, are expressed in neural progenitors in the mouse developing neocortex. Increasing the dosage of both proteins in neural progenitors leads to a delay in neuronal differentiation, resulting ultimately in alteration of their laminar fate. This defect is mediated by the cooperative actions of DYRK1A and DSCR1 in suppressing the activity of the transcription factor NFATc. In Ts1Cje mice, a DS mouse model, dysregulation of NFATc in conjunction with increased levels of DYRK1A and DSCR1 was observed. Furthermore, counteracting the dysregulated pathway ameliorates the delayed neuronal differentiation observed in Ts1Cje mice. In sum, our findings suggest that dosage of DYRK1A and DSCR1 is critical for proper neurogenesis through NFATc and provide a potential mechanism to explain the neurodevelopmental defects in DS. PMID:24352425

Theory of biaxial graded-index optical fiber. M.S. Thesis

NASA Technical Reports Server (NTRS)

Kawalko, Stephen F.

1990-01-01

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

NASA Astrophysics Data System (ADS)

Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

2017-11-01

When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

Strategic Development for Middle School Students Struggling With Fractions: Assessment and Intervention.

PubMed

Zhang, Dake; Stecker, Pamela; Huckabee, Sloan; Miller, Rhonda

2016-09-01

Research has suggested that different strategies used when solving fraction problems are highly correlated with students' problem-solving accuracy. This study (a) utilized latent profile modeling to classify students into three different strategic developmental levels in solving fraction comparison problems and (b) accordingly provided differentiated strategic training for students starting from two different strategic developmental levels. In Study 1 we assessed 49 middle school students' performance on fraction comparison problems and categorized students into three clusters of strategic developmental clusters: a cross-multiplication cluster with the highest accuracy, a representation strategy cluster with medium accuracy, and a whole-number strategy cluster with the lowest accuracy. Based on the strategic developmental levels identified in Study 1, in Study 2 we selected three students from the whole-number strategy cluster and another three students from the representation strategy cluster and implemented a differentiated strategic training intervention within a multiple-baseline design. Results showed that both groups of students transitioned from less advanced to more advanced strategies and improved their problem-solving accuracy during the posttest, the maintenance test, and the generalization test. © Hammill Institute on Disabilities 2014.

Mesoporous silica nanoparticle-based substrates for cell directed delivery of Notch signalling modulators to control myoblast differentiation

NASA Astrophysics Data System (ADS)

Böcking, Dominique; Wiltschka, Oliver; Niinimäki, Jenni; Shokry, Hussein; Brenner, Rolf; Lindén, Mika; Sahlgren, Cecilia

2014-01-01

Biochemical cues are critical to control stem cell function and can be utilized to develop smart biomaterials for stem cell engineering. The challenge is to deliver these cues in a restricted manner with spatial and temporal control. Here we have developed bilayer films of mesoporous silica nanoparticles for delayed cellular delivery of Notch modulators to promote muscle stem cell differentiation. We demonstrate that drug-loaded particles are internalized from the particle-covered surface, which allows for direct delivery of the drug into the cell and a delayed and confined drug release. Substrates of particles loaded with γ-secretase-inhibitors, which block the Notch signalling pathway, promoted efficient differentiation of myoblasts. The particle substrates were fully biocompatible and did not interfere with the inherent differentiation process. We further demonstrate that impregnating commercially available, biocompatible polymer scaffolds with MSNs allows for a free standing substrate for cell directed drug delivery.Biochemical cues are critical to control stem cell function and can be utilized to develop smart biomaterials for stem cell engineering. The challenge is to deliver these cues in a restricted manner with spatial and temporal control. Here we have developed bilayer films of mesoporous silica nanoparticles for delayed cellular delivery of Notch modulators to promote muscle stem cell differentiation. We demonstrate that drug-loaded particles are internalized from the particle-covered surface, which allows for direct delivery of the drug into the cell and a delayed and confined drug release. Substrates of particles loaded with γ-secretase-inhibitors, which block the Notch signalling pathway, promoted efficient differentiation of myoblasts. The particle substrates were fully biocompatible and did not interfere with the inherent differentiation process. We further demonstrate that impregnating commercially available, biocompatible polymer scaffolds with MSNs allows for a free standing substrate for cell directed drug delivery. Electronic supplementary information (ESI) available: (1) Particle characterization. (2) Immunohistochemistry and SEM analyses of C2C12 cells grown on films for 3, 6, 24 and 72 h. Light microscopy and WST1 analyses of cells grown on cover slips and films for 6, 24 and 72 h (3) Quantification of protein levels of C2C12 cells differentiating on cover slips versus MSN films. (4) Stability of MSN films in biological solution and the influence on cell viability. (5) Cell internalization of particles from MSN films and intracellular drug release at 12 and 24 h (6) Cell internalization and intracellular DiI release of MSNs from (3Dtro®) fiber scaffolds impregnated with MSNs. See DOI: 10.1039/c3nr04022d

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm

PubMed Central

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

PubMed

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

Optimal timing of pulse onset for language mapping with navigated repetitive transcranial magnetic stimulation.

PubMed

Krieg, Sandro M; Tarapore, Phiroz E; Picht, Thomas; Tanigawa, Noriko; Houde, John; Sollmann, Nico; Meyer, Bernhard; Vajkoczy, Peter; Berger, Mitchel S; Ringel, Florian; Nagarajan, Srikantan

2014-10-15

Within the primary motor cortex, navigated transcranial magnetic stimulation (nTMS) has been shown to yield maps strongly correlated with those generated by direct cortical stimulation (DCS). However, the stimulation parameters for repetitive nTMS (rTMS)-based language mapping are still being refined. For this purpose, the present study compares two rTMS protocols, which differ in the timing of pulse train onset relative to picture presentation onset during object naming. Results were the correlated with DCS language mapping during awake surgery. Thirty-two patients with left-sided perisylvian tumors were examined by rTMS prior to awake surgery. Twenty patients underwent rTMS pulse trains starting at 300 ms after picture presentation onset (delayed TMS), whereas another 12 patients received rTMS pulse trains starting at the picture presentation onset (ONSET TMS). These rTMS results were then evaluated for correlation with intraoperative DCS results as gold standard in terms of differential consistencies in receiver operating characteristics (ROC) statistics. Logistic regression analysis by protocols and brain regions were conducted. Within and around Broca's area, there was no difference in sensitivity (onset TMS: 100%, delayed TMS: 100%), negative predictive value (NPV) (onset TMS: 100%, delayed TMS: 100%), and positive predictive value (PPV) (onset TMS: 55%, delayed TMS: 54%) between the two protocols compared to DCS. However, specificity differed significantly (onset TMS: 67%, delayed TMS: 28%). In contrast, for posterior language regions, such as supramarginal gyrus, angular gyrus, and posterior superior temporal gyrus, early pulse train onset stimulation showed greater specificity (onset TMS: 92%, delayed TMS: 20%), NPV (onset TMS: 92%, delayed TMS: 57%) and PPV (onset TMS: 75%, delayed TMS: 30%) with comparable sensitivity (onset TMS: 75%, delayed TMS: 70%). Logistic regression analysis also confirmed the greater fit of the predictions by rTMS that had the pulse train onset coincident with the picture presentation onset when compared to the delayed stimulation. Analyses of differential disruption patterns of mapped cortical regions were further able to distinguish clusters of cortical regions standardly associated with semantic and pre-vocalization phonological networks proposed in various models of word production. Repetitive nTMS predictions by both protocols correlate well with DCS outcomes especially in Broca's region, particularly with regard to TMS negative predictions. With this study, we have demonstrated that rTMS stimulation onset coincident with picture presentation onset improves the accuracy of preoperative language maps, particularly within posterior language areas. Moreover, immediate and delayed pulse train onsets may have complementary disruption patterns that could differentially capture cortical regions causally necessary for semantic and pre-vocalization phonological networks. Published by Elsevier Inc.

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Extending the Constant Coefficient Solution Technique to Variable Coefficient Ordinary Differential Equations

ERIC Educational Resources Information Center

Mohammed, Ahmed; Zeleke, Aklilu

2015-01-01

We introduce a class of second-order ordinary differential equations (ODEs) with variable coefficients whose closed-form solutions can be obtained by the same method used to solve ODEs with constant coefficients. General solutions for the homogeneous case are discussed.

Contribution of methylglyoxal to delayed healing of bone injury in diabetes.

PubMed

Aikawa, Takao; Matsubara, Hidenori; Ugaji, Shuhei; Shirakawa, Junichi; Nagai, Ryoji; Munesue, Seiichi; Harashima, Ai; Yamamoto, Yasuhiko; Tsuchiya, Hiroyuki

2017-07-01

Patients with diabetes are vulnerable to delayed bone fracture healing or pseudoarthrosis. Chronic sustained hyperglycemia, reactive intermediate derivatives of glucose metabolism, such as methylglyoxal (MGO), and advanced glycation end‑products (AGEs) are implicated in diabetic complications. In the present study, it was examined whether MGO is able to cause disturbed bone healing in diabetes. Diabetes was induced in male mice by injection of streptozotocin (50 mg/kg) for 5 days. A bone defect (1.0‑mm diameter) was created in the left distal femur, and bone repair was assessed from an examination of computed tomography scans. ST2 cells were exposed to MGO (0‑400 µM) to investigate osteoblastic differentiation, cell viability, and damage. Consequently, blood glucose and hemoglobin A1c levels in diabetic mice were determined to be 493±14.1 mg/dl and 8.0±0.05%, respectively. Compared with non‑diabetic control mice, diabetic mice exhibited markedly delayed bone healing, with increased levels of the MGO‑derived AGEs, Nε‑(carboxymethyl)‑lysine and Nδ‑(5‑hydro‑5‑methyl‑4‑imidazolone‑2‑yl)‑ornithine, in the sera and femurs. MGO inhibited the osteoblastic differentiation of ST2 cells in a dose‑dependent manner, and markedly decreased cell proliferation through cytotoxicity. In conclusion, MGO has been demonstrated to cause impaired osteoblastic differentiation and delayed bone repair in diabetes. Therefore, detoxification of MGO may be a potentially useful strategy against bone problems in patients with diabetes.

Response to Intervention and the Pyramid Model

ERIC Educational Resources Information Center

Fox, Lise; Carta, Judith; Strain, Phil; Dunlap, Glen; Hemmeter, Mary Louise

2009-01-01

Response to Intervention (RtI) offers a comprehensive model for the prevention of delays in learning and behavior. While this problem-solving framework was initially designed for application within Kindergarten to 12th grade programs, there is substantial research that supports the value of the model for application within early childhood…

Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

PubMed

Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

2012-09-01

This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

Solving differential equations with unknown constitutive relations as recurrent neural networks

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

Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.

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 learningmore » 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.« less

Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells.

PubMed

Sundnes, J; Lines, G T; Tveito, A

2001-08-01

The contraction of the heart is preceded and caused by a cellular electro-chemical reaction, causing an electrical field to be generated. Performing realistic computer simulations of this process involves solving a set of partial differential equations, as well as a large number of ordinary differential equations (ODEs) characterizing the reactive behavior of the cardiac tissue. Experiments have shown that the solution of the ODEs contribute significantly to the total work of a simulation, and there is thus a strong need to utilize efficient solution methods for this part of the problem. This paper presents how an efficient implicit Runge-Kutta method may be adapted to solve a complicated cardiac cell model consisting of 31 ODEs, and how this solver may be coupled to a set of PDE solvers to provide complete simulations of the electrical activity.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

An Automatic Orthonormalization Method for Solving Stiff Boundary-Value Problems

NASA Astrophysics Data System (ADS)

Davey, A.

1983-08-01

A new initial-value method is described, based on a remark by Drury, for solving stiff linear differential two-point cigenvalue and boundary-value problems. The method is extremely reliable, it is especially suitable for high-order differential systems, and it is capable of accommodating realms of stiffness which other methods cannot reach. The key idea behind the method is to decompose the stiff differential operator into two non-stiff operators, one of which is nonlinear. The nonlinear one is specially chosen so that it advances an orthonormal frame, indeed the method is essentially a kind of automatic orthonormalization; the second is auxiliary but it is needed to determine the required function. The usefulness of the method is demonstrated by calculating some eigenfunctions for an Orr-Sommerfeld problem when the Reynolds number is as large as 10°.

State feedback controller design for the synchronization of Boolean networks with time delays

NASA Astrophysics Data System (ADS)

Li, Fangfei; Li, Jianning; Shen, Lijuan

2018-01-01

State feedback control design to make the response Boolean network synchronize with the drive Boolean network is far from being solved in the literature. Motivated by this, this paper studies the feedback control design for the complete synchronization of two coupled Boolean networks with time delays. A necessary condition for the existence of a state feedback controller is derived first. Then the feedback control design procedure for the complete synchronization of two coupled Boolean networks is provided based on the necessary condition. Finally, an example is given to illustrate the proposed design procedure.

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Bains, N. J. C.

1986-01-01

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

NASA Astrophysics Data System (ADS)

Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An

2012-12-01

This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Estimation of nonlinear pilot model parameters including time delay.

NASA Technical Reports Server (NTRS)

Schiess, J. R.; Roland, V. R.; Wells, W. R.

1972-01-01

Investigation of the feasibility of using a Kalman filter estimator for the identification of unknown parameters in nonlinear dynamic systems with a time delay. The problem considered is the application of estimation theory to determine the parameters of a family of pilot models containing delayed states. In particular, the pilot-plant dynamics are described by differential-difference equations of the retarded type. The pilot delay, included as one of the unknown parameters to be determined, is kept in pure form as opposed to the Pade approximations generally used for these systems. Problem areas associated with processing real pilot response data are included in the discussion.

Global stabilization analysis of inertial memristive recurrent neural networks with discrete and distributed delays.

PubMed

Wang, Leimin; Zeng, Zhigang; Ge, Ming-Feng; Hu, Junhao

2018-05-02

This paper deals with the stabilization problem of memristive recurrent neural networks with inertial items, discrete delays, bounded and unbounded distributed delays. First, for inertial memristive recurrent neural networks (IMRNNs) with second-order derivatives of states, an appropriate variable substitution method is invoked to transfer IMRNNs into a first-order differential form. Then, based on nonsmooth analysis theory, several algebraic criteria are established for the global stabilizability of IMRNNs under proposed feedback control, where the cases with both bounded and unbounded distributed delays are successfully addressed. Finally, the theoretical results are illustrated via the numerical simulations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling.

PubMed

Bai, Neng; Li, Guifang

2014-02-24

The equalizer tap length requirement is investigated analytically and numerically for differential modal group delay (DMGD) compensated fiber link with weakly random mode coupling. Each span of the DMGD compensated link comprises multiple pairs of fibers which have opposite signs of DMGD. The result reveals that under weak random mode coupling, the required tap length of the equalizer is proportional to modal group delay of a single DMGD compensated pair, instead of the total modal group delay (MGD) of the entire link. By using small DMGD compensation step sizes, the required tap length (RTL) can be potentially reduced by 2 orders of magnitude.

Arbitrary-step randomly delayed robust filter with application to boost phase tracking

NASA Astrophysics Data System (ADS)

Qin, Wutao; Wang, Xiaogang; Bai, Yuliang; Cui, Naigang

2018-04-01

The conventional filters such as extended Kalman filter, unscented Kalman filter and cubature Kalman filter assume that the measurement is available in real-time and the measurement noise is Gaussian white noise. But in practice, both two assumptions are invalid. To solve this problem, a novel algorithm is proposed by taking the following four steps. At first, the measurement model is modified by the Bernoulli random variables to describe the random delay. Then, the expression of predicted measurement and covariance are reformulated, which could get rid of the restriction that the maximum number of delay must be one or two and the assumption that probabilities of Bernoulli random variables taking the value one are equal. Next, the arbitrary-step randomly delayed high-degree cubature Kalman filter is derived based on the 5th-degree spherical-radial rule and the reformulated expressions. Finally, the arbitrary-step randomly delayed high-degree cubature Kalman filter is modified to the arbitrary-step randomly delayed high-degree cubature Huber-based filter based on the Huber technique, which is essentially an M-estimator. Therefore, the proposed filter is not only robust to the randomly delayed measurements, but robust to the glint noise. The application to the boost phase tracking example demonstrate the superiority of the proposed algorithms.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

A recurrent neural network for solving bilevel linear programming problem.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

2014-04-01

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

NASA Astrophysics Data System (ADS)

Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

2016-11-01

Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Design of Linear Quadratic Regulators and Kalman Filters

NASA Technical Reports Server (NTRS)

Lehtinen, B.; Geyser, L.

1986-01-01

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Capacity to Delay Reward Differentiates Obsessive Compulsive Disorder and Obsessive Compulsive Personality Disorder

PubMed Central

Pinto, Anthony; Steinglass, Joanna E.; Greene, Ashley L.; Weber, Elke U.; Simpson, H. Blair

2013-01-01

Background Although the relationship between obsessive compulsive disorder (OCD) and obsessive compulsive personality disorder (OCPD) has long been debated, clinical samples of OCD (without OCPD) and OCPD (without OCD) have never been systematically compared. We studied whether individuals with OCD, OCPD, or both conditions differ on symptomatology, functioning, and a measure of self-control: the capacity to delay reward. Methods 25 OCD, 25 OCPD, 25 comorbid OCD+OCPD, and 25 healthy controls (HC) completed clinical assessments and a validated intertemporal choice task that measures capacity to forego small immediate rewards for larger delayed rewards. Results OCD and OCPD subjects both showed impairment in psychosocial functioning and quality of life, as well as compulsive behavior, but only subjects with OCD reported obsessions. Individuals with OCPD, with or without comorbid OCD, discounted the value of delayed monetary rewards significantly less than OCD and HC. This excessive capacity to delay reward discriminates OCPD from OCD, and is associated with perfectionism and rigidity. Conclusions OCD and OCPD are both impairing disorders marked by compulsive behaviors, but they can be differentiated by the presence of obsessions in OCD and by excessive capacity to delay reward in OCPD. That individuals with OCPD show less temporal discounting (suggestive of excessive self-control) whereas prior studies have shown that individuals with substance use disorders show greater discounting (suggestive of impulsivity) supports the premise that this component of self-control lies on a continuum in which both extremes (impulsivity and overcontrol) contribute to psychopathology. PMID:24199665

Extensions to the Speech Disorders Classification System (SDCS)

ERIC Educational Resources Information Center

Shriberg, Lawrence D.; Fourakis, Marios; Hall, Sheryl D.; Karlsson, Heather B.; Lohmeier, Heather L.; McSweeny, Jane L.; Potter, Nancy L.; Scheer-Cohen, Alison R.; Strand, Edythe A.; Tilkens, Christie M.; Wilson, David L.

2010-01-01

This report describes three extensions to a classification system for paediatric speech sound disorders termed the Speech Disorders Classification System (SDCS). Part I describes a classification extension to the SDCS to differentiate motor speech disorders from speech delay and to differentiate among three sub-types of motor speech disorders.…

Discounting of Monetary Rewards that are Both Delayed and Probabilistic: Delay and Probability Combine Multiplicatively, not Additively

PubMed Central

Vanderveldt, Ariana; Green, Leonard; Myerson, Joel

2014-01-01

The value of an outcome is affected both by the delay until its receipt (delay discounting) and by the likelihood of its receipt (probability discounting). Despite being well-described by the same hyperboloid function, delay and probability discounting involve fundamentally different processes, as revealed, for example, by the differential effects of reward amount. Previous research has focused on the discounting of delayed and probabilistic rewards separately, with little research examining more complex situations in which rewards are both delayed and probabilistic. In two experiments, participants made choices between smaller rewards that were both immediate and certain and larger rewards that were both delayed and probabilistic. Analyses revealed significant interactions between delay and probability factors inconsistent with an additive model. In contrast, a hyperboloid discounting model in which delay and probability were combined multiplicatively provided an excellent fit to the data. These results suggest that the hyperboloid is a good descriptor of decision making in complicated monetary choice situations like those people encounter in everyday life. PMID:24933696

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

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.

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

A Second-Year Undergraduate Course in Applied Differential Equations.

ERIC Educational Resources Information Center

Fahidy, Thomas Z.

1991-01-01

Presents the framework for a chemical engineering course using ordinary differential equations to solve problems with the underlying strategy of concisely discussing the theory behind each solution technique without extensions to formal proofs. Includes typical class illustrations, student responses to this strategy, and reaction of the…

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

PubMed

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

2013-06-01

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

The Mars Observer differential one-way range demonstration

NASA Technical Reports Server (NTRS)

Kroger, P. M.; Border, J. S.; Nandi, S.

1994-01-01

Current methods of angular spacecraft positioning using station differenced range data require an additional observation of an extragalactic radio source (quasar) to estimate the timing offset between the reference clocks at the two Deep Space Stations. The quasar observation is also used to reduce the effects of instrumental and media delays on the radio metric observable by forming a difference with the spacecraft observation (delta differential one-way range, delta DOR). An experiment has been completed using data from the Global Positioning System satellites to estimate the station clock offset, eliminating the need for the quasar observation. The requirements for direct measurement of the instrumental delays that must be made in the absence of a quasar observation are assessed. Finally, the results of the 'quasar-free' differential one-way range, or DOR, measurements of the Mars Observer spacecraft are compared with those of simultaneous conventional delta DOR measurements.

Undermining belief in false memories leads to less efficient problem-solving behaviour.

PubMed

Wang, Jianqin; Otgaar, Henry; Howe, Mark L; Smeets, Tom; Merckelbach, Harald; Nahouli, Zacharia

2017-08-01

Memories of events for which the belief in the occurrence of those events is undermined, but recollection is retained, are called nonbelieved memories (NBMs). The present experiments examined the effects of NBMs on subsequent problem-solving behaviour. In Experiment 1, we challenged participants' beliefs in their memories and examined whether NBMs affected subsequent solution rates on insight-based problems. True and false memories were elicited using the Deese/Roediger-McDermott (DRM) paradigm. Then participants' belief in true and false memories was challenged by telling them the item had not been presented. We found that when the challenge led to undermining belief in false memories, fewer problems were solved than when belief was not challenged. In Experiment 2, a similar procedure was used except that some participants solved the problems one week rather than immediately after the feedback. Again, our results showed that undermining belief in false memories resulted in lower problem solution rates. These findings suggest that for false memories, belief is an important agent in whether memories serve as effective primes for immediate and delayed problem-solving.

Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

PubMed Central

Lin, S. H.; Eyring, H.

1971-01-01

The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898

Differential Relations between Facets of Complex Problem Solving and Students' Immigration Background

ERIC Educational Resources Information Center

Sonnleitner, Philipp; Brunner, Martin; Keller, Ulrich; Martin, Romain

2014-01-01

Whereas the assessment of complex problem solving (CPS) has received increasing attention in the context of international large-scale assessments, its fairness in regard to students' cultural background has gone largely unexplored. On the basis of a student sample of 9th-graders (N = 299), including a representative number of immigrant students (N…

Comparative Analysis.

DTIC Science & Technology

1987-11-01

differential qualita- tive (DQ) analysis, which solves the task, providing explanations suitable for use by design systems, automated diagnosis, intelligent...solves the task, providing explanations suitable for use by design systems, automated diagnosis, intelligent tutoring systems, and explanation based...comparative analysis as an important component; the explanation is used in many different ways. * One way method of automated design is the principlvd

A Life History Approach to Delineating How Harsh Environments and Hawk Temperament Traits Differentially Shape Children's Problem-Solving Skills

ERIC Educational Resources Information Center

Suor, Jennifer H.; Sturge-Apple, Melissa L.; Davies, Patrick T.; Cicchetti, Dante

2017-01-01

Harsh environments are known to predict deficits in children's cognitive abilities. Life history theory approaches challenge this interpretation, proposing stressed children's cognition becomes specialized to solve problems in fitness-enhancing ways. The goal of this study was to examine associations between early environmental harshness and…

Cited2 Gene Controls Pluripotency and Cardiomyocyte Differentiation of Murine Embryonic Stem Cells through Oct4 Gene*

PubMed Central

Li, Qiang; Ramírez-Bergeron, Diana L.; Dunwoodie, Sally L.; Yang, Yu-Chung

2012-01-01

Cited2 (CBP/p300-interacting transactivator with glutamic acid (E)/aspartic acid (D)-rich tail 2) is a transcriptional modulator critical for the development of multiple organs. Although many Cited2-mediated phenotypes and molecular events have been well characterized using in vivo genetic murine models, Cited2-directed cell fate decision in embryonic stem cells (ESCs) remains elusive. In this study, we examined the role of Cited2 in the maintenance of stemness and pluripotency of murine ESCs by a gene-targeting approach. Cited2 knock-out (Cited2Δ/−, KO) ESCs display defective differentiation. Loss of Cited2 in differentiating ESCs results in delayed silencing of the genes involved in the maintenance of pluripotency and self-renewal of stem cells (Oct4, Klf4, Sox2, and c-Myc) and the disturbance in cardiomyocyte, hematopoietic, and neuronal differentiation. In addition, Cited2 KO ESCs experience a delayed induction of cardiomyocyte differentiation-associated proteins, NFAT3 (along with the reduced expression of NFAT3 target genes, Nkx2.5 and β-MHC), N-cadherin, and smooth muscle actin. CITED2 is recruited to the Oct4 promoter to regulate its expression during early ESC differentiation. This is the first demonstration that Cited2 controls ESC pluripotency and differentiation via direct regulation of Oct4 gene expression. PMID:22761414

Biennial-Aligned Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models

NASA Astrophysics Data System (ADS)

Pukite, P. R.

2017-12-01

By solving Laplace's tidal equations along the equatorial Pacific thermocline, assuming a delayed-differential effective gravity forcing due to a combined lunar+solar (lunisolar) stimulus, we are able to precisely match ENSO periodic variations over wide intervals. The underlying pattern is difficult to decode by conventional means such as spectral analysis, which is why it has remained hidden for so long, despite the excellent agreement in the time-domain. What occurs is that a non-linear seasonal modulation with monthly and fortnightly lunar impulses along with a biennially-aligned "see-saw" is enough to cause a physical aliasing and thus multiple folding in the frequency spectrum. So, instead of a conventional spectral tidal decomposition, we opted for a time-domain cross-validating approach to calibrate the amplitude and phasing of the lunisolar cycles. As the lunar forcing consists of three fundamental periods (draconic, anomalistic, synodic), we used the measured Earth's length-of-day (LOD) decomposed and resolved at a monthly time-scale [1] to align the amplitude and phase precisely. Even slight variations from the known values of the long-period tides will degrade the fit, so a high-resolution calibration is possible. Moreover, a narrow training segment from 1880-1920 using NINO34/SOI data is adequate to extrapolate the cycles of the past 100 years (see attached figure). To further understand the biennial impact of a yearly differential-delay, we were able to also decompose using difference equations the historical sea-level-height readings at Sydney harbor to clearly expose the ENSO behavior. Finally, the ENSO lunisolar model was validated by back-extrapolating to Unified ENSO coral proxy (UEP) records dating to 1650. The quasi-biennial oscillation (QBO) behavior of equatorial stratospheric winds derives following a similar pattern to ENSO via the tidal equations, but with an emphasis on draconic forcing. This improvement in ENSO and QBO understanding has implications for vastly simplifying global climate models due to the straightforward application of a well-known and well-calibrated forcing. [1] Na, Sung-Ho, et al. "Characteristics of Perturbations in Recent Length of Day and Polar Motion." Journal of Astronomy and Space Sciences 30 (2013): 33-41.

Method to fabricate multi-level silicon-based microstructures via use of an etching delay layer

DOEpatents

Manginell, Ronald P.; Schubert, W. Kent; Shul, Randy J.

2005-08-16

New methods for fabrication of silicon microstructures have been developed. In these methods, an etching delay layer is deposited and patterned so as to provide differential control on the depth of features being etched into a substrate material. Structures having features with different depth can be formed thereby in a single etching step.

EXPOSURE TO DIETHYL HEXYL PHTHALATE (DEHP) DELAYS PUBERTY AND REDUCES ANDROGEN-DEPENDENT TISSUE WEIGHTS IN LONG EVANS HOODED AND SPRAGUE DAWLEY MALE RATS

EPA Science Inventory

DEHP is a plasticizer that alters sexual differentiation in the male rat by reducing fetal Leydig cell testosterone synthesis and insl3 mRNA levels. When exposure includes the pubertal stage of life, DEHP and other phthalates delay puberty and reduce androgen-dependent tissue wei...

Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller.

PubMed

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.

Playing Newtonian Games with Modellus

ERIC Educational Resources Information Center

Teodoro, Vitor Duarte

2004-01-01

This article is a short introduction on how to use Modellus (a computer package that is freely available on the Internet and used in the IOP "Advancing Physics" course) to build physics games using Newton's laws, expressed as differential equations. Solving systems of differential equations is beyond most secondary-school or first-year college…

Solving Nonlinear Coupled Differential Equations

NASA Technical Reports Server (NTRS)

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.

Ectopic Expression of Capsicum-Specific Cell Wall Protein Capsicum annuum Senescence-Delaying 1 (CaSD1) Delays Senescence and Induces Trichome Formation in Nicotiana benthamiana

PubMed Central

Seo, Eunyoung; Yeom, Seon-In; Jo, SungHwan; Jeong, Heejin; Kang, Byoung-Cheorl; Choi, Doil

2012-01-01

Secreted proteins are known to have multiple roles in plant development, metabolism, and stress response. In a previous study to understand the roles of secreted proteins, Capsicum annuum secreted proteins (CaS) were isolated by yeast secretion trap. Among the secreted proteins, we further characterized Capsicum annuum senescence-delaying 1 (CaSD1), a gene encoding a novel secreted protein that is present only in the genus Capsicum. The deduced CaSD1 contains multiple repeats of the amino acid sequence KPPIHNHKPTDYDRS. Interestingly, the number of repeats varied among cultivars and species in the Capsicum genus. CaSD1 is constitutively expressed in roots, and Agrobacterium-mediated transient overexpression of CaSD1 in Nicotiana benthamiana leaves resulted in delayed senescence with a dramatically increased number of trichomes and enlarged epidermal cells. Furthermore, senescence- and cell division-related genes were differentially regulated by CaSD1-overexpressing plants. These observations imply that the pepper-specific cell wall protein CaSD1 plays roles in plant growth and development by regulating cell division and differentiation. PMID:22441673

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Numerical solution of second order ODE directly by two point block backward differentiation formula

NASA Astrophysics Data System (ADS)

Zainuddin, Nooraini; Ibrahim, Zarina Bibi; Othman, Khairil Iskandar; Suleiman, Mohamed; Jamaludin, Noraini

2015-12-01

Direct Two Point Block Backward Differentiation Formula, (BBDF2) for solving second order ordinary differential equations (ODEs) will be presented throughout this paper. The method is derived by differentiating the interpolating polynomial using three back values. In BBDF2, two approximate solutions are produced simultaneously at each step of integration. The method derived is implemented by using fixed step size and the numerical results that follow demonstrate the advantage of the direct method as compared to the reduction method.

A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves

NASA Astrophysics Data System (ADS)

Pecora, Nicolò; Sodini, Mauro

2018-05-01

This article considers a Cournot duopoly model in a continuous-time framework and analyze its dynamic behavior when the competitors are heterogeneous in determining their output decision. Specifically the model is expressed in the form of differential equations with discrete delays. The stability conditions of the unique Nash equilibrium of the system are determined and the emergence of Hopf bifurcations is shown. Applying some recent mathematical techniques (stability switching curves) and performing numerical simulations, the paper confirms how different time delays affect the stability of the economy.

Inverse optimal design of input-to-state stabilisation for affine nonlinear systems with input delays

NASA Astrophysics Data System (ADS)

Cai, Xiushan; Meng, Lingxin; Zhang, Wei; Liu, Leipo

2018-03-01

We establish robustness of the predictor feedback control law to perturbations appearing at the system input for affine nonlinear systems with time-varying input delay and additive disturbances. Furthermore, it is shown that it is inverse optimal with respect to a differential game problem. All of the stability and inverse optimality proofs are based on the infinite-dimensional backstepping transformation and an appropriate Lyapunov functional. A single-link manipulator subject to input delays and disturbances is given to illustrate the validity of the proposed method.

Finite-time hybrid projective synchronization of the drive-response complex networks with distributed-delay via adaptive intermittent control

NASA Astrophysics Data System (ADS)

Cheng, Lin; Yang, Yongqing; Li, Li; Sui, Xin

2018-06-01

This paper studies the finite-time hybrid projective synchronization of the drive-response complex networks. In the model, general transmission delays and distributed delays are also considered. By designing the adaptive intermittent controllers, the response network can achieve hybrid projective synchronization with the drive system in finite time. Based on finite-time stability theory and several differential inequalities, some simple finite-time hybrid projective synchronization criteria are derived. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Finite-Dimensional Representations for Controlled Diffusions with Delay

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

Federico, Salvatore, E-mail: salvatore.federico@unimi.it; Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr

2015-02-15

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.

Cloud-based shaft torque estimation for electric vehicle equipped with integrated motor-transmission system

NASA Astrophysics Data System (ADS)

Zhu, Xiaoyuan; Zhang, Hui; Yang, Bo; Zhang, Guichen

2018-01-01

In order to improve oscillation damping control performance as well as gear shift quality of electric vehicle equipped with integrated motor-transmission system, a cloud-based shaft torque estimation scheme is proposed in this paper by using measurable motor and wheel speed signals transmitted by wireless network. It can help reduce computational burden of onboard controllers and also relief network bandwidth requirement of individual vehicle. Considering possible delays during signal wireless transmission, delay-dependent full-order observer design is proposed to estimate the shaft torque in cloud server. With these random delays modeled by using homogenous Markov chain, robust H∞ performance is adopted to minimize the effect of wireless network-induced delays, signal measurement noise as well as system modeling uncertainties on shaft torque estimation error. Observer parameters are derived by solving linear matrix inequalities, and simulation results using acceleration test and tip-in, tip-out test demonstrate the effectiveness of proposed shaft torque observer design.

A Space Affine Matching Approach to fMRI Time Series Analysis.

PubMed

Chen, Liang; Zhang, Weishi; Liu, Hongbo; Feng, Shigang; Chen, C L Philip; Wang, Huili

2016-07-01

For fMRI time series analysis, an important challenge is to overcome the potential delay between hemodynamic response signal and cognitive stimuli signal, namely the same frequency but different phase (SFDP) problem. In this paper, a novel space affine matching feature is presented by introducing the time domain and frequency domain features. The time domain feature is used to discern different stimuli, while the frequency domain feature to eliminate the delay. And then we propose a space affine matching (SAM) algorithm to match fMRI time series by our affine feature, in which a normal vector is estimated using gradient descent to explore the time series matching optimally. The experimental results illustrate that the SAM algorithm is insensitive to the delay between the hemodynamic response signal and the cognitive stimuli signal. Our approach significantly outperforms GLM method while there exists the delay. The approach can help us solve the SFDP problem in fMRI time series matching and thus of great promise to reveal brain dynamics.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

Delayed temporal discrimination in pigeons: A comparison of two procedures

PubMed Central

Chatlosh, Diane L.; Wasserman, Edward A.

1987-01-01

A within-subjects comparison was made of pigeons' performance on two temporal discrimination procedures that were signaled by differently colored keylight samples. During stimulus trials, a peck on the key displaying a slanted line was reinforced following short keylight samples, and a peck on the key displaying a horizontal line was reinforced following long keylight samples, regardless of the location of the stimuli on those two choice keys. During position trials, a peck on the left key was reinforced following short keylight samples and a peck on the right key was reinforced following long keylight samples, regardless of which line stimulus appeared on the correct key. Thus, on stimulus trials, the correct choice key could not be discriminated prior to the presentation of the test stimuli, whereas on position trials, the correct choice key could be discriminated during the presentation of the sample stimulus. During Phase 1, with a 0-s delay between sample and choice stimuli, discrimination learning was faster on position trials than on stimulus trials for all 4 birds. During Phase 2, 0-, 0.5-, and 1.0-s delays produced differential loss of stimulus control under the two tasks for 2 birds. Response patterns during the delay intervals provided some evidence for differential mediation of the two delayed discriminations. These between-task differences suggest that the same processes may not mediate performance in each. PMID:16812483

A high-resolution programmable Vernier delay generator based on carry chains in FPGA

NASA Astrophysics Data System (ADS)

Cui, Ke; Li, Xiangyu; Zhu, Rihong

2017-06-01

This paper presents an architecture of a high-resolution delay generator implemented in a single field programmable gate array chip by exploiting the method of utilizing dedicated carry chains. It serves as the core component in various physical instruments. The proposed delay generator contains the coarse delay step and the fine delay step to guarantee both large dynamic range and high resolution. The carry chains are organized in the Vernier delay loop style to fulfill the fine delay step with high precision and high linearity. The delay generator was implemented in the EP3SE110F1152I3 Stratix III device from Altera on a self-designed test board. Test results show that the obtained resolution is 38.6 ps, and the differential nonlinearity/integral nonlinearity is in the range of [-0.18 least significant bit (LSB), 0.24 LSB]/(-0.02 LSB, 0.01 LSB) under the nominal supply voltage of 1100 mV and environmental temperature of 2 0°C. The delay generator is rather efficient concerning resource cost, which uses only 668 look-up tables and 146 registers in total.

The Role of Government and NGO in Promoting Wellness of People with Down Syndrome

ERIC Educational Resources Information Center

Jiar, Yeo Kee; Handayani, Lina; Xi, Lu

2014-01-01

People with Down Syndrome (PWDS) experience cognitive delays indicated by difficulties with cognition, long-term memory and non-verbal problem solving skills. PWDS have specific speech and language impairments which affect all aspects of development. Some children develop difficult behaviors which cause family stress and affect social and…

Cross-layer Joint Relay Selection and Power Allocation Scheme for Cooperative Relaying System

NASA Astrophysics Data System (ADS)

Zhi, Hui; He, Mengmeng; Wang, Feiyue; Huang, Ziju

2018-03-01

A novel cross-layer joint relay selection and power allocation (CL-JRSPA) scheme over physical layer and data-link layer is proposed for cooperative relaying system in this paper. Our goal is finding the optimal relay selection and power allocation scheme to maximize system achievable rate when satisfying total transmit power constraint in physical layer and statistical delay quality-of-service (QoS) demand in data-link layer. Using the concept of effective capacity (EC), our goal can be formulated into an optimal joint relay selection and power allocation (JRSPA) problem to maximize the EC when satisfying total transmit power limitation. We first solving optimal power allocation (PA) problem with Lagrange multiplier approach, and then solving optimal relay selection (RS) problem. Simulation results demonstrate that CL-JRSPA scheme gets larger EC than other schemes when satisfying delay QoS demand. In addition, the proposed CL-JRSPA scheme achieves the maximal EC when relay located approximately halfway between source and destination, and EC becomes smaller when the QoS exponent becomes larger.

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

PubMed

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A 100-Gb/s noncoherent silicon receiver for PDM-DBPSK/DQPSK signals.

PubMed

Klamkin, Jonathan; Gambini, Fabrizio; Faralli, Stefano; Malacarne, Antonio; Meloni, Gianluca; Berrettini, Gianluca; Contestabile, Giampiero; Potì, Luca

2014-01-27

An integrated noncoherent silicon receiver for demodulation of 100-Gb/s polarization-division multiplexed differential quadrature phase-shift keying and polarization-division multiplexed differential binary phase-shift keying signals is demonstrated. The receiver consists of a 2D surface grating coupler, four Mach-Zehnder delay interferometers and four germanium balanced photodetectors.

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ishihara, Abraham K.; Krishnakumar, Kalmanje Srinlvas; Bakhtiari-Nejad, Maryam

2009-01-01

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

An Evaluation of the Effects of a Mild Delayed Verbal Punisher on Choice of an Immediate Reinforcer by Children With Autism.

PubMed

Sy, Jolene R; Green, Leonard; Gratz, Olivia; Ervin, Thea

2016-09-01

Different combinations of immediate and delayed consequences differentially affect choice. Basic research has found that nonhuman animals are more likely to choose an alternative that produces an immediate reinforcer that is followed by a delayed punisher as the delay to punishment increases. The purpose of the current effort was to examine the choices of three individuals with autism when they were given the choice between receiving a larger amount of preferred food followed by a mild, delayed verbal punisher and a smaller amount of the preferred food. A secondary purpose was to determine whether signal presence and duration would affect the efficacy of the punisher (i.e., whether children would be more likely to select the smaller reward that was not followed by a delayed punisher). Results were idiosyncratic across children and highlight the need to evaluate choice under multiple arrangements. © The Author(s) 2016.

Application values of 99mTc-methoxyisobutylisonitrile imaging for differentiating benign and malignant thymic masses.

PubMed

Lu, Chenghui; Wang, Xufu; Liu, Bin; Liu, Xinfeng; Wang, Guoming; Zhang, Qin

2017-08-01

The aim of the present study was to investigate the application value of 99m Tc-methoxyisobutylisonitrile (MIBI) imaging to differentiate between benign and malignant thymic masses. A total of 32 patients with space-occupying mediastinal masses were enrolled and early and delayed-phase images were collected following injection with the imaging agent. The tumor to background ratio (T/N) values at the different phases were also recorded. The sensitivity of the qualitative analysis to distinguish between benign and malignant thymic masses was 95.24%, with specificity as 90.91%. The T/N values in the early and delayed phases were not significantly different in the group with benign thymic masses, but demonstrated statistical significant differences in the groups with low- and intermediate-grade malignant thymic masses. The T/N values at the above early and delayed phase were significantly different between the benign and low-grade malignancy groups, as well as between low- and moderate-grade malignancy groups. Those between the benign and moderate-grade malignancy groups demonstrated no significant difference. 99m Tc-MIBI imaging was able to differentiate between benign and malignant thymic masses, and the simultaneous semi-quantitative analysis of the T/N values of the tumors may be able to initially determine the degree of malignancy of thymoma.

Robust Real-Time Wide-Area Differential GPS Navigation

NASA Technical Reports Server (NTRS)

Yunck, Thomas P. (Inventor); Bertiger, William I. (Inventor); Lichten, Stephen M. (Inventor); Mannucci, Anthony J. (Inventor); Muellerschoen, Ronald J. (Inventor); Wu, Sien-Chong (Inventor)

1998-01-01

The present invention provides a method and a device for providing superior differential GPS positioning data. The system includes a group of GPS receiving ground stations covering a wide area of the Earth's surface. Unlike other differential GPS systems wherein the known position of each ground station is used to geometrically compute an ephemeris for each GPS satellite. the present system utilizes real-time computation of satellite orbits based on GPS data received from fixed ground stations through a Kalman-type filter/smoother whose output adjusts a real-time orbital model. ne orbital model produces and outputs orbital corrections allowing satellite ephemerides to be known with considerable greater accuracy than from die GPS system broadcasts. The modeled orbits are propagated ahead in time and differenced with actual pseudorange data to compute clock offsets at rapid intervals to compensate for SA clock dither. The orbital and dock calculations are based on dual frequency GPS data which allow computation of estimated signal delay at each ionospheric point. These delay data are used in real-time to construct and update an ionospheric shell map of total electron content which is output as part of the orbital correction data. thereby allowing single frequency users to estimate ionospheric delay with an accuracy approaching that of dual frequency users.

Using delay differential equations to induce alternans in a model of cardiac electrophysiology.

PubMed

Eastman, Justin; Sass, Julian; Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M

2016-09-07

Cardiac electrical alternans is a period-2 dynamical behavior with alternating long and short action potential durations (APD) that often precedes dangerous arrhythmias associated with cardiac arrest. Despite the importance of alternans, many current ordinary differential equations models of cardiac electrophysiology do not produce alternans, thereby limiting the use of these models for studying the mechanisms that underlie this condition. Because delay differential equations (DDEs) commonly induce complex dynamics in other biological systems, we investigate whether incorporating DDEs can lead to alternans development in cardiac models by studying the Fox et al. canine ventricular action potential model. After suppressing the alternans in the original model, we show that alternans can be obtained by introducing DDEs in the model gating variables, and we quantitatively compare the DDE-induced alternans with the alternans present in the original model. We analyze the behavior of the voltage, currents, and gating variables of the model to study the effects of the delays and to determine how alternans develops in that setting, and we discuss the mathematical and physiological implications of our findings. In future work, we aim to apply our approach to induce alternans in models that do not naturally exhibit such dynamics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Security barriers with automated reconnaissance

DOEpatents

McLaughlin, James O; Baird, Adam D; Tullis, Barclay J; Nolte, Roger Allen

2015-04-07

An intrusion delaying barrier includes primary and secondary physical structures and can be instrumented with multiple sensors incorporated into an electronic monitoring and alarm system. Such an instrumented intrusion delaying barrier may be used as a perimeter intrusion defense and assessment system (PIDAS). Problems with not providing effective delay to breaches by intentional intruders and/or terrorists who would otherwise evade detection are solved by attaching the secondary structures to the primary structure, and attaching at least some of the sensors to the secondary structures. By having multiple sensors of various types physically interconnected serves to enable sensors on different parts of the overall structure to respond to common disturbances and thereby provide effective corroboration that a disturbance is not merely a nuisance or false alarm. Use of a machine learning network such as a neural network exploits such corroboration.

Short-term retention of pictures and words as a function of type of distraction and length of delay interval.

PubMed

Pellegrino, J W; Siegel, A W; Dhawan, M

1976-01-01

Picture and word triads were tested in a Brown-Peterson short-term retention task at varying delay intervals (3, 10, or 30 sec) and under acoustic and simultaneous acoustic and visual distraction. Pictures were superior to words at all delay intervals under single acoustic distraction. Dual distraction consistently reduced picture retention while simultaneously facilitating word retention. The results were interpreted in terms of the dual coding hypothesis with modality-specific interference effects in the visual and acoustic processing systems. The differential effects of dual distraction were related to the introduction of visual interference and differential levels of functional acoustic interference across dual and single distraction tasks. The latter was supported by a constant 2/1 ratio in the backward counting rates of the acoustic vs. dual distraction tasks. The results further suggest that retention may not depend on total processing load of the distraction task, per se, but rather that processing load operates within modalities.

Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain

NASA Astrophysics Data System (ADS)

Yi, Taishan; Zou, Xingfu

In this paper, we study the global dynamics of a class of differential equations with temporal delay and spatial non-locality in an unbounded domain. Adopting the compact open topology, we describe the delicate asymptotic properties of the nonlocal delayed effect and establish some a priori estimate for nontrivial solutions which enables us to show the permanence of the equation. Combining these results with a dynamical systems approach, we determine the global dynamics of the equation under appropriate conditions. Applying the main results to the model with Ricker's birth function and Mackey-Glass's hematopoiesis function, we obtain threshold results for the global dynamics of these two models. We explain why our results on the global attractivity of the positive equilibrium in C∖{0} under the compact open topology becomes invalid in C∖{0} with respect to the usual supremum norm, and we identify a subset of C∖{0} in which the positive equilibrium remains attractive with respect to the supremum norm.

Analysis of RDSS positioning accuracy based on RNSS wide area differential technique

NASA Astrophysics Data System (ADS)

Xing, Nan; Su, RanRan; Zhou, JianHua; Hu, XiaoGong; Gong, XiuQiang; Liu, Li; He, Feng; Guo, Rui; Ren, Hui; Hu, GuangMing; Zhang, Lei

2013-10-01

The BeiDou Navigation Satellite System (BDS) provides Radio Navigation Service System (RNSS) as well as Radio Determination Service System (RDSS). RDSS users can obtain positioning by responding the Master Control Center (MCC) inquiries to signal transmitted via GEO satellite transponder. The positioning result can be calculated with elevation constraint by MCC. The primary error sources affecting the RDSS positioning accuracy are the RDSS signal transceiver delay, atmospheric trans-mission delay and GEO satellite position error. During GEO orbit maneuver, poor orbit forecast accuracy significantly impacts RDSS services. A real-time 3-D orbital correction method based on wide-area differential technique is raised to correct the orbital error. Results from the observation shows that the method can successfully improve positioning precision during orbital maneuver, independent from the RDSS reference station. This improvement can reach 50% in maximum. Accurate calibration of the RDSS signal transceiver delay precision and digital elevation map may have a critical role in high precise RDSS positioning services.

Impulsive effect on global exponential stability of BAM fuzzy cellular neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Li, Kelin

2010-02-01

In this article, a class of impulsive bidirectional associative memory (BAM) fuzzy cellular neural networks (FCNNs) with time-varying delays is formulated and investigated. By employing delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM FCNNs with time-varying delays are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM FCNNs. An example is given to show the effectiveness of the results obtained here.

The role of early visual cortex in visual short-term memory and visual attention.

PubMed

Offen, Shani; Schluppeck, Denis; Heeger, David J

2009-06-01

We measured cortical activity with functional magnetic resonance imaging to probe the involvement of early visual cortex in visual short-term memory and visual attention. In four experimental tasks, human subjects viewed two visual stimuli separated by a variable delay period. The tasks placed differential demands on short-term memory and attention, but the stimuli were visually identical until after the delay period. Early visual cortex exhibited sustained responses throughout the delay when subjects performed attention-demanding tasks, but delay-period activity was not distinguishable from zero when subjects performed a task that required short-term memory. This dissociation reveals different computational mechanisms underlying the two processes.

A Novel Approach to Solve Linearized Stellar Pulsation Equations

NASA Astrophysics Data System (ADS)

Bard, Christopher; Teitler, S.

2011-01-01

We present a new approach to modeling linearized, non-radial pulsations in differentially rotating, massive stars. As a first step in this direction, we consider adiabatic pulsations and adopt the Cowling approximation that perturbations of the gravitational potential and its radial derivative are negligible. The angular dependence of the pulsation modes is expressed as a series expansion of associated Legendre polynomials; the resulting coupled system of differential equations is then solved by finding the eigenfrequencies at which the determinant of a characteristic matrix vanishes. Our method improves on previous treatments by removing the requirement that an arbitrary normalization be applied to the eigenfunctions; this brings the benefit of improved numerical robustness.

Neural network for solving convex quadratic bilevel programming problems.

PubMed

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

2014-03-01

In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

Time delay estimation using new spectral and adaptive filtering methods with applications to underwater target detection

NASA Astrophysics Data System (ADS)

Hasan, Mohammed A.

1997-11-01

In this dissertation, we present several novel approaches for detection and identification of targets of arbitrary shapes from the acoustic backscattered data and using the incident waveform. This problem is formulated as time- delay estimation and sinusoidal frequency estimation problems which both have applications in many other important areas in signal processing. Solving time-delay estimation problem allows the identification of the specular components in the backscattered signal from elastic and non-elastic targets. Thus, accurate estimation of these time delays would help in determining the existence of certain clues for detecting targets. Several new methods for solving these two problems in the time, frequency and wavelet domains are developed. In the time domain, a new block fast transversal filter (BFTF) is proposed for a fast implementation of the least squares (LS) method. This BFTF algorithm is derived by using data-related constrained block-LS cost function to guarantee global optimality. The new soft-constrained algorithm provides an efficient way of transferring weight information between blocks of data and thus it is computationally very efficient compared with other LS- based schemes. Additionally, the tracking ability of the algorithm can be controlled by varying the block length and/or a soft constrained parameter. The effectiveness of this algorithm is tested on several underwater acoustic backscattered data for elastic targets and non-elastic (cement chunk) objects. In the frequency domain, the time-delay estimation problem is converted to a sinusoidal frequency estimation problem by using the discrete Fourier transform. Then, the lagged sample covariance matrices of the resulting signal are computed and studied in terms of their eigen- structure. These matrices are shown to be robust and effective in extracting bases for the signal and noise subspaces. New MUSIC and matrix pencil-based methods are derived these subspaces. The effectiveness of the method is demonstrated on the problem of detection of multiple specular components in the acoustic backscattered data. Finally, a method for the estimation of time delays using wavelet decomposition is derived. The sub-band adaptive filtering uses discrete wavelet transform for multi- resolution or sub-band decomposition. Joint time delay estimation for identifying multi-specular components and subsequent adaptive filtering processes are performed on the signal in each sub-band. This would provide multiple 'look' of the signal at different resolution scale which results in more accurate estimates for delays associated with the specular components. Simulation results on the simulated and real shallow water data are provided which show the promise of this new scheme for target detection in a heavy cluttered environment.

Accurate solution of the Poisson equation with discontinuities

NASA Astrophysics Data System (ADS)

Nave, Jean-Christophe; Marques, Alexandre; Rosales, Rodolfo

2017-11-01

Solving the Poisson equation in the presence of discontinuities is of great importance in many applications of science and engineering. In many cases, the discontinuities are caused by interfaces between different media, such as in multiphase flows. These interfaces are themselves solutions to differential equations, and can assume complex configurations. For this reason, it is convenient to embed the interface into a regular triangulation or Cartesian grid and solve the Poisson equation in this regular domain. We present an extension of the Correction Function Method (CFM), which was developed to solve the Poisson equation in the context of embedded interfaces. The distinctive feature of the CFM is that it uses partial differential equations to construct smooth extensions of the solution in the vicinity of interfaces. A consequence of this approach is that it can achieve high order of accuracy while maintaining compact discretizations. The extension we present removes the restrictions of the original CFM, and yields a method that can solve the Poisson equation when discontinuities are present in the solution, the coefficients of the equation (material properties), and the source term. We show results computed to fourth order of accuracy in two and three dimensions. This work was partially funded by DARPA, NSF, and NSERC.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Capacity to delay reward differentiates obsessive-compulsive disorder and obsessive-compulsive personality disorder.

PubMed

Pinto, Anthony; Steinglass, Joanna E; Greene, Ashley L; Weber, Elke U; Simpson, H Blair

2014-04-15

Although the relationship between obsessive-compulsive disorder (OCD) and obsessive-compulsive personality disorder (OCPD) has long been debated, clinical samples of OCD (without OCPD) and OCPD (without OCD) have never been systematically compared. We studied whether individuals with OCD, OCPD, or both conditions differ on symptomatology, functioning, and a measure of self-control: the capacity to delay reward. Twenty-five OCD, 25 OCPD, 25 comorbid OCD + OCPD, and 25 healthy control subjects completed clinical assessments and a validated intertemporal choice task that measures capacity to forego small immediate rewards for larger delayed rewards. OCD and OCPD subjects both showed impairment in psychosocial functioning and quality of life, as well as compulsive behavior, but only subjects with OCD reported obsessions. Individuals with OCPD, with or without comorbid OCD, discounted the value of delayed monetary rewards significantly less than OCD and healthy control subjects. This excessive capacity to delay reward discriminates OCPD from OCD and is associated with perfectionism and rigidity. OCD and OCPD are both impairing disorders marked by compulsive behaviors, but they can be differentiated by the presence of obsessions in OCD and by excessive capacity to delay reward in OCPD. That individuals with OCPD show less temporal discounting (suggestive of excessive self-control), whereas prior studies have shown that individuals with substance use disorders show greater discounting (suggestive of impulsivity), supports the premise that this component of self-control lies on a continuum in which both extremes (impulsivity and overcontrol) contribute to psychopathology. © 2013 Society of Biological Psychiatry Published by Society of Biological Psychiatry All rights reserved.

Preconditioning Strategies for Solving Elliptic Difference Equations on a Multiprocessor.

DTIC Science & Technology

1982-01-01

162, 1977. (MiGr8O] Mitchell, A., Griffiths, D., The Finite Difference Method in Partial Differential Equations , John Wiley & Sons, 1980. [Munk80...ADAL1b T35 AIR FO"CE INST OF TECH WRITG-PATTERSON AFS OH F/6 12/17PR CO ITIONIN STRATEGIES FOR SOLVING ELLIPTIC DIFFERENCE EWA-ETClU) 9UN S C K...TI TLE (ard S.tbr,,I) 5 TYPE OF REP’ORT & F IFIOD C_JVEFO Preconditioning Strategies for Solving Elliptic THESIS/VYYRY#YY0N Difference Equations on

The Future of Electronic Device Design: Device and Process Simulation Find Intelligence on the World Wide Web

NASA Technical Reports Server (NTRS)

Biegel, Bryan A.

1999-01-01

We are on the path to meet the major challenges ahead for TCAD (technology computer aided design). The emerging computational grid will ultimately solve the challenge of limited computational power. The Modular TCAD Framework will solve the TCAD software challenge once TCAD software developers realize that there is no other way to meet industry's needs. The modular TCAD framework (MTF) also provides the ideal platform for solving the TCAD model challenge by rapid implementation of models in a partial differential solver.

The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVPs (Initial-Value Problems) for ODEs (Ordinary Differential Equations).

DTIC Science & Technology

1984-04-01

numerical solution, of sstem ot stiff Wh-f Cr ODs. Fro- qontl. a substantial portia of the total computationskwok and cooap required! to solve stiff...exep, possl- bly, foreciadalms of problem. That is% a syste of linewat o nonlinear algebrac equa- tion mumt be solved at auk step of the numerical ...onjugate gradient method [431 is a mall-know ezuze, have prove to be particularly -2- efecti for solving the linear stwem that &ise in the numerical

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Estimating the circuit delay of FPGA with a transfer learning method

NASA Astrophysics Data System (ADS)

Cui, Xiuhai; Liu, Datong; Peng, Yu; Peng, Xiyuan

2017-10-01

With the increase of FPGA (Field Programmable Gate Array, FPGA) functionality, FPGA has become an on-chip system platform. Due to increase the complexity of FPGA, estimating the delay of FPGA is a very challenge work. To solve the problems, we propose a transfer learning estimation delay (TLED) method to simplify the delay estimation of different speed grade FPGA. In fact, the same style different speed grade FPGA comes from the same process and layout. The delay has some correlation among different speed grade FPGA. Therefore, one kind of speed grade FPGA is chosen as a basic training sample in this paper. Other training samples of different speed grade can get from the basic training samples through of transfer learning. At the same time, we also select a few target FPGA samples as training samples. A general predictive model is trained by these samples. Thus one kind of estimation model is used to estimate different speed grade FPGA circuit delay. The framework of TRED includes three phases: 1) Building a basic circuit delay library which includes multipliers, adders, shifters, and so on. These circuits are used to train and build the predictive model. 2) By contrasting experiments among different algorithms, the forest random algorithm is selected to train predictive model. 3) The target circuit delay is predicted by the predictive model. The Artix-7, Kintex-7, and Virtex-7 are selected to do experiments. Each of them includes -1, -2, -2l, and -3 different speed grade. The experiments show the delay estimation accuracy score is more than 92% with the TLED method. This result shows that the TLED method is a feasible delay assessment method, especially in the high-level synthesis stage of FPGA tool, which is an efficient and effective delay assessment method.

Task Difficulty Differentially Affects Two Measures of Processing Load: The Pupil Response during Sentence Processing and Delayed Cued Recall of the Sentences

ERIC Educational Resources Information Center

Zekveld, Adriana A.; Festen, Joost M.; Kramer, Kramera

2013-01-01

Purpose: In this study, the authors assessed the influence of masking level (29% or 71% sentence perception) and test modality on the processing load during language perception as reflected by the pupil response. In addition, the authors administered a delayed cued stimulus recall test to examine whether processing load affected the encoding of…

Which DSM-IV-TR Criteria Best Differentiate High-Functioning Autism Spectrum Disorder from ADHD and Anxiety Disorders in Older Children?

ERIC Educational Resources Information Center

Hartley, Sigan L.; Sikora, Darryn M.

2009-01-01

Diagnosis of autism spectrum disorder (ASD) is often delayed in high-functioning children with milder and more varied forms of ASD. The substantial overlap between ASD and other psychiatric disorders is thought to contribute to this delay. This study examined the endorsement of DSM-IV-TR diagnostic criteria for ASD based on semi-structured parent…

Uncertainty in Damage Detection, Dynamic Propagation and Just-in-Time Networks

DTIC Science & Technology

2015-08-03

estimated parameter uncertainty in dynamic data sets; high order compact finite difference schemes for Helmholtz equations with discontinuous wave numbers...delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the...schemes for Helmholtz equations with discontinuous wave numbers across interfaces. • We carried out numerical sensitivity analysis with respect to

Determination of differential arrival times by cross-correlating worldwide seismological data

NASA Astrophysics Data System (ADS)

Godano, M.; Nolet, G.; Zaroli, C.

2012-12-01

Cross-correlation delays are the preferred body wave observables in global tomography. Heterogeneity is the main factor influencing delay times found by cross-correlation. Not only the waveform, but also the arrival time itself is affected by differences in seismic velocity encountered along the way. An accurate method for estimating differential times of seismic arrivals across a regional array by cross-correlation was developed by VanDecar and Crosson [1990]. For the estimation of global travel time delays in different frequency bands, Sigloch and Nolet [2006] developed a method for the estimation of body wave delays using a matched filter, which requires the separate estimation of the source time function. Sigloch et al. [2008] found that waveforms often cluster in and opposite the direction of rupture propagation on the fault, confirming that the directivity effect is a major factor in shaping the waveform of large events. We propose a generalization of the VanDecar-Crosson method to which we add a correction for the directivity effect in the seismological data. The new method allows large events to be treated without the need to estimate the source time function for the computation of a matched synthetic waveform. The procedure consists in (1) the detection of the directivity effect in the data and the determination of a rupture model (unilateral or bilateral) explaining the differences in pulse duration among the stations, (2) the determination of an apparent fault rupture length explaining the pulse durations, (3) the removal of the delay due to the directivity effect in the pulse duration , by stretching or contracting the seismograms for directive and anti-directive stations respectively and (4) the application of a generalized VanDecar and Crosson method using only delays between pairs of stations that have an acceptable correlation coefficient. We validate our method by performing tests on synthetic data. Results show that the error between theoretical and measured differential arrival time are significantly reduced for the corrected data. We illustrate our method on data from several real earthquakes.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Differentiated Staffing and Non-Teamed Organizational Structures as They Affect Elementary School Teacher-Pupil Interaction.

ERIC Educational Resources Information Center

Petrie, Thomas A.; And Others

A study was conducted of the differences in the frequency of selected student-teacher interaction in differentiated staffs and in non-teamed schools. The interaction processes studied were synthesized from Erikson's four stages of childhood: student behaviors--information processing, choice-making, reflection, problem solving, and procedures or…

Introduction to the Difference Calculus through the Fibonacci Numbers

ERIC Educational Resources Information Center

Shannon, A. G.; Atanassov, K. T.

2002-01-01

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

ERIC Educational Resources Information Center

Maat, Siti Mistima; Zakaria, Effandi

2011-01-01

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

Matrix Solution of Coupled Differential Equations and Looped Car Following Models

ERIC Educational Resources Information Center

McCartney, Mark

2008-01-01

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Hybrid finite element method for describing the electrical response of biological cells to applied fields.

PubMed

Ying, Wenjun; Henriquez, Craig S

2007-04-01

A novel hybrid finite element method (FEM) for modeling the response of passive and active biological membranes to external stimuli is presented. The method is based on the differential equations that describe the conservation of electric flux and membrane currents. By introducing the electric flux through the cell membrane as an additional variable, the algorithm decouples the linear partial differential equation part from the nonlinear ordinary differential equation part that defines the membrane dynamics of interest. This conveniently results in two subproblems: a linear interface problem and a nonlinear initial value problem. The linear interface problem is solved with a hybrid FEM. The initial value problem is integrated by a standard ordinary differential equation solver such as the Euler and Runge-Kutta methods. During time integration, these two subproblems are solved alternatively. The algorithm can be used to model the interaction of stimuli with multiple cells of almost arbitrary geometries and complex ion-channel gating at the plasma membrane. Numerical experiments are presented demonstrating the uses of the method for modeling field stimulation and action potential propagation.

Dual time point fluorodeoxyglucose positron emission tomography/computed tomography in differentiation between malignant and benign lesions in cancer patients. Does it always work?

PubMed

Saleh Farghaly, Hussein Rabie; Mohamed Sayed, Mohamed Hosny; Nasr, Hatem Ahmed; Abdelaziz Maklad, Ahmed Marzok

2015-01-01

Assess the added value of dual time point F-18-fluorodeoxyglucose positron emission tomography/computed tomography (DTP F-18-FDG-PET/CT) in the differentiation of malignant from a benign lesion in cancer patients. Totally, 140 F-18-FDG PET/CT scans of 60 cancer patients who underwent DTP protocol (early whole body PET/CT [E] at 60 min [range, 45-76 min] and delayed limited PET/CT [D] on areas of interest at 120 min [range, 108-153 min] after the tracer injection) were retrospectively reviewed. Visual and semi-quantitative analysis was performed on both early and delayed images. All findings were confirmed by histopathology and/or at least 3 months follow-up (F-18-FDG PET/CT, CT, or magnetic resonance imaging). The result was considered true positive (TP) if delayed standardized uptake value (SUV) of suspicious lesions increased and confirmed to be malignant, false positive (FP) if delayed SUV increased and confirmed to be benign, true negative (TN) if delayed SUV unchanged or decreased and confirmed to be benign, and false negative (FN) if delayed SUV unchanged or decreased and confirmed to be malignant. A total of 164 suspicious lesions were detected (20 presacral lesions, 18 lung nodules, 18 Hodgkin's disease (HD) lesions, 16 rectal lesions, 16 head and neck (H and N) lesions, 14 hepatic lesions, 14 non-Hodgkin's lymphoma (NHL) lesions, 12 mediastinal lymph nodes (LNs), 10 focal gastric uptake, 10 soft tissue lesions, 8 breast lesions, 4 peritoneal nodule, and 4 others). Sixty-four lesions were pathologically confirmed, and 100 lesions were confirmed based on 3-6 months follow-up. There were 62 TP lesions, 44 FP, 58 TN and no FN results. The overall sensitivity was 100% of DTP F-18-FDG PET/CT in detecting suspicious lesions. The specificity was 57% in differentiating malignant from benign lesions, and the accuracy was 73%. Positive predictive value was 59%, negative predictive value (NPV) 100%. All hepatic lesions were TP. Accuracy in metastatic hepatic lesions HD, presacral soft tissue, lung nodules, H, and N cancer, breast cancer, NHL and mediastinal LN was100%, 88.8%, 80%, 78%, 75%, 75%, 71%, and 33.3%, respectively. DTP F-18-FDG-PET/CT protocol does not always work in differentiation between benign and malignant lesions. However; it has high NPV, and promising results was noted in hepatic lesions, lymphoma, and recurrent rectal cancer.

BCDP: Budget Constrained and Delay-Bounded Placement for Hybrid Roadside Units in Vehicular Ad Hoc Networks

PubMed Central

Li, Peng; Huang, Chuanhe; Liu, Qin

2014-01-01

In vehicular ad hoc networks, roadside units (RSUs) placement has been proposed to improve the the overall network performance in many ITS applications. This paper addresses the budget constrained and delay-bounded placement problem (BCDP) for roadside units in vehicular ad hoc networks. There are two types of RSUs: cable connected RSU (c-RSU) and wireless RSU (w-RSU). c-RSUs are interconnected through wired lines, and they form the backbone of VANETs, while w-RSUs connect to other RSUs through wireless communication and serve as an economical extension of the coverage of c-RSUs. The delay-bounded coverage range and deployment cost of these two cases are totally different. We are given a budget constraint and a delay bound, the problem is how to find the optimal candidate sites with the maximal delay-bounded coverage to place RSUs such that a message from any c-RSU in the region can be disseminated to the more vehicles within the given budget constraint and delay bound. We first prove that the BCDP problem is NP-hard. Then we propose several algorithms to solve the BCDP problem. Simulation results show the heuristic algorithms can significantly improve the coverage range and reduce the total deployment cost, compared with other heuristic methods. PMID:25436656

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY.

PubMed

Rackauckas, Christopher; Nie, Qing

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs.

ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY

PubMed Central

Rackauckas, Christopher

2017-01-01

Adaptive time-stepping with high-order embedded Runge-Kutta pairs and rejection sampling provides efficient approaches for solving differential equations. While many such methods exist for solving deterministic systems, little progress has been made for stochastic variants. One challenge in developing adaptive methods for stochastic differential equations (SDEs) is the construction of embedded schemes with direct error estimates. We present a new class of embedded stochastic Runge-Kutta (SRK) methods with strong order 1.5 which have a natural embedding of strong order 1.0 methods. This allows for the derivation of an error estimate which requires no additional function evaluations. Next we derive a general method to reject the time steps without losing information about the future Brownian path termed Rejection Sampling with Memory (RSwM). This method utilizes a stack data structure to do rejection sampling, costing only a few floating point calculations. We show numerically that the methods generate statistically-correct and tolerance-controlled solutions. Lastly, we show that this form of adaptivity can be applied to systems of equations, and demonstrate that it solves a stiff biological model 12.28x faster than common fixed timestep algorithms. Our approach only requires the solution to a bridging problem and thus lends itself to natural generalizations beyond SDEs. PMID:29527134

Dynamics of the Pin Pallet Runaway Escapement

DTIC Science & Technology

1978-06-01

for Continued Work 29 References 32 I Appendixes A Kinematics of Coupled Motion 34 B Differential Equation of Coupled Motion 38 f C Moment Arms 42 D...Expressions for these quantities are derived in appendix D. The differential equations for the free motion of the pallet and the escape-wheel are...Coupled Motion (location 100) To solve the differential equation of coupled motion (see equation .B (-10) of appendix B)- the main program calls on

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.