Interpreting Significant Discrete-Time Periods in Survival Analysis.

ERIC Educational Resources Information Center

Schumacker, Randall E.; Denson, Kathleen B.

Discrete-time survival analysis is a new method for educational researchers to employ when looking at the timing of certain educational events. Previous continuous-time methods do not allow for the flexibility inherent in a discrete-time method. Because both time-invariant and time-varying predictor variables can now be used, the interaction of…

Lectures on algebraic system theory: Linear systems over rings

NASA Technical Reports Server (NTRS)

Kamen, E. W.

1978-01-01

The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.

Discrete-time stability of continuous-time controller designs for large space structures

NASA Technical Reports Server (NTRS)

Balas, M. J.

1982-01-01

In most of the stable control designs for flexible structures, continuous time is assumed. However, in view of the implementation of the controllers by on-line digital computers, the discrete-time stability of such controllers is an important consideration. In the case of direct-velocity feedback (DVFB), involving negative feedback from collocated force actuators and velocity sensors, it is not immediately apparent how much delay due to digital implementation of DVFB can be tolerated without loss of stability. The present investigation is concerned with such questions. A study is conducted of the discrete-time stability of DVFB, taking into account an employment of Euler's method of approximation of the time derivative. The obtained result gives an indication of the acceptable time-step size for stable digital implementation of DVFB. A result derived in connection with the consideration of the discrete-time stability of stable continuous-time systems provides a general condition under which digital implementation of such a system will remain stable.

The Selection of Computed Tomography Scanning Schemes for Lengthy Symmetric Objects

NASA Astrophysics Data System (ADS)

Trinh, V. B.; Zhong, Y.; Osipov, S. P.

2017-04-01

. The article describes the basic computed tomography scan schemes for lengthy symmetric objects: continuous (discrete) rotation with a discrete linear movement; continuous (discrete) rotation with discrete linear movement to acquire 2D projection; continuous (discrete) linear movement with discrete rotation to acquire one-dimensional projection and continuous (discrete) rotation to acquire of 2D projection. The general method to calculate the scanning time is discussed in detail. It should be extracted the comparison principle to select a scanning scheme. This is because data are the same for all scanning schemes: the maximum energy of the X-ray radiation; the power of X-ray radiation source; the angle of the X-ray cone beam; the transverse dimension of a single detector; specified resolution and the maximum time, which is need to form one point of the original image and complies the number of registered photons). It demonstrates the possibilities of the above proposed method to compare the scanning schemes. Scanning object was a cylindrical object with the mass thickness is 4 g/cm2, the effective atomic number is 15 and length is 1300 mm. It analyzes data of scanning time and concludes about the efficiency of scanning schemes. It examines the productivity of all schemes and selects the effective one.

Continuous- and discrete-time stimulus sequences for high stimulus rate paradigm in evoked potential studies.

PubMed

Wang, Tao; Huang, Jiang-hua; Lin, Lin; Zhan, Chang'an A

2013-01-01

To obtain reliable transient auditory evoked potentials (AEPs) from EEGs recorded using high stimulus rate (HSR) paradigm, it is critical to design the stimulus sequences of appropriate frequency properties. Traditionally, the individual stimulus events in a stimulus sequence occur only at discrete time points dependent on the sampling frequency of the recording system and the duration of stimulus sequence. This dependency likely causes the implementation of suboptimal stimulus sequences, sacrificing the reliability of resulting AEPs. In this paper, we explicate the use of continuous-time stimulus sequence for HSR paradigm, which is independent of the discrete electroencephalogram (EEG) recording system. We employ simulation studies to examine the applicability of the continuous-time stimulus sequences and the impacts of sampling frequency on AEPs in traditional studies using discrete-time design. Results from these studies show that the continuous-time sequences can offer better frequency properties and improve the reliability of recovered AEPs. Furthermore, we find that the errors in the recovered AEPs depend critically on the sampling frequencies of experimental systems, and their relationship can be fitted using a reciprocal function. As such, our study contributes to the literature by demonstrating the applicability and advantages of continuous-time stimulus sequences for HSR paradigm and by revealing the relationship between the reliability of AEPs and sampling frequencies of the experimental systems when discrete-time stimulus sequences are used in traditional manner for the HSR paradigm.

Discrete Events as Units of Perceived Time

ERIC Educational Resources Information Center

Liverence, Brandon M.; Scholl, Brian J.

2012-01-01

In visual images, we perceive both space (as a continuous visual medium) and objects (that inhabit space). Similarly, in dynamic visual experience, we perceive both continuous time and discrete events. What is the relationship between these units of experience? The most intuitive answer may be similar to the spatial case: time is perceived as an…

A latent class multiple constraint multiple discrete-continuous extreme value model of time use and goods consumption.

DOT National Transportation Integrated Search

2016-06-01

This paper develops a microeconomic theory-based multiple discrete continuous choice model that considers: (a) that both goods consumption and time allocations (to work and non-work activities) enter separately as decision variables in the utility fu...

Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

DOE PAGES

Rudinger, Kenneth; Gamble, John King; Bach, Eric; ...

2013-07-01

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erencesmore » in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.« less

Adaptive feedback synchronisation of complex dynamical network with discrete-time communications and delayed nodes

NASA Astrophysics Data System (ADS)

Wang, Tong; Ding, Yongsheng; Zhang, Lei; Hao, Kuangrong

2016-08-01

This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov-Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.

Variability of a "force signature" during windmill softball pitching and relationship between discrete force variables and pitch velocity.

PubMed

Nimphius, Sophia; McGuigan, Michael R; Suchomel, Timothy J; Newton, Robert U

2016-06-01

This study assessed reliability of discrete ground reaction force (GRF) variables over multiple pitching trials, investigated the relationships between discrete GRF variables and pitch velocity (PV) and assessed the variability of the "force signature" or continuous force-time curve during the pitching motion of windmill softball pitchers. Intraclass correlation coefficient (ICC) for all discrete variables was high (0.86-0.99) while the coefficient of variance (CV) was low (1.4-5.2%). Two discrete variables were significantly correlated to PV; second vertical peak force (r(5)=0.81, p=0.03) and time between peak forces (r(5)=-0.79; p=0.03). High ICCs and low CVs support the reliability of discrete GRF and PV variables over multiple trials and significant correlations indicate there is a relationship between the ability to produce force and the timing of this force production with PV. The mean of all pitchers' curve-average standard deviation of their continuous force-time curves demonstrated low variability (CV=4.4%) indicating a repeatable and identifiable "force signature" pattern during this motion. As such, the continuous force-time curve in addition to discrete GRF variables should be examined in future research as a potential method to monitor or explain changes in pitching performance. Copyright © 2016 Elsevier B.V. All rights reserved.

Convergence of discrete Aubry–Mather model in the continuous limit

NASA Astrophysics Data System (ADS)

Su, Xifeng; Thieullen, Philippe

2018-05-01

We develop two approximation schemes for solving the cell equation and the discounted cell equation using Aubry–Mather–Fathi theory. The Hamiltonian is supposed to be Tonelli, time-independent and periodic in space. By Legendre transform it is equivalent to find a fixed point of some nonlinear operator, called Lax-Oleinik operator, which may be discounted or not. By discretizing in time, we are led to solve an additive eigenvalue problem involving a discrete Lax–Oleinik operator. We show how to approximate the effective Hamiltonian and some weak KAM solutions by letting the time step in the discrete model tend to zero. We also obtain a selected discrete weak KAM solution as in Davini et al (2016 Invent. Math. 206 29–55), and show that it converges to a particular solution of the cell equation. In order to unify the two settings, continuous and discrete, we develop a more general formalism of the short-range interactions.

Galerkin v. discrete-optimal projection in nonlinear model reduction

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

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

NASA Astrophysics Data System (ADS)

Gross, Jonathan A.; Caves, Carlton M.; Milburn, Gerard J.; Combes, Joshua

2018-04-01

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

Algorithms for Brownian first-passage-time estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

PubMed

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

A comparison of continuous- and discrete- time three-state models for rodent tumorigenicity experiments.

PubMed Central

Lindsey, J C; Ryan, L M

1994-01-01

The three-state illness-death model provides a useful way to characterize data from a rodent tumorigenicity experiment. Most parametrizations proposed recently in the literature assume discrete time for the death process and either discrete or continuous time for the tumor onset process. We compare these approaches with a third alternative that uses a piecewise continuous model on the hazards for tumor onset and death. All three models assume proportional hazards to characterize tumor lethality and the effect of dose on tumor onset and death rate. All of the models can easily be fitted using an Expectation Maximization (EM) algorithm. The piecewise continuous model is particularly appealing in this context because the complete data likelihood corresponds to a standard piecewise exponential model with tumor presence as a time-varying covariate. It can be shown analytically that differences between the parameter estimates given by each model are explained by varying assumptions about when tumor onsets, deaths, and sacrifices occur within intervals. The mixed-time model is seen to be an extension of the grouped data proportional hazards model [Mutat. Res. 24:267-278 (1981)]. We argue that the continuous-time model is preferable to the discrete- and mixed-time models because it gives reasonable estimates with relatively few intervals while still making full use of the available information. Data from the ED01 experiment illustrate the results. PMID:8187731

A discrete epidemic model for bovine Babesiosis disease and tick populations

NASA Astrophysics Data System (ADS)

Aranda, Diego F.; Trejos, Deccy Y.; Valverde, Jose C.

2017-06-01

In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.

Numerical Evaluation of the "Dual-Kernel Counter-flow" Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory

NASA Technical Reports Server (NTRS)

Nixon, Douglas D.

2009-01-01

Discrete/Continuous (D/C) control theory is a new generalized theory of discrete-time control that expands the concept of conventional (exact) discrete-time control to create a framework for design and implementation of discretetime control systems that include a continuous-time command function generator so that actuator commands need not be constant between control decisions, but can be more generally defined and implemented as functions that vary with time across sample period. Because the plant/control system construct contains two linear subsystems arranged in tandem, a novel dual-kernel counter-flow convolution integral appears in the formulation. As part of the D/C system design and implementation process, numerical evaluation of that integral over the sample period is required. Three fundamentally different evaluation methods and associated algorithms are derived for the constant-coefficient case. Numerical results are matched against three available examples that have closed-form solutions.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\\infty }$ Performances.

PubMed

Choi, Hyun Duck; Ahn, Choon Ki; Karimi, Hamid Reza; Lim, Myo Taeg

2017-10-01

This paper studies delay-dependent exponential dissipative and l 2 - l ∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l 2 - l ∞ senses. The design of the desired exponential dissipative and l 2 - l ∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays.

PubMed

Hu, Jin; Wang, Jun

2015-06-01

In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given. Copyright © 2015 Elsevier Ltd. All rights reserved.

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

NASA Astrophysics Data System (ADS)

Aurzada, Frank; Buck, Micha

2018-02-01

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97-111, 1999) and Molchan (J Stat Phys 167(6):1546-1554, 2017) to a wide class of discrete-time processes.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

EnvironmentalWaveletTool: Continuous and discrete wavelet analysis and filtering for environmental time series

NASA Astrophysics Data System (ADS)

Galiana-Merino, J. J.; Pla, C.; Fernandez-Cortes, A.; Cuezva, S.; Ortiz, J.; Benavente, D.

2014-10-01

A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of several environmental time series, particularly focused on the analyses of cave monitoring data. The continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform have been implemented to provide a fast and precise time-period examination of the time series at different period bands. Moreover, statistic methods to examine the relation between two signals have been included. Finally, the entropy of curves and splines based methods have also been developed for segmenting and modeling the analyzed time series. All these methods together provide a user-friendly and fast program for the environmental signal analysis, with useful, practical and understandable results.

Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

NASA Astrophysics Data System (ADS)

Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.

2017-07-01

It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.

Hybrid Discrete-Continuous Markov Decision Processes

NASA Technical Reports Server (NTRS)

Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich

2003-01-01

This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

NASA Technical Reports Server (NTRS)

Jones, Robert L.; Goode, Plesent W. (Technical Monitor)

2000-01-01

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Continuous sweep versus discrete step protocols for studying effects of wearable robot assistance magnitude.

PubMed

Malcolm, Philippe; Rossi, Denise Martineli; Siviy, Christopher; Lee, Sangjun; Quinlivan, Brendan Thomas; Grimmer, Martin; Walsh, Conor J

2017-07-12

Different groups developed wearable robots for walking assistance, but there is still a need for methods to quickly tune actuation parameters for each robot and population or sometimes even for individual users. Protocols where parameters are held constant for multiple minutes have traditionally been used for evaluating responses to parameter changes such as metabolic rate or walking symmetry. However, these discrete protocols are time-consuming. Recently, protocols have been proposed where a parameter is changed in a continuous way. The aim of the present study was to compare effects of continuously varying assistance magnitude with a soft exosuit against discrete step conditions. Seven participants walked on a treadmill wearing a soft exosuit that assists plantarflexion and hip flexion. In Continuous-up, peak exosuit ankle moment linearly increased from approximately 0 to 38% of biological moment over 10 min. Continuous-down was the opposite. In Discrete, participants underwent five periods of 5 min with steady peak moment levels distributed over the same range as Continuous-up and Continuous-down. We calculated metabolic rate for the entire Continuous-up and Continuous-down conditions and the last 2 min of each Discrete force level. We compared kinematics, kinetics and metabolic rate between conditions by curve fitting versus peak moment. Reduction in metabolic rate compared to Powered-off was smaller in Continuous-up than in Continuous-down at most peak moment levels, due to physiological dynamics causing metabolic measurements in Continuous-up and Continuous-down to lag behind the values expected during steady-state testing. When evaluating the average slope of metabolic reduction over the entire peak moment range there was no significant difference between Continuous-down and Discrete. Attempting to correct the lag in metabolics by taking the average of Continuous-up and Continuous-down removed all significant differences versus Discrete. For kinematic and kinetic parameters, there were no differences between all conditions. The finding that there were no differences in biomechanical parameters between all conditions suggests that biomechanical parameters can be recorded with the shortest protocol condition (i.e. single Continuous directions). The shorter time and higher resolution data of continuous sweep protocols hold promise for the future study of human interaction with wearable robots.

Complex discrete dynamics from simple continuous population models.

PubMed

Gamarra, Javier G P; Solé, Ricard V

2002-05-01

Nonoverlapping generations have been classically modelled as difference equations in order to account for the discrete nature of reproductive events. However, other events such as resource consumption or mortality are continuous and take place in the within-generation time. We have realistically assumed a hybrid ODE bidimensional model of resources and consumers with discrete events for reproduction. Numerical and analytical approaches showed that the resulting dynamics resembles a Ricker map, including the doubling route to chaos. Stochastic simulations with a handling-time parameter for indirect competition of juveniles may affect the qualitative behaviour of the model.

An Empirical Development of Parallelization Guidelines for Time-Driven Simulation

DTIC Science & Technology

1989-12-01

wives, who though not Cub fans, put on a good show during our trip, to waich some games . I would also like to recognize the help of my professors at...program parallelization. in this research effort a Ballistic Missile Defense (BMD) time driven simulation program, developed by DESE Research and...continuously, or continuously with discrete changes superimposed. The distinguishing feature of these simulations is the interaction between discretely

Integrated simulation of continuous-scale and discrete-scale radiative transfer in metal foams

NASA Astrophysics Data System (ADS)

Xia, Xin-Lin; Li, Yang; Sun, Chuang; Ai, Qing; Tan, He-Ping

2018-06-01

A novel integrated simulation of radiative transfer in metal foams is presented. It integrates the continuous-scale simulation with the direct discrete-scale simulation in a single computational domain. It relies on the coupling of the real discrete-scale foam geometry with the equivalent continuous-scale medium through a specially defined scale-coupled zone. This zone holds continuous but nonhomogeneous volumetric radiative properties. The scale-coupled approach is compared to the traditional continuous-scale approach using volumetric radiative properties in the equivalent participating medium and to the direct discrete-scale approach employing the real 3D foam geometry obtained by computed tomography. All the analyses are based on geometrical optics. The Monte Carlo ray-tracing procedure is used for computations of the absorbed radiative fluxes and the apparent radiative behaviors of metal foams. The results obtained by the three approaches are in tenable agreement. The scale-coupled approach is fully validated in calculating the apparent radiative behaviors of metal foams composed of very absorbing to very reflective struts and that composed of very rough to very smooth struts. This new approach leads to a reduction in computational time by approximately one order of magnitude compared to the direct discrete-scale approach. Meanwhile, it can offer information on the local geometry-dependent feature and at the same time the equivalent feature in an integrated simulation. This new approach is promising to combine the advantages of the continuous-scale approach (rapid calculations) and direct discrete-scale approach (accurate prediction of local radiative quantities).

Model documentation for relations between continuous real-time and discrete water-quality constituents in the North Fork Ninnescah River upstream from Cheney Reservoir, south-central Kansas, 1999--2009

USGS Publications Warehouse

Stone, Mandy L.; Graham, Jennifer L.; Gatotho, Jackline W.

2013-01-01

Cheney Reservoir in south-central Kansas is one of the primary sources of water for the city of Wichita. The North Fork Ninnescah River is the largest contributing tributary to Cheney Reservoir. The U.S. Geological Survey has operated a continuous real-time water-quality monitoring station since 1998 on the North Fork Ninnescah River. Continuously measured water-quality physical properties include streamflow, specific conductance, pH, water temperature, dissolved oxygen, and turbidity. Discrete water-quality samples were collected during 1999 through 2009 and analyzed for sediment, nutrients, bacteria, and other water-quality constituents. Regression models were developed to establish relations between discretely sampled constituent concentrations and continuously measured physical properties to estimate concentrations of those constituents of interest that are not easily measured in real time because of limitations in sensor technology and fiscal constraints. Regression models were published in 2006 that were based on a different dataset collected during 1997 through 2003. This report updates those models using discrete and continuous data collected during January 1999 through December 2009. Models also were developed for five new constituents, including additional nutrient species and indicator bacteria. The water-quality information in this report is important to the city of Wichita because it allows the concentrations of many potential pollutants of interest, including nutrients and sediment, to be estimated in real time and characterized over conditions and time scales that would not be possible otherwise.

The value of continuity: Refined isogeometric analysis and fast direct solvers

DOE PAGES

Garcia, Daniel; Pardo, David; Dalcin, Lisandro; ...

2016-08-24

Here, we propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method “refined Isogeometric Analysis (rIGA)”. To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing themore » Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p 2 and p 3, with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to p 2. In a 2D mesh with four million elements and p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a 3D mesh with one million elements and p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.« less

Discretization chaos - Feedback control and transition to chaos

NASA Technical Reports Server (NTRS)

Grantham, Walter J.; Athalye, Amit M.

1990-01-01

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

A hybrid-system model of the coagulation cascade: simulation, sensitivity, and validation.

PubMed

Makin, Joseph G; Narayanan, Srini

2013-10-01

The process of human blood clotting involves a complex interaction of continuous-time/continuous-state processes and discrete-event/discrete-state phenomena, where the former comprise the various chemical rate equations and the latter comprise both threshold-limited behaviors and binary states (presence/absence of a chemical). Whereas previous blood-clotting models used only continuous dynamics and perforce addressed only portions of the coagulation cascade, we capture both continuous and discrete aspects by modeling it as a hybrid dynamical system. The model was implemented as a hybrid Petri net, a graphical modeling language that extends ordinary Petri nets to cover continuous quantities and continuous-time flows. The primary focus is simulation: (1) fidelity to the clinical data in terms of clotting-factor concentrations and elapsed time; (2) reproduction of known clotting pathologies; and (3) fine-grained predictions which may be used to refine clinical understanding of blood clotting. Next we examine sensitivity to rate-constant perturbation. Finally, we propose a method for titrating between reliance on the model and on prior clinical knowledge. For simplicity, we confine these last two analyses to a critical purely-continuous subsystem of the model.

Time crystals: a review

NASA Astrophysics Data System (ADS)

Sacha, Krzysztof; Zakrzewski, Jakub

2018-01-01

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals—the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek’s idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

Fronts in extended systems of bistable maps coupled via convolutions

NASA Astrophysics Data System (ADS)

Coutinho, Ricardo; Fernandez, Bastien

2004-01-01

An analysis of front dynamics in discrete time and spatially extended systems with general bistable nonlinearity is presented. The spatial coupling is given by the convolution with distribution functions. It allows us to treat in a unified way discrete, continuous or partly discrete and partly continuous diffusive interactions. We prove the existence of fronts and the uniqueness of their velocity. We also prove that the front velocity depends continuously on the parameters of the system. Finally, we show that every initial configuration that is an interface between the stable phases propagates asymptotically with the front velocity.

Using a new discretization approach to design a delayed LQG controller

NASA Astrophysics Data System (ADS)

Haraguchi, M.; Hu, H. Y.

2008-07-01

In general, discrete-time controls have become more and more preferable in engineering because of their easy implementation and simple computations. However, the available discretization approaches for the systems having time delays increase the system dimensions and have a high computational cost. This paper presents an effective discretization approach for the continuous-time systems with an input delay. The approach enables one to transform the input-delay system into a delay-free system, but retain the system dimensions unchanged in the state transformation. To demonstrate an application of the approach, this paper presents the design of an LQ regulator for continuous-time systems with an input delay and gives a state observer with a Kalman filter for estimating the full-state vector from some measurements of the system as well. The case studies in the paper well support the efficacy and efficiency of the proposed approach applied to the vibration control of a three-story structure model with the actuator delay taken into account.

2D discontinuous piecewise linear map: Emergence of fashion cycles.

PubMed

Gardini, L; Sushko, I; Matsuyama, K

2018-05-01

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

NASA Astrophysics Data System (ADS)

Mabuza, Sibusiso; Shadid, John N.; Kuzmin, Dmitri

2018-05-01

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. For time discretization, Crank-Nicolson scheme and backward Euler scheme are utilized.

Fast Mix Table Construction for Material Discretization

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

Johnson, Seth R

2013-01-01

An effective hybrid Monte Carlo--deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a ``mix table,'' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table inmore » $$O(\\text{number of voxels}\\times \\log \\text{number of mixtures})$$ time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation.« less

The ultimatum game: Discrete vs. continuous offers

NASA Astrophysics Data System (ADS)

Dishon-Berkovits, Miriam; Berkovits, Richard

2014-09-01

In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.

The effectiveness of robotic training depends on motor task characteristics.

PubMed

Marchal-Crespo, Laura; Rappo, Nicole; Riener, Robert

2017-12-01

Previous research suggests that the effectiveness of robotic training depends on the motor task to be learned. However, it is still an open question which specific task's characteristics influence the efficacy of error-modulating training strategies. Motor tasks can be classified based on the time characteristics of the task, in particular the task's duration (discrete vs. continuous). Continuous tasks require movements without distinct beginning or end. Discrete tasks require fast movements that include well-defined postures at the beginning and the end. We developed two games, one that requires a continuous movement-a tracking task-and one that requires discrete movements-a fast reaching task. We conducted an experiment with thirty healthy subjects to evaluate the effectiveness of three error-modulating training strategies-no guidance, error amplification (i.e., repulsive forces proportional to errors) and haptic guidance-on self-reported motivation and learning of the continuous and discrete games. Training with error amplification resulted in better motor learning than haptic guidance, besides the fact that error amplification reduced subjects' interest/enjoyment and perceived competence during training. Only subjects trained with error amplification improved their performance after training the discrete game. In fact, subjects trained without guidance improved the performance in the continuous game significantly more than in the discrete game, probably because the continuous task required greater attentional levels. Error-amplifying training strategies have a great potential to provoke better motor learning in continuous and discrete tasks. However, their long-lasting negative effects on motivation might limit their applicability in intense neurorehabilitation programs.

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

Properties of the Magnitude Terms of Orthogonal Scaling Functions.

PubMed

Tay, Peter C; Havlicek, Joseph P; Acton, Scott T; Hossack, John A

2010-09-01

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the contiuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine an robust lower bound on conjoint localization of orthogonal scaling functions.

Consensus for linear multi-agent system with intermittent information transmissions using the time-scale theory

NASA Astrophysics Data System (ADS)

Taousser, Fatima; Defoort, Michael; Djemai, Mohamed

2016-01-01

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.

Robust inference in discrete hazard models for randomized clinical trials.

PubMed

Nguyen, Vinh Q; Gillen, Daniel L

2012-10-01

Time-to-event data in which failures are only assessed at discrete time points are common in many clinical trials. Examples include oncology studies where events are observed through periodic screenings such as radiographic scans. When the survival endpoint is acknowledged to be discrete, common methods for the analysis of observed failure times include the discrete hazard models (e.g., the discrete-time proportional hazards and the continuation ratio model) and the proportional odds model. In this manuscript, we consider estimation of a marginal treatment effect in discrete hazard models where the constant treatment effect assumption is violated. We demonstrate that the estimator resulting from these discrete hazard models is consistent for a parameter that depends on the underlying censoring distribution. An estimator that removes the dependence on the censoring mechanism is proposed and its asymptotic distribution is derived. Basing inference on the proposed estimator allows for statistical inference that is scientifically meaningful and reproducible. Simulation is used to assess the performance of the presented methodology in finite samples.

On the discretization and control of an SEIR epidemic model with a periodic impulsive vaccination

NASA Astrophysics Data System (ADS)

Alonso-Quesada, S.; De la Sen, M.; Ibeas, A.

2017-01-01

This paper deals with the discretization and control of an SEIR epidemic model. Such a model describes the transmission of an infectious disease among a time-varying host population. The model assumes mortality from causes related to the disease. Our study proposes a discretization method including a free-design parameter to be adjusted for guaranteeing the positivity of the resulting discrete-time model. Such a method provides a discrete-time model close to the continuous-time one without the need for the sampling period to be as small as other commonly used discretization methods require. This fact makes possible the design of impulsive vaccination control strategies with less burden of measurements and related computations if one uses the proposed instead of other discretization methods. The proposed discretization method and the impulsive vaccination strategy designed on the resulting discretized model are the main novelties of the paper. The paper includes (i) the analysis of the positivity of the obtained discrete-time SEIR model, (ii) the study of stability of the disease-free equilibrium point of a normalized version of such a discrete-time model and (iii) the existence and the attractivity of a globally asymptotically stable disease-free periodic solution under a periodic impulsive vaccination. Concretely, the exposed and infectious subpopulations asymptotically converge to zero as time tends to infinity while the normalized subpopulations of susceptible and recovered by immunization individuals oscillate in the context of such a solution. Finally, a numerical example illustrates the theoretic results.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

PubMed

Salceanu, Paul L

2011-07-01

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.

Continuous scanning mode for ptychography

DOE PAGES

Clark, Jesse N.; Huang, Xiaojing; Harder, Ross J.; ...

2014-10-15

We outline how ptychographic imaging can be performed without the need for discrete scan positions. Through an idealized experiment, we demonstrate how a discrete-position scan regime can be replaced with a continuously scanned one with suitable modification of the reconstruction scheme based on coherent modes. Thus, the impact of this is that acquisition times can be reduced, significantly aiding ptychographic imaging with x rays, electrons, or visible light.

Approximate Locality for Quantum Systems on Graphs

NASA Astrophysics Data System (ADS)

Osborne, Tobias J.

2008-10-01

In this Letter we make progress on a long-standing open problem of Aaronson and Ambainis [Theory Comput. 1, 47 (2005)1557-2862]: we show that if U is a sparse unitary operator with a gap Δ in its spectrum, then there exists an approximate logarithm H of U which is also sparse. The sparsity pattern of H gets more dense as 1/Δ increases. This result can be interpreted as a way to convert between local continuous-time and local discrete-time quantum processes. As an example we show that the discrete-time coined quantum walk can be realized stroboscopically from an approximately local continuous-time quantum walk.

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods

USGS Publications Warehouse

Coes, Alissa L.; Paretti, Nicholas V.; Foreman, William T.; Iverson, Jana L.; Alvarez, David A.

2014-01-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19–23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method.

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods.

PubMed

Coes, Alissa L; Paretti, Nicholas V; Foreman, William T; Iverson, Jana L; Alvarez, David A

2014-03-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19-23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method. Published by Elsevier B.V.

Simulating Soft Shadows with Graphics Hardware,

DTIC Science & Technology

1997-01-15

This radiance texture is analogous to the mesh of radiosity values computed in a radiosity algorithm. Unlike a radiosity algorithm, however, our...discretely. Several researchers have explored continuous visibility methods for soft shadow computation and radiosity mesh generation. With this approach...times of several seconds [9]. Most radiosity methods discretize each surface into a mesh of elements and then use discrete methods such as ray

An Approach To Using All Location Tagged Numerical Data Sets As Continuous Fields With User-Assigned Continuity As A Basis For User-Driven Data Assimilation

NASA Astrophysics Data System (ADS)

Vernon, F.; Arrott, M.; Orcutt, J. A.; Mueller, C.; Case, J.; De Wardener, G.; Kerfoot, J.; Schofield, O.

2013-12-01

Any approach sophisticated enough to handle a variety of data sources and scale, yet easy enough to promote wide use and mainstream adoption is required to address the following mappings: - From the authored domain of observation to the requested domain of interest; - From the authored spatiotemporal resolution to the requested resolution; and - From the representation of data placed on wide variety of discrete mesh types to the use of that data as a continuos field with a selectable continuity. The Open Geospatial Consortium's (OGC) Reference Model[1] with its direct association with the ISO 19000 series standards provides a comprehensive foundation to represent all data on any type of mesh structure, aka "Discrete Coverages". The Reference Model also provides the specification for the core operations required to utilize any Discrete Coverage. The FEniCS Project[2] provides a comprehensive model for how to represent the Basis Functions on mesh structures as "Degrees of Freedom" to present discrete data as continuous fields with variable continuity. In this talk, we will present the research and development the OOI Cyberinfrastructure Project is pursuing to integrate these approaches into a comprehensive Application Programming Interface (API) to author, acquire and operate on the broad range of data formulation from time series, trajectories and tables through to time variant finite difference grids and finite element meshes.

Fast mix table construction for material discretization

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

Johnson, S. R.

2013-07-01

An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mixmore » table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)« less

Waiting time distribution for continuous stochastic systems

NASA Astrophysics Data System (ADS)

Gernert, Robert; Emary, Clive; Klapp, Sabine H. L.

2014-12-01

The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012), 10.1103/PhysRevE.86.061135]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

Stochastic thermodynamics across scales: Emergent inter-attractoral discrete Markov jump process and its underlying continuous diffusion

NASA Astrophysics Data System (ADS)

Santillán, Moisés; Qian, Hong

2013-01-01

We investigate the internal consistency of a recently developed mathematical thermodynamic structure across scales, between a continuous stochastic nonlinear dynamical system, i.e., a diffusion process with Langevin and Fokker-Planck equations, and its emergent discrete, inter-attractoral Markov jump process. We analyze how the system’s thermodynamic state functions, e.g. free energy F, entropy S, entropy production ep, free energy dissipation Ḟ, etc., are related when the continuous system is described with coarse-grained discrete variables. It is shown that the thermodynamics derived from the underlying, detailed continuous dynamics gives rise to exactly the free-energy representation of Gibbs and Helmholtz. That is, the system’s thermodynamic structure is the same as if one only takes a middle road and starts with the natural discrete description, with the corresponding transition rates empirically determined. By natural we mean in the thermodynamic limit of a large system, with an inherent separation of time scales between inter- and intra-attractoral dynamics. This result generalizes a fundamental idea from chemistry, and the theory of Kramers, by incorporating thermodynamics: while a mechanical description of a molecule is in terms of continuous bond lengths and angles, chemical reactions are phenomenologically described by a discrete representation, in terms of exponential rate laws and a stochastic thermodynamics.

Analysis of discrete and continuous distributions of ventilatory time constants from dynamic computed tomography

NASA Astrophysics Data System (ADS)

Doebrich, Marcus; Markstaller, Klaus; Karmrodt, Jens; Kauczor, Hans-Ulrich; Eberle, Balthasar; Weiler, Norbert; Thelen, Manfred; Schreiber, Wolfgang G.

2005-04-01

In this study, an algorithm was developed to measure the distribution of pulmonary time constants (TCs) from dynamic computed tomography (CT) data sets during a sudden airway pressure step up. Simulations with synthetic data were performed to test the methodology as well as the influence of experimental noise. Furthermore the algorithm was applied to in vivo data. In five pigs sudden changes in airway pressure were imposed during dynamic CT acquisition in healthy lungs and in a saline lavage ARDS model. The fractional gas content in the imaged slice (FGC) was calculated by density measurements for each CT image. Temporal variations of the FGC were analysed assuming a model with a continuous distribution of exponentially decaying time constants. The simulations proved the feasibility of the method. The influence of experimental noise could be well evaluated. Analysis of the in vivo data showed that in healthy lungs ventilation processes can be more likely characterized by discrete TCs whereas in ARDS lungs continuous distributions of TCs are observed. The temporal behaviour of lung inflation and deflation can be characterized objectively using the described new methodology. This study indicates that continuous distributions of TCs reflect lung ventilation mechanics more accurately compared to discrete TCs.

Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably more difficult to solve. Unlike the continuous problems, discrete or mixed discrete-continuous problems normally cannot be recast as convex problems. In contrast to the common heuristic of relaxing the discrete variables, this work reformulates the original problem in an FP form amenable to distributed combinatorial optimization. The paper illustrates this methodology by tackling the important and challenging problem of uplink coordinated multi-cell user scheduling in wireless cellular systems. Uplink scheduling is more challenging than downlink scheduling, because uplink user scheduling decisions significantly affect the interference pattern in nearby cells. Further, the discrete scheduling variable needs to be optimized jointly with continuous variables such as transmit power levels and beamformers. The main idea of the proposed FP approach is to decouple the interaction among the interfering links, thereby permitting a distributed and joint optimization of the discrete and continuous variables with provable convergence. The paper shows that the well-known weighted minimum mean-square-error (WMMSE) algorithm can also be derived from a particular use of FP; but our proposed FP-based method significantly outperforms WMMSE when discrete user scheduling variables are involved, both in term of run-time efficiency and optimizing results.

Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

PubMed

Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L

2016-09-01

Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Behaviour of a series of reservoirs separated by drowned gates

NASA Astrophysics Data System (ADS)

Kolechkina, Alla; van Nooijen, Ronald

2017-04-01

Modern control systems tend to be based on computers and therefore to operate by sending commands to structures at given intervals (discrete time control system). Moreover, for almost all water management control systems there are practical lower limits on the time interval between structure adjustments and even between measurements. The water resource systems that are being controlled are physical systems whose state changes continuously. If we combine a continuously changing system and a discrete time controller we get a hybrid system. We use material from recent control theory literature to examine the behaviour of a series of reservoirs separated by drowned gates where the gates are under computer control.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

PubMed

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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

Ng, B

This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Functional data analysis: An approach for environmental ordination and matching discrete with continuous observations

EPA Science Inventory

Investigators are frequently confronted with data sets that include both discrete observations and extended time series of environmental data that had been collected by autonomous recorders. Evaluating the relationships between these two kinds of data is challenging. A common a...

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

Universal scaling function in discrete time asymmetric exclusion processes

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-03-01

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz' original publication this universality has been verified for a variety of continuous time systems in the KPZ universality class. We study the Derrida-Lebowitz scaling function for multi-particle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the Derrida-Lebowitz scaling function not only properly characterizes the large system size limit, but even accurately describes surprisingly small systems. These results have immediate applications in searching biological sequence databases.

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Time-domain damping models in structural acoustics using digital filtering

NASA Astrophysics Data System (ADS)

Parret-Fréaud, Augustin; Cotté, Benjamin; Chaigne, Antoine

2016-02-01

This paper describes a new approach in order to formulate well-posed time-domain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam, etc.), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws.

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

PubMed

Pross, Sabrina; Bachmann, Bernhard

2011-01-20

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

Small-kernel, constrained least-squares restoration of sampled image data

NASA Technical Reports Server (NTRS)

Hazra, Rajeeb; Park, Stephen K.

1992-01-01

Following the work of Park (1989), who extended a derivation of the Wiener filter based on the incomplete discrete/discrete model to a more comprehensive end-to-end continuous/discrete/continuous model, it is shown that a derivation of the constrained least-squares (CLS) filter based on the discrete/discrete model can also be extended to this more comprehensive continuous/discrete/continuous model. This results in an improved CLS restoration filter, which can be efficiently implemented as a small-kernel convolution in the spatial domain.

Generalized predictive control for a coupled four tank MIMO system using a continuous-discrete time observer.

PubMed

Gouta, Houssemeddine; Hadj Saïd, Salim; Barhoumi, Nabil; M'Sahli, Faouzi

2017-03-01

This paper deals with the problem of the observer based control design for a coupled four-tank liquid level system. For this MIMO system's dynamics, motivated by a desire to provide precise and sensorless liquid level control, a nonlinear predictive controller based on a continuous-discrete observer is presented. First, an analytical solution from the model predictive control (MPC) technique is developed for a particular class of nonlinear MIMO systems and its corresponding exponential stability is proven. Then, a high gain observer that runs in continuous-time with an output error correction time that is updated in a mixed continuous-discrete fashion is designed in order to estimate the liquid levels in the two upper tanks. The effectiveness of the designed control schemes are validated by two tests; The first one is maintaining a constant level in the first bottom tank while making the level in the second bottom tank to follow a sinusoidal reference signal. The second test is more difficult and it is made using two trapezoidal reference signals in order to see the decoupling performance of the system's outputs. Simulation and experimental results validate the objective of the paper. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations

NASA Technical Reports Server (NTRS)

Parrish, E. A.; Mcvey, E. S.; Cook, G.; Henderson, K. C.

1976-01-01

The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.

Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables.

PubMed

Heck, Daniel W; Erdfelder, Edgar; Kieslich, Pascal J

2018-05-24

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.

On the time-weighted quadratic sum of linear discrete systems

NASA Technical Reports Server (NTRS)

Jury, E. I.; Gutman, S.

1975-01-01

A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

A simple method to calculate first-passage time densities with arbitrary initial conditions

NASA Astrophysics Data System (ADS)

Nyberg, Markus; Ambjörnsson, Tobias; Lizana, Ludvig

2016-06-01

Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of general purpose analytical tools for computing first-passage time densities (FPTDs) for complex problems, we propose a new simple method based on the independent interval approximation (IIA). We generalise previous formulations of the IIA to include arbitrary initial conditions as well as to deal with discrete time and non-smooth continuous time processes. We derive a closed form expression for the FPTD in z and Laplace-transform space to a boundary in one dimension. Two classes of problems are analysed in detail: discrete time symmetric random walks (Markovian) and continuous time Gaussian stationary processes (Markovian and non-Markovian). Our results are in good agreement with Langevin dynamics simulations.

Discrete event simulation tool for analysis of qualitative models of continuous processing systems

NASA Technical Reports Server (NTRS)

Malin, Jane T. (Inventor); Basham, Bryan D. (Inventor); Harris, Richard A. (Inventor)

1990-01-01

An artificial intelligence design and qualitative modeling tool is disclosed for creating computer models and simulating continuous activities, functions, and/or behavior using developed discrete event techniques. Conveniently, the tool is organized in four modules: library design module, model construction module, simulation module, and experimentation and analysis. The library design module supports the building of library knowledge including component classes and elements pertinent to a particular domain of continuous activities, functions, and behavior being modeled. The continuous behavior is defined discretely with respect to invocation statements, effect statements, and time delays. The functionality of the components is defined in terms of variable cluster instances, independent processes, and modes, further defined in terms of mode transition processes and mode dependent processes. Model construction utilizes the hierarchy of libraries and connects them with appropriate relations. The simulation executes a specialized initialization routine and executes events in a manner that includes selective inherency of characteristics through a time and event schema until the event queue in the simulator is emptied. The experimentation and analysis module supports analysis through the generation of appropriate log files and graphics developments and includes the ability of log file comparisons.

Gauge properties of the guiding center variational symplectic integrator

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

Squire, J.; Tang, W. M.; Qin, H.

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed formore » this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t{yields}0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and {phi} are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)].« less

Continuous-time discrete-space models for animal movement

USGS Publications Warehouse

Hanks, Ephraim M.; Hooten, Mevin B.; Alldredge, Mat W.

2015-01-01

The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.

Adaptive critic designs for discrete-time zero-sum games with application to H(infinity) control.

PubMed

Al-Tamimi, Asma; Abu-Khalaf, Murad; Lewis, Frank L

2007-02-01

In this correspondence, adaptive critic approximate dynamic programming designs are derived to solve the discrete-time zero-sum game in which the state and action spaces are continuous. This results in a forward-in-time reinforcement learning algorithm that converges to the Nash equilibrium of the corresponding zero-sum game. The results in this correspondence can be thought of as a way to solve the Riccati equation of the well-known discrete-time H(infinity) optimal control problem forward in time. Two schemes are presented, namely: 1) a heuristic dynamic programming and 2) a dual-heuristic dynamic programming, to solve for the value function and the costate of the game, respectively. An H(infinity) autopilot design for an F-16 aircraft is presented to illustrate the results.

Discrete Space-Time: History and Recent Developments

NASA Astrophysics Data System (ADS)

Crouse, David

2017-01-01

Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.

Hybrid Automated Diagnosis of Discrete/Continuous Systems

NASA Technical Reports Server (NTRS)

Park, Han; James, Mark; MacKey, Ryan; Cannon, Howard; Bajwa, Anapa; Maul, William

2007-01-01

A recently conceived method of automated diagnosis of a complex electromechanical system affords a complete set of capabilities for hybrid diagnosis in the case in which the state of the electromechanical system is characterized by both continuous and discrete values (as represented by analog and digital signals, respectively). The method is an integration of two complementary diagnostic systems: (1) beacon-based exception analysis for multi-missions (BEAM), which is primarily useful in the continuous domain and easily performs diagnoses in the presence of transients; and (2) Livingstone, which is primarily useful in the discrete domain and is typically restricted to quasi-steady conditions. BEAM has been described in several prior NASA Tech Briefs articles: "Software for Autonomous Diagnosis of Complex Systems" (NPO-20803), Vol. 26, No. 3 (March 2002), page 33; "Beacon-Based Exception Analysis for Multimissions" (NPO-20827), Vol. 26, No. 9 (September 2002), page 32; "Wavelet-Based Real-Time Diagnosis of Complex Systems" (NPO-20830), Vol. 27, No. 1 (January 2003), page 67; and "Integrated Formulation of Beacon-Based Exception Analysis for Multimissions" (NPO-21126), Vol. 27, No. 3 (March 2003), page 74. Briefly, BEAM is a complete data-analysis method, implemented in software, for real-time or off-line detection and characterization of faults. The basic premise of BEAM is to characterize a system from all available observations and train the characterization with respect to normal phases of operation. The observations are primarily continuous in nature. BEAM isolates anomalies by analyzing the deviations from nominal for each phase of operation. Livingstone is a model-based reasoner that uses a model of a system, controller commands, and sensor observations to track the system s state, and detect and diagnose faults. Livingstone models a system within the discrete domain. Therefore, continuous sensor readings, as well as time, must be discretized. To reason about continuous systems, Livingstone uses monitors that discretize the sensor readings using trending and thresholding techniques. In development of the a hybrid method, BEAM results were sent to Livingstone to serve as an independent source of evidence that is in addition to the evidence gathered by Livingstone standard monitors. The figure depicts the flow of data in an early version of a hybrid system dedicated to diagnosing a simulated electromechanical system. In effect, BEAM served as a "smart" monitor for Livingstone. BEAM read the simulation data, processed the data to form observations, and stored the observations in a file. A monitor stub synchronized the events recorded by BEAM with the output of the Livingstone standard monitors according to time tags. This information was fed to a real-time interface, which buffered and fed the information to Livingstone, and requested diagnoses at the appropriate times. In a test, the hybrid system was found to correctly identify a failed component in an electromechanical system for which neither BEAM nor Livingstone alone yielded the correct diagnosis.

The Effect of Haptic Guidance on Learning a Hybrid Rhythmic-Discrete Motor Task.

PubMed

Marchal-Crespo, Laura; Bannwart, Mathias; Riener, Robert; Vallery, Heike

2015-01-01

Bouncing a ball with a racket is a hybrid rhythmic-discrete motor task, combining continuous rhythmic racket movements with discrete impact events. Rhythmicity is exceptionally important in motor learning, because it underlies fundamental movements such as walking. Studies suggested that rhythmic and discrete movements are governed by different control mechanisms at different levels of the Central Nervous System. The aim of this study is to evaluate the effect of fixed/fading haptic guidance on learning to bounce a ball to a desired apex in virtual reality with varying gravity. Changing gravity changes dominance of rhythmic versus discrete control: The higher the value of gravity, the more rhythmic the task; lower values reduce the bouncing frequency and increase dwell times, eventually leading to a repetitive discrete task that requires initiation and termination, resembling target-oriented reaching. Although motor learning in the ball-bouncing task with varying gravity has been studied, the effect of haptic guidance on learning such a hybrid rhythmic-discrete motor task has not been addressed. We performed an experiment with thirty healthy subjects and found that the most effective training condition depended on the degree of rhythmicity: Haptic guidance seems to hamper learning of continuous rhythmic tasks, but it seems to promote learning for repetitive tasks that resemble discrete movements.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

Reply to "Comment on `Route from discreteness to the continuum for the Tsallis q -entropy' "

NASA Astrophysics Data System (ADS)

Oikonomou, Thomas; Bagci, G. Baris

2018-06-01

It has been known for some time that the usual q -entropy Sq(n ) cannot be shown to converge to the continuous case. In Phys. Rev. E 97, 012104 (2018), 10.1103/PhysRevE.97.012104, we have shown that the discrete q -entropy S˜q(n ) converges to the continuous case when the total number of states are properly taken into account in terms of a convergence factor. Ou and Abe [previous Comment, Phys. Rev. E 97, 066101 (2018), 10.1103/PhysRevE.97.066101] noted that this form of the discrete q -entropy does not conform to the Shannon-Khinchin expandability axiom. As a reply, we note that the fulfillment or not of the expandability property by the discrete q -entropy strongly depends on the origin of the convergence factor, presenting an example in which S˜q(n ) is expandable.

A discrete mechanics framework for real time virtual surgical simulations with application to virtual laparoscopic nephrectomy.

PubMed

Zhou, Xiangmin; Zhang, Nan; Sha, Desong; Shen, Yunhe; Tamma, Kumar K; Sweet, Robert

2009-01-01

The inability to render realistic soft-tissue behavior in real time has remained a barrier to face and content aspects of validity for many virtual reality surgical training systems. Biophysically based models are not only suitable for training purposes but also for patient-specific clinical applications, physiological modeling and surgical planning. When considering the existing approaches for modeling soft tissue for virtual reality surgical simulation, the computer graphics-based approach lacks predictive capability; the mass-spring model (MSM) based approach lacks biophysically realistic soft-tissue dynamic behavior; and the finite element method (FEM) approaches fail to meet the real-time requirement. The present development stems from physics fundamental thermodynamic first law; for a space discrete dynamic system directly formulates the space discrete but time continuous governing equation with embedded material constitutive relation and results in a discrete mechanics framework which possesses a unique balance between the computational efforts and the physically realistic soft-tissue dynamic behavior. We describe the development of the discrete mechanics framework with focused attention towards a virtual laparoscopic nephrectomy application.

A Surrogate Technique for Investigating Deterministic Dynamics in Discrete Human Movement.

PubMed

Taylor, Paul G; Small, Michael; Lee, Kwee-Yum; Landeo, Raul; O'Meara, Damien M; Millett, Emma L

2016-10-01

Entropy is an effective tool for investigation of human movement variability. However, before applying entropy, it can be beneficial to employ analyses to confirm that observed data are not solely the result of stochastic processes. This can be achieved by contrasting observed data with that produced using surrogate methods. Unlike continuous movement, no appropriate method has been applied to discrete human movement. This article proposes a novel surrogate method for discrete movement data, outlining the processes for determining its critical values. The proposed technique reliably generated surrogates for discrete joint angle time series, destroying fine-scale dynamics of the observed signal, while maintaining macro structural characteristics. Comparison of entropy estimates indicated observed signals had greater regularity than surrogates and were not only the result of stochastic but also deterministic processes. The proposed surrogate method is both a valid and reliable technique to investigate determinism in other discrete human movement time series.

Robust passivity analysis for discrete-time recurrent neural networks with mixed delays

NASA Astrophysics Data System (ADS)

Huang, Chuan-Kuei; Shu, Yu-Jeng; Chang, Koan-Yuh; Shou, Ho-Nien; Lu, Chien-Yu

2015-02-01

This article considers the robust passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with mixed time-delays and uncertain parameters. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays in a given range are presented, and the uncertain parameters are norm-bounded. The activation functions are assumed to be globally Lipschitz continuous. Based on new bounding technique and appropriate type of Lyapunov functional, a sufficient condition is investigated to guarantee the existence of the desired robust passivity condition for the DRNNs, which can be derived in terms of a family of linear matrix inequality (LMI). Some free-weighting matrices are introduced to reduce the conservatism of the criterion by using the bounding technique. A numerical example is given to illustrate the effectiveness and applicability.

Stability of continuous-time quantum filters with measurement imperfections

NASA Astrophysics Data System (ADS)

Amini, H.; Pellegrini, C.; Rouchon, P.

2014-07-01

The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes and that takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems and where the measurement imperfections are modelled by a left stochastic matrix.

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking

PubMed Central

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-01-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time rescaling theorem provides a goodness of fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model’s spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies upon assumptions of continuously defined time and instantaneous events. However spikes have finite width and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time rescaling theorem which analytically corrects for the effects of finite resolution. This allows us to define a rescaled time which is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting Generalized Linear Models (GLMs) to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false positive rate of the KS test and greatly increasing the reliability of model evaluation based upon the time rescaling theorem. PMID:20608868

Discrete time rescaling theorem: determining goodness of fit for discrete time statistical models of neural spiking.

PubMed

Haslinger, Robert; Pipa, Gordon; Brown, Emery

2010-10-01

One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem.

Relations between continuous real-time physical properties and discrete water-quality constituents in the Little Arkansas River, south-central Kansas, 1998-2014

USGS Publications Warehouse

Rasmussen, Patrick P.; Eslick, Patrick J.; Ziegler, Andrew C.

2016-08-11

Water from the Little Arkansas River is used as source water for artificial recharge of the Equus Beds aquifer, one of the primary water-supply sources for the city of Wichita, Kansas. The U.S. Geological Survey has operated two continuous real-time water-quality monitoring stations since 1995 on the Little Arkansas River in Kansas. Regression models were developed to establish relations between discretely sampled constituent concentrations and continuously measured physical properties to compute concentrations of those constituents of interest. Site-specific regression models were originally published in 2000 for the near Halstead and near Sedgwick U.S. Geological Survey streamgaging stations and the site-specific regression models were then updated in 2003. This report updates those regression models using discrete and continuous data collected during May 1998 through August 2014. In addition to the constituents listed in the 2003 update, new regression models were developed for total organic carbon. The real-time computations of water-quality concentrations and loads are available at http://nrtwq.usgs.gov. The water-quality information in this report is important to the city of Wichita because water-quality information allows for real-time quantification and characterization of chemicals of concern (including chloride), in addition to nutrients, sediment, bacteria, and atrazine transported in the Little Arkansas River. The water-quality information in this report aids in the decision making for water treatment before artificial recharge.

Bell-Curve Genetic Algorithm for Mixed Continuous and Discrete Optimization Problems

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.; Griffith, Michelle; Sykes, Ruth; Sobieszczanski-Sobieski, Jaroslaw

2002-01-01

In this manuscript we have examined an extension of BCB that encompasses a mix of continuous and quasi-discrete, as well as truly-discrete applications. FVe began by testing two refinements to the discrete version of BCB. The testing of midpoint versus fitness (Tables 1 and 2) proved inconclusive. The testing of discrete normal tails versus standard mutation showed was conclusive and demonstrated that the discrete normal tails are better. Next, we implemented these refinements in a combined continuous and discrete BCB and compared the performance of two discrete distance on the hub problem. Here we found when "order does matter" it pays to take it into account.

Bayesian functional integral method for inferring continuous data from discrete measurements.

PubMed

Heuett, William J; Miller, Bernard V; Racette, Susan B; Holloszy, John O; Chow, Carson C; Periwal, Vipul

2012-02-08

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Discrete linear canonical transforms based on dilated Hermite functions.

PubMed

Pei, Soo-Chang; Lai, Yun-Chiu

2011-08-01

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

Optimal control of a hybrid rhythmic-discrete task: the bouncing ball revisited.

PubMed

Ronsse, Renaud; Wei, Kunlin; Sternad, Dagmar

2010-05-01

Rhythmically bouncing a ball with a racket is a hybrid task that combines continuous rhythmic actuation of the racket with the control of discrete impact events between racket and ball. This study presents experimental data and a two-layered modeling framework that explicitly addresses the hybrid nature of control: a first discrete layer calculates the state to reach at impact and the second continuous layer smoothly drives the racket to this desired state, based on optimality principles. The testbed for this hybrid model is task performance at a range of increasingly slower tempos. When slowing the rhythm of the bouncing actions, the continuous cycles become separated into a sequence of discrete movements interspersed by dwell times and directed to achieve the desired impact. Analyses of human performance show increasing variability of performance measures with slower tempi, associated with a change in racket trajectories from approximately sinusoidal to less symmetrical velocity profiles. Matching results of model simulations give support to a hybrid control model based on optimality, and therefore suggest that optimality principles are applicable to the sensorimotor control of complex movements such as ball bouncing.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Proportional exponentiated link transformed hazards (ELTH) models for discrete time survival data with application

PubMed Central

Joeng, Hee-Koung; Chen, Ming-Hui; Kang, Sangwook

2015-01-01

Discrete survival data are routinely encountered in many fields of study including behavior science, economics, epidemiology, medicine, and social science. In this paper, we develop a class of proportional exponentiated link transformed hazards (ELTH) models. We carry out a detailed examination of the role of links in fitting discrete survival data and estimating regression coefficients. Several interesting results are established regarding the choice of links and baseline hazards. We also characterize the conditions for improper survival functions and the conditions for existence of the maximum likelihood estimates under the proposed ELTH models. An extensive simulation study is conducted to examine the empirical performance of the parameter estimates under the Cox proportional hazards model by treating discrete survival times as continuous survival times, and the model comparison criteria, AIC and BIC, in determining links and baseline hazards. A SEER breast cancer dataset is analyzed in details to further demonstrate the proposed methodology. PMID:25772374

Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong

2018-02-01

To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu-Eckhaus equation is derived from the reduction in an extended Ablowitz-Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu-Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.

Differential results integrated with continuous and discrete gravity measurements between nearby stations

NASA Astrophysics Data System (ADS)

Xu, Weimin; Chen, Shi; Lu, Hongyan

2016-04-01

Integrated gravity is an efficient way in studying spatial and temporal characteristics of the dynamics and tectonics. Differential measurements based on the continuous and discrete gravity observations shows highly competitive in terms of both efficiency and precision with single result. The differential continuous gravity variation between the nearby stations, which is based on the observation of Scintrex g-Phone relative gravimeters in every single station. It is combined with the repeated mobile relative measurements or absolute results to study the regional integrated gravity changes. Firstly we preprocess the continuous records by Tsoft software, and calculate the theoretical earth tides and ocean tides by "MT80TW" program through high precision tidal parameters from "WPARICET". The atmospheric loading effects and complex drift are strictly considered in the procedure. Through above steps we get the continuous gravity in every station and we can calculate the continuous gravity variation between nearby stations, which is called the differential continuous gravity changes. Then the differential results between related stations is calculated based on the repeated gravity measurements, which are carried out once or twice every year surrounding the gravity stations. Hence we get the discrete gravity results between the nearby stations. Finally, the continuous and discrete gravity results are combined in the same related stations, including the absolute gravity results if necessary, to get the regional integrated gravity changes. This differential gravity results is more accurate and effective in dynamical monitoring, regional hydrologic effects studying, tectonic activity and other geodynamical researches. The time-frequency characteristics of continuous gravity results are discussed to insure the accuracy and efficiency in the procedure.

The Tactile Continuity Illusion

ERIC Educational Resources Information Center

Kitagawa, Norimichi; Igarashi, Yuka; Kashino, Makio

2009-01-01

We can perceive the continuity of an object or event by integrating spatially/temporally discrete sensory inputs. The mechanism underlying this perception of continuity has intrigued many researchers and has been well documented in both the visual and auditory modalities. The present study shows for the first time to our knowledge that an illusion…

Slow cortical potentials and "inner time consciousness" - A neuro-phenomenal hypothesis about the "width of present".

PubMed

Northoff, Georg

2016-05-01

William James postulated a "stream of consciousness" that presupposes temporal continuity. The neuronal mechanisms underlying the construction of such temporal continuity remain unclear, however, in my contribution, I propose a neuro-phenomenal hypothesis that is based on slow cortical potentials and their extension of the present moment as described in the phenomenal term of "width of present". More specifically, I focus on the way the brain's neural activity needs to be encoded in order to make possible the "stream of consciousness." This leads us again to the low-frequency fluctuations of the brain's neural activity and more specifically to slow cortical potentials (SCPs). Due to their long phase duration as low-frequency fluctuations, SCPs can integrate different stimuli and their associated neural activity from different regions in one converging region. Such integration may be central for consciousness to occur, as it was recently postulated by He and Raichle. They leave open, however, the question of the exact neuronal mechanisms, like the encoding strategy, that make possible the association of the otherwise purely neuronal SCP with consciousness and its phenomenal features. I hypothesize that SCPs allow for linking and connecting different discrete points in physical time by encoding their statistically based temporal differences rather than the single discrete time points by themselves. This presupposes difference-based coding rather than stimulus-based coding. The encoding of such statistically based temporal differences makes it possible to "go beyond" the merely physical features of the stimuli; that is, their single discrete time points and their conduction delays (as related to their neural processing in the brain). This, in turn, makes possible the constitution of "local temporal continuity" of neural activity in one particular region. The concept of "local temporal continuity" signifies the linkage and integration of different discrete time points into one neural activity in a particular region. How does such local temporal continuity predispose the experience of time in consciousness? For that, I turn to phenomenological philosopher Edmund Husserl and his description of what he calls "inner time consciousness" (Husserl and Brough, 1990). One hallmark of humans' "inner time consciousness" is that we experience events and objects in succession and duration in our consciousness; according to Husserl, this amounts to what he calls the "width of [the] present." The concept of the width of present describes the extension of the present beyond the single discrete time point, such as, for instance, when we perceive different tones as a melody. I now hypothesize the degree of the width of present to be directly dependent upon and thus predisposed by the degree of the temporal differences between two (or more) discrete time points as they are encoded into neural activity. I therefore conclude that the SCPs and their encoding of neural activity in terms of temporal differences must be regarded a neural predisposition of consciousness (NPC) as distinguished from a neural correlate of consciousness (NCC). Copyright © 2015 Elsevier B.V. All rights reserved.

Biomechanical contributions of the trunk and upper extremity in discrete versus cyclic reaching in survivors of stroke.

PubMed

Massie, Crystal L; Malcolm, Matthew P; Greene, David P; Browning, Raymond C

2014-01-01

Stroke rehabilitation interventions and assessments incorporate discrete and/or cyclic reaching tasks, yet no biomechanical comparison exists between these 2 movements in survivors of stroke. To characterize the differences between discrete (movements bounded by stationary periods) and cyclic (continuous repetitive movements) reaching in survivors of stroke. Seventeen survivors of stroke underwent kinematic motion analysis of discrete and cyclic reaching movements. Outcomes collected for each side included shoulder, elbow, and trunk range of motion (ROM); peak velocity; movement time; and spatial variability at target contact. Participants used significantly less shoulder and elbow ROM and significantly more trunk flexion ROM when reaching with the stroke-affected side compared with the less-affected side (P < .001). Participants used significantly more trunk rotation during cyclic reaching than discrete reaching with the stroke-affected side (P = .01). No post hoc differences were observed between tasks within the stroke-affected side for elbow, shoulder, and trunk flexion ROM. Peak velocity, movement time, and spatial variability were not different between discrete and cyclic reaching in the stroke-affected side. Survivors of stroke reached with altered kinematics when the stroke-affected side was compared with the less-affected side, yet there were few differences between discrete and cyclic reaching within the stroke-affected side. The greater trunk rotation during cyclic reaching represents a unique segmental strategy when using the stroke-affected side without consequences to end-point kinematics. These findings suggest that clinicians should consider the type of reaching required in therapeutic activities because of the continuous movement demands required with cyclic reaching.

Reliable gain-scheduled control of discrete-time systems and its application to CSTR model

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.

2016-10-01

This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.

SIMULATION FROM ENDPOINT-CONDITIONED, CONTINUOUS-TIME MARKOV CHAINS ON A FINITE STATE SPACE, WITH APPLICATIONS TO MOLECULAR EVOLUTION.

PubMed

Hobolth, Asger; Stone, Eric A

2009-09-01

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length T. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix Q of the CTMC, its beginning and ending states, and the length of sampling time T. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given Q, T, and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.

Fine motor movements while drawing during the encoding phase of a serial verbal recall task reduce working memory performance.

PubMed

Tindle, Richard; Longstaff, Mitchell G

2016-02-01

The time-based resource-sharing (TBRS) model of working memory indicates that secondary tasks that capture attention for relatively long periods can result in the interference of working memory processing and maintenance. The current study investigates if discrete and continuous movements have differing effects on a concurrent, verbal serial recall task. In the listening condition, participants were asked to recall spoken words presented in lists of six. In the drawing conditions, participants performed the same task while producing discrete (star) or continuous (circle) movements. As hypothesised, participants recalled more words overall in the listening condition compared to the combined drawing conditions. The prediction that the continuous movement condition would reduce recall compared to listening was also supported. Fine-grained analysis at each serial position revealed significantly more words were recalled at mid serial positions in the listening condition, with worst recall for the continuous condition at position 5 compared to the listening and discrete conditions. Kinematic analysis showed that participants increased the size and speed of the continuous movements resulting in a similar duration and number of strokes for each condition. The duration of brief pauses in the discrete condition was associated with the number of words recalled. The results indicate that fine motor movements reduced working memory performance; however, it was not merely performing a movement but the type of the movement that determined how resources were diverted. In the context of the TBRS, continuous movements could be capturing attention for longer periods relative to discrete movements, reducing verbal serial recall. Copyright © 2016 Elsevier B.V. All rights reserved.

Comparing performance in discrete and continuous comparison tasks.

PubMed

Leibovich, Tali; Henik, Avishai

2014-05-01

The approximate number system (ANS) theory suggests that all magnitudes, discrete (i.e., number of items) or continuous (i.e., size, density, etc.), are processed by a shared system and comply with Weber's law. The current study reexamined this notion by comparing performance in discrete (comparing numerosities of dot arrays) and continuous (comparisons of area of squares) tasks. We found that: (a) threshold of discrimination was higher for continuous than for discrete comparisons; (b) while performance in the discrete task complied with Weber's law, performance in the continuous task violated it; and (c) performance in the discrete task was influenced by continuous properties (e.g., dot density, dot cumulative area) of the dot array that were not predictive of numerosities or task relevant. Therefore, we propose that the magnitude processing system (MPS) is actually divided into separate (yet interactive) systems for discrete and continuous magnitude processing. Further subdivisions are discussed. We argue that cooperation between these systems results in a holistic comparison of magnitudes, one that takes into account continuous properties in addition to numerosities. Considering the MPS as two systems opens the door to new and important questions that shed light on both normal and impaired development of the numerical system.

Discrete-Slots Models of Visual Working-Memory Response Times

PubMed Central

Donkin, Christopher; Nosofsky, Robert M.; Gold, Jason M.; Shiffrin, Richard M.

2014-01-01

Much recent research has aimed to establish whether visual working memory (WM) is better characterized by a limited number of discrete all-or-none slots or by a continuous sharing of memory resources. To date, however, researchers have not considered the response-time (RT) predictions of discrete-slots versus shared-resources models. To complement the past research in this field, we formalize a family of mixed-state, discrete-slots models for explaining choice and RTs in tasks of visual WM change detection. In the tasks under investigation, a small set of visual items is presented, followed by a test item in 1 of the studied positions for which a change judgment must be made. According to the models, if the studied item in that position is retained in 1 of the discrete slots, then a memory-based evidence-accumulation process determines the choice and the RT; if the studied item in that position is missing, then a guessing-based accumulation process operates. Observed RT distributions are therefore theorized to arise as probabilistic mixtures of the memory-based and guessing distributions. We formalize an analogous set of continuous shared-resources models. The model classes are tested on individual subjects with both qualitative contrasts and quantitative fits to RT-distribution data. The discrete-slots models provide much better qualitative and quantitative accounts of the RT and choice data than do the shared-resources models, although there is some evidence for “slots plus resources” when memory set size is very small. PMID:24015956

Ecological monitoring in a discrete-time prey-predator model.

PubMed

Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J

2017-09-21

The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

Single-crossover recombination in discrete time.

PubMed

von Wangenheim, Ute; Baake, Ellen; Baake, Michael

2010-05-01

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.

A survival tree method for the analysis of discrete event times in clinical and epidemiological studies.

PubMed

Schmid, Matthias; Küchenhoff, Helmut; Hoerauf, Achim; Tutz, Gerhard

2016-02-28

Survival trees are a popular alternative to parametric survival modeling when there are interactions between the predictor variables or when the aim is to stratify patients into prognostic subgroups. A limitation of classical survival tree methodology is that most algorithms for tree construction are designed for continuous outcome variables. Hence, classical methods might not be appropriate if failure time data are measured on a discrete time scale (as is often the case in longitudinal studies where data are collected, e.g., quarterly or yearly). To address this issue, we develop a method for discrete survival tree construction. The proposed technique is based on the result that the likelihood of a discrete survival model is equivalent to the likelihood of a regression model for binary outcome data. Hence, we modify tree construction methods for binary outcomes such that they result in optimized partitions for the estimation of discrete hazard functions. By applying the proposed method to data from a randomized trial in patients with filarial lymphedema, we demonstrate how discrete survival trees can be used to identify clinically relevant patient groups with similar survival behavior. Copyright © 2015 John Wiley & Sons, Ltd.

Subjective and objective evaluation of visual fatigue on viewing 3D display continuously

NASA Astrophysics Data System (ADS)

Wang, Danli; Xie, Yaohua; Yang, Xinpan; Lu, Yang; Guo, Anxiang

2015-03-01

In recent years, three-dimensional (3D) displays become more and more popular in many fields. Although they can provide better viewing experience, they cause extra problems, e.g., visual fatigue. Subjective or objective methods are usually used in discrete viewing processes to evaluate visual fatigue. However, little research combines subjective indicators and objective ones in an entirely continuous viewing process. In this paper, we propose a method to evaluate real-time visual fatigue both subjectively and objectively. Subjects watch stereo contents on a polarized 3D display continuously. Visual Reaction Time (VRT), Critical Flicker Frequency (CFF), Punctum Maximum Accommodation (PMA) and subjective scores of visual fatigue are collected before and after viewing. During the viewing process, the subjects rate the visual fatigue whenever it changes, without breaking the viewing process. At the same time, the blink frequency (BF) and percentage of eye closure (PERCLOS) of each subject is recorded for comparison to a previous research. The results show that the subjective visual fatigue and PERCLOS increase with time and they are greater in a continuous process than a discrete one. The BF increased with time during the continuous viewing process. Besides, the visual fatigue also induced significant changes of VRT, CFF and PMA.

Integrating continuous stocks and flows into state-and-transition simulation models of landscape change

USGS Publications Warehouse

Daniel, Colin J.; Sleeter, Benjamin M.; Frid, Leonardo; Fortin, Marie-Josée

2018-01-01

State-and-transition simulation models (STSMs) provide a general framework for forecasting landscape dynamics, including projections of both vegetation and land-use/land-cover (LULC) change. The STSM method divides a landscape into spatially-referenced cells and then simulates the state of each cell forward in time, as a discrete-time stochastic process using a Monte Carlo approach, in response to any number of possible transitions. A current limitation of the STSM method, however, is that all of the state variables must be discrete.Here we present a new approach for extending a STSM, in order to account for continuous state variables, called a state-and-transition simulation model with stocks and flows (STSM-SF). The STSM-SF method allows for any number of continuous stocks to be defined for every spatial cell in the STSM, along with a suite of continuous flows specifying the rates at which stock levels change over time. The change in the level of each stock is then simulated forward in time, for each spatial cell, as a discrete-time stochastic process. The method differs from the traditional systems dynamics approach to stock-flow modelling in that the stocks and flows can be spatially-explicit, and the flows can be expressed as a function of the STSM states and transitions.We demonstrate the STSM-SF method by integrating a spatially-explicit carbon (C) budget model with a STSM of LULC change for the state of Hawai'i, USA. In this example, continuous stocks are pools of terrestrial C, while the flows are the possible fluxes of C between these pools. Importantly, several of these C fluxes are triggered by corresponding LULC transitions in the STSM. Model outputs include changes in the spatial and temporal distribution of C pools and fluxes across the landscape in response to projected future changes in LULC over the next 50 years.The new STSM-SF method allows both discrete and continuous state variables to be integrated into a STSM, including interactions between them. With the addition of stocks and flows, STSMs provide a conceptually simple yet powerful approach for characterizing uncertainties in projections of a wide range of questions regarding landscape change.

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

NASA Astrophysics Data System (ADS)

Morita, Satoru

2018-05-01

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Adaptive control of periodic systems

NASA Astrophysics Data System (ADS)

Tian, Zhiling

2009-12-01

Adaptive control is needed to cope with parametric uncertainty in dynamical systems. The adaptive control of LTI systems in both discrete and continuous time has been studied for four decades and the results are currently used widely in many different fields. In recent years, interest has shifted to the adaptive control of time-varying systems. It is known that the adaptive control of arbitrarily rapidly time-varying systems is in general intractable, but systems with periodically time-varying parameters (LTP systems) which have much more structure, are amenable to mathematical analysis. Further, there is also a need for such control in practical problems which have arisen in industry during the past twenty years. This thesis is the first attempt to deal with the adaptive control of LTP systems. Adaptive Control involves estimation of unknown parameters, adjusting the control parameters based on the estimates, and demonstrating that the overall system is stable. System theoretic properties such as stability, controllability, and observability play an important role both in formulating of the problems, as well as in generating solutions for them. For LTI systems, these properties have been studied since 1960s, and algebraic conditions that have to be satisfied to assure these properties are now well established. In the case of LTP systems, these properties can be expressed only in terms of transition matrices that are much more involved than those for LTI systems. Since adaptive control problems can be formulated only when these properties are well understood, it is not surprising that systematic efforts have not been made thus far for formulating and solving adaptive control problems that arise in LTP systems. Even in the case of LTI systems, it is well recognized that problems related to adaptive discrete-time system are not as difficult as those that arise in the continuous-time systems. This is amply evident in the solutions that were derived in the 1980s and 1990s for all the important problems. These differences are even more amplified in the LTP case; some problems in continuous time cannot even be formulated precisely. This thesis consequently focuses primarily on the adaptive identification and control of discrete-time systems, and derives most of the results that currently exist in the literature for LTI systems. Based on these investigations of discrete-time adaptive systems, attempts are made in the thesis to examine their continuous-time counterparts, and discuss the principal difficulties encountered. The dissertation examines critically the system theoretic properties of LTP systems in Chapter 2, and the mathematical framework provided for their analysis by Floquet theory in Chapter 3. Assuming that adaptive identification and control problems can be formulated precisely, a unified method of developing stable adaptive laws using error models is treated in Chapter 4. Chapter 5 presents a detailed study of the adaptation in SISO discrete-time LTP systems, and represents the core of the thesis. The important problems of identification, stabilization, regulation, and tracking of arbitrary signals are investigated, and practically implementable stable adaptive laws are derived. The dissertation concludes with a discussion of continuous-time adaptive control in Chapter 6 and discrete multivariable systems in Chapter 7. Directions for future research are indicated towards the end of the dissertation.

Exploration Supply Chain Simulation

NASA Technical Reports Server (NTRS)

2008-01-01

The Exploration Supply Chain Simulation project was chartered by the NASA Exploration Systems Mission Directorate to develop a software tool, with proper data, to quantitatively analyze supply chains for future program planning. This tool is a discrete-event simulation that uses the basic supply chain concepts of planning, sourcing, making, delivering, and returning. This supply chain perspective is combined with other discrete or continuous simulation factors. Discrete resource events (such as launch or delivery reviews) are represented as organizational functional units. Continuous resources (such as civil service or contractor program functions) are defined as enabling functional units. Concepts of fixed and variable costs are included in the model to allow the discrete events to interact with cost calculations. The definition file is intrinsic to the model, but a blank start can be initiated at any time. The current definition file is an Orion Ares I crew launch vehicle. Parameters stretch from Kennedy Space Center across and into other program entities (Michaud Assembly Facility, Aliant Techsystems, Stennis Space Center, Johnson Space Center, etc.) though these will only gain detail as the file continues to evolve. The Orion Ares I file definition in the tool continues to evolve, and analysis from this tool is expected in 2008. This is the first application of such business-driven modeling to a NASA/government-- aerospace contractor endeavor.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells.

PubMed

Nguyen, P T T; Challis, K J; Jack, M W

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Local discretization method for overdamped Brownian motion on a potential with multiple deep wells

NASA Astrophysics Data System (ADS)

Nguyen, P. T. T.; Challis, K. J.; Jack, M. W.

2016-11-01

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Discrete disorder models for many-body localization

NASA Astrophysics Data System (ADS)

Janarek, Jakub; Delande, Dominique; Zakrzewski, Jakub

2018-04-01

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

Discrete-Time Demodulator Architectures for Free-Space Broadband Optical Pulse-Position Modulation

NASA Technical Reports Server (NTRS)

Gray, A. A.; Lee, C.

2004-01-01

The objective of this work is to develop discrete-time demodulator architectures for broadband optical pulse-position modulation (PPM) that are capable of processing Nyquist or near-Nyquist data rates. These architectures are motivated by the numerous advantages of realizing communications demodulators in digital very large scale integrated (VLSI) circuits. The architectures are developed within a framework that encompasses a large body of work in optical communications, synchronization, and multirate discrete-time signal processing and are constrained by the limitations of the state of the art in digital hardware. This work attempts to create a bridge between theoretical communication algorithms and analysis for deep-space optical PPM and modern digital VLSI. The primary focus of this work is on the synthesis of discrete-time processing architectures for accomplishing the most fundamental functions required in PPM demodulators, post-detection filtering, synchronization, and decision processing. The architectures derived are capable of closely approximating the theoretical performance of the continuous-time algorithms from which they are derived. The work concludes with an outline of the development path that leads to hardware.

Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses

NASA Astrophysics Data System (ADS)

Mohamad, Sannay; Gopalsamy, K.

2009-01-01

This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.

Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function.

PubMed

Shang, Jin; Li, Bingtuan; Barnard, Michael R

2015-05-01

We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a period-doubling bifurcation curve in the model. The bifurcation curve divides the parameter space into the region of stability and the region of instability. We demonstrate through numerical bifurcation diagrams that the regions of periodic cycles are intermixed with the regions of chaos. We also study the global stability of the model. Copyright © 2015 Elsevier Inc. All rights reserved.

Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning

NASA Technical Reports Server (NTRS)

Fayyad, U.; Irani, K.

1993-01-01

Since most real-world applications of classification learning involve continuous-valued attributes, properly addressing the discretization process is an important problem. This paper addresses the use of the entropy minimization heuristic for discretizing the range of a continuous-valued attribute into multiple intervals.

Modeling and control of operator functional state in a unified framework of fuzzy inference petri nets.

PubMed

Zhang, Jian-Hua; Xia, Jia-Jun; Garibaldi, Jonathan M; Groumpos, Petros P; Wang, Ru-Bin

2017-06-01

In human-machine (HM) hybrid control systems, human operator and machine cooperate to achieve the control objectives. To enhance the overall HM system performance, the discrete manual control task-load by the operator must be dynamically allocated in accordance with continuous-time fluctuation of psychophysiological functional status of the operator, so-called operator functional state (OFS). The behavior of the HM system is hybrid in nature due to the co-existence of discrete task-load (control) variable and continuous operator performance (system output) variable. Petri net is an effective tool for modeling discrete event systems, but for hybrid system involving discrete dynamics, generally Petri net model has to be extended. Instead of using different tools to represent continuous and discrete components of a hybrid system, this paper proposed a method of fuzzy inference Petri nets (FIPN) to represent the HM hybrid system comprising a Mamdani-type fuzzy model of OFS and a logical switching controller in a unified framework, in which the task-load level is dynamically reallocated between the operator and machine based on the model-predicted OFS. Furthermore, this paper used a multi-model approach to predict the operator performance based on three electroencephalographic (EEG) input variables (features) via the Wang-Mendel (WM) fuzzy modeling method. The membership function parameters of fuzzy OFS model for each experimental participant were optimized using artificial bee colony (ABC) evolutionary algorithm. Three performance indices, RMSE, MRE, and EPR, were computed to evaluate the overall modeling accuracy. Experiment data from six participants are analyzed. The results show that the proposed method (FIPN with adaptive task allocation) yields lower breakdown rate (from 14.8% to 3.27%) and higher human performance (from 90.30% to 91.99%). The simulation results of the FIPN-based adaptive HM (AHM) system on six experimental participants demonstrate that the FIPN framework provides an effective way to model and regulate/optimize the OFS in HM hybrid systems composed of continuous-time OFS model and discrete-event switching controller. Copyright © 2017 Elsevier B.V. All rights reserved.

Asynchronous discrete control of continuous processes

NASA Astrophysics Data System (ADS)

Kaliski, M. E.; Johnson, T. L.

1984-07-01

The research during this second contract year continued to deal with the development of sound theoretical models for asynchronous systems. Two criteria served to shape the research pursued: the first, that the developed models extend and generalize previously developed research for synchronous discrete control; the second, that the models explicitly address the question of how to incorporate system transition times into themselves. The following sections of this report concisely delineate this year's work. Our original proposal for this research identified four general tasks of investigation: (1.1) Analysis of Qualitative Properties of Asynchronous Hybrid Systems; (1.2) Acceptance and Control for Asynchronous Hybrid Systems.

Interesting examples of supervised continuous variable systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joe; Ramadge, Peter

1990-01-01

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of the closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.

Broadband Time-Frequency Analysis Using a Multicomputer

DTIC Science & Technology

2004-09-30

FFT 512 pt Waterfall WVD display 8© 2004 Mercury Computer Systems, Inc. Smoothed Pseudo Wigner - Ville Distribution One of many interference reduction...The Wigner - Ville distribution , the scalogram, and the discrete Gabor transform are among the most well-known of these methods. Due to specific...based upon FFT Accumulation Method • Continuous Wavelet Transform (Scalogram) • Discrete Wigner - Ville Distribution with a selected set of interference

Modeling commodity salam contract between two parties for discrete and continuous time series

NASA Astrophysics Data System (ADS)

Hisham, Azie Farhani Badrol; Jaffar, Maheran Mohd

2017-08-01

In order for Islamic finance to remain competitive as the conventional, there needs a new development of Islamic compliance product such as Islamic derivative that can be used to manage the risk. However, under syariah principles and regulations, all financial instruments must not be conflicting with five syariah elements which are riba (interest paid), rishwah (corruption), gharar (uncertainty or unnecessary risk), maysir (speculation or gambling) and jahl (taking advantage of the counterparty's ignorance). This study has proposed a traditional Islamic contract namely salam that can be built as an Islamic derivative product. Although a lot of studies has been done on discussing and proposing the implementation of salam contract as the Islamic product however they are more into qualitative and law issues. Since there is lack of quantitative study of salam contract being developed, this study introduces mathematical models that can value the appropriate salam price for a commodity salam contract between two parties. In modeling the commodity salam contract, this study has modified the existing conventional derivative model and come out with some adjustments to comply with syariah rules and regulations. The cost of carry model has been chosen as the foundation to develop the commodity salam model between two parties for discrete and continuous time series. However, the conventional time value of money results from the concept of interest that is prohibited in Islam. Therefore, this study has adopted the idea of Islamic time value of money which is known as the positive time preference, in modeling the commodity salam contract between two parties for discrete and continuous time series.

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue.

PubMed

Saleem, M; Agrawal, Tanuja; Anees, Afzal

2014-01-01

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K (+))-limited environment. Our both continuous and discrete models illustrate 'cancer immunoediting' as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202-206].

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue

PubMed Central

Saleem, M.; Agrawal, Tanuja; Anees, Afzal

2014-01-01

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K +)-limited environment. Our both continuous and discrete models illustrate ‘cancer immunoediting’ as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202–206]. PMID:24963981

SfM with MRFs: discrete-continuous optimization for large-scale structure from motion.

PubMed

Crandall, David J; Owens, Andrew; Snavely, Noah; Huttenlocher, Daniel P

2013-12-01

Recent work in structure from motion (SfM) has built 3D models from large collections of images downloaded from the Internet. Many approaches to this problem use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the image collection grows, and can suffer from drift or local minima. We present an alternative framework for SfM based on finding a coarse initial solution using hybrid discrete-continuous optimization and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and points, including noisy geotags and vanishing point (VP) estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it produces models that are similar to or better than those produced by incremental bundle adjustment, but more robustly and in a fraction of the time.

A Short-Segment Fourier Transform Methodology

DTIC Science & Technology

2009-03-01

defined sampling of the continuous-valued discrete-time Fourier transform, superresolution in the frequency domain and allowance of Dirac delta functions associated with pure sinusoidal input data components.

Covariant information-density cutoff in curved space-time.

PubMed

Kempf, Achim

2004-06-04

In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be equivalent to lattice theories. There is a close connection to generalized uncertainty relations which have appeared in string theory and other studies of quantum gravity.

Recent developments in learning control and system identification for robots and structures

NASA Technical Reports Server (NTRS)

Phan, M.; Juang, J.-N.; Longman, R. W.

1990-01-01

This paper reviews recent results in learning control and learning system identification, with particular emphasis on discrete-time formulation, and their relation to adaptive theory. Related continuous-time results are also discussed. Among the topics presented are proportional, derivative, and integral learning controllers, time-domain formulation of discrete learning algorithms. Newly developed techniques are described including the concept of the repetition domain, and the repetition domain formulation of learning control by linear feedback, model reference learning control, indirect learning control with parameter estimation, as well as related basic concepts, recursive and non-recursive methods for learning identification.

Stochastic resetting in backtrack recovery by RNA polymerases

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Lisica, Ana; Sánchez-Taltavull, Daniel; Grill, Stephan W.

2016-06-01

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally inactive backtracked state is determined by a kinetic competition between one-dimensional diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of one-dimensional diffusion is large compared to the rate of cleavage.

A space-time discretization procedure for wave propagation problems

NASA Technical Reports Server (NTRS)

Davis, Sanford

1989-01-01

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

ARMA models for earthquake ground motions. Seismic safety margins research program

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

Chang, M. K.; Kwiatkowski, J. W.; Nau, R. F.

1981-02-01

Four major California earthquake records were analyzed by use of a class of discrete linear time-domain processes commonly referred to as ARMA (Autoregressive/Moving-Average) models. It was possible to analyze these different earthquakes, identify the order of the appropriate ARMA model(s), estimate parameters, and test the residuals generated by these models. It was also possible to show the connections, similarities, and differences between the traditional continuous models (with parameter estimates based on spectral analyses) and the discrete models with parameters estimated by various maximum-likelihood techniques applied to digitized acceleration data in the time domain. The methodology proposed is suitable for simulatingmore » earthquake ground motions in the time domain, and appears to be easily adapted to serve as inputs for nonlinear discrete time models of structural motions. 60 references, 19 figures, 9 tables.« less

Model documentation for relations between continuous real-time and discrete water-quality constituents in Indian Creek, Johnson County, Kansas, June 2004 through May 2013

USGS Publications Warehouse

Stone, Mandy L.; Graham, Jennifer L.

2014-01-01

Johnson County is the fastest growing county in Kansas, with a population of about 560,000 people in 2012. Urban growth and development can have substantial effects on water quality, and streams in Johnson County are affected by nonpoint-source pollutants from stormwater runoff and point-source discharges such as municipal wastewater effluent. Understanding of current (2014) water-quality conditions and the effects of urbanization is critical for the protection and remediation of aquatic resources in Johnson County, Kansas and downstream reaches located elsewhere. The Indian Creek Basin is 194 square kilometers and includes parts of Johnson County, Kansas and Jackson County, Missouri. Approximately 86 percent of the Indian Creek Basin is located in Johnson County, Kansas. The U.S. Geological Survey, in cooperation with Johnson County Wastewater, operated a series of six continuous real-time water-quality monitoring stations in the Indian Creek Basin during June 2011 through May 2013; one of these sites has been operating since February 2004. Five monitoring sites were located on Indian Creek and one site was located on Tomahawk Creek. The purpose of this report is to document regression models that establish relations between continuously measured water-quality properties and discretely collected water-quality constituents. Continuously measured water-quality properties include streamflow, specific conductance, pH, water temperature, dissolved oxygen, turbidity, and nitrate. Discrete water-quality samples were collected during June 2011 through May 2013 at five new sites and June 2004 through May 2013 at a long-term site and analyzed for sediment, nutrients, bacteria, and other water-quality constituents. Regression models were developed to establish relations between discretely sampled constituent concentrations and continuously measured physical properties to estimate concentrations of those constituents of interest that are not easily measured in real time because of limitations in sensor technology and fiscal constraints. Regression models for 28 water-quality constituents were developed and documented. The water-quality information in this report is important to Johnson County Wastewater because it allows the concentrations of many potential pollutants of interest, including nutrients and sediment, to be estimated in real time and characterized during conditions and time scales that would not be possible otherwise.

Adaptive hybrid simulations for multiscale stochastic reaction networks

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

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

Continuous time wavelet entropy of auditory evoked potentials.

PubMed

Cek, M Emre; Ozgoren, Murat; Savaci, F Acar

2010-01-01

In this paper, the continuous time wavelet entropy (CTWE) of auditory evoked potentials (AEP) has been characterized by evaluating the relative wavelet energies (RWE) in specified EEG frequency bands. Thus, the rapid variations of CTWE due to the auditory stimulation could be detected in post-stimulus time interval. This approach removes the probability of missing the information hidden in short time intervals. The discrete time and continuous time wavelet based wavelet entropy variations were compared on non-target and target AEP data. It was observed that CTWE can also be an alternative method to analyze entropy as a function of time. 2009 Elsevier Ltd. All rights reserved.

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

The Integration of Continuous and Discrete Latent Variable Models: Potential Problems and Promising Opportunities

ERIC Educational Resources Information Center

Bauer, Daniel J.; Curran, Patrick J.

2004-01-01

Structural equation mixture modeling (SEMM) integrates continuous and discrete latent variable models. Drawing on prior research on the relationships between continuous and discrete latent variable models, the authors identify 3 conditions that may lead to the estimation of spurious latent classes in SEMM: misspecification of the structural model,…

Optimization and Quantization in Gradient Symbol Systems: A Framework for Integrating the Continuous and the Discrete in Cognition

ERIC Educational Resources Information Center

Smolensky, Paul; Goldrick, Matthew; Mathis, Donald

2014-01-01

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The…

A Two-Phase Model of Resource Allocation in Visual Working Memory

ERIC Educational Resources Information Center

Ye, Chaoxiong; Hu, Zhonghua; Li, Hong; Ristaniemi, Tapani; Liu, Qiang; Liu, Taosheng

2017-01-01

Two broad theories of visual working memory (VWM) storage have emerged from current research, a discrete slot-based theory and a continuous resource theory. However, neither the discrete slot-based theory or continuous resource theory clearly stipulates how the mental commodity for VWM (discrete slot or continuous resource) is allocated.…

Input-output characterization of an ultrasonic testing system by digital signal analysis

NASA Technical Reports Server (NTRS)

Williams, J. H., Jr.; Lee, S. S.; Karagulle, H.

1986-01-01

Ultrasonic test system input-output characteristics were investigated by directly coupling the transmitting and receiving transducers face to face without a test specimen. Some of the fundamentals of digital signal processing were summarized. Input and output signals were digitized by using a digital oscilloscope, and the digitized data were processed in a microcomputer by using digital signal-processing techniques. The continuous-time test system was modeled as a discrete-time, linear, shift-invariant system. In estimating the unit-sample response and frequency response of the discrete-time system, it was necessary to use digital filtering to remove low-amplitude noise, which interfered with deconvolution calculations. A digital bandpass filter constructed with the assistance of a Blackman window and a rectangular time window were used. Approximations of the impulse response and the frequency response of the continuous-time test system were obtained by linearly interpolating the defining points of the unit-sample response and the frequency response of the discrete-time system. The test system behaved as a linear-phase bandpass filter in the frequency range 0.6 to 2.3 MHz. These frequencies were selected in accordance with the criterion that they were 6 dB below the maximum peak of the amplitude of the frequency response. The output of the system to various inputs was predicted and the results were compared with the corresponding measurements on the system.

Controlling the Shannon Entropy of Quantum Systems

PubMed Central

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the shannon entropy of quantum systems.

PubMed

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Specific Instructions Are Important for Continuous Bimanual Drumming in Adults with Down Syndrome

ERIC Educational Resources Information Center

Ringenbach, Shannon D.; Allen, Heather; Chung, Susan; Jung, Michelle L.

2006-01-01

The present study examined continuous and discrete bimanual drumming in response to different instructions in 10 adults with Down syndrome, 10 mental age-matched and 10 chronological age-matched groups. For continuous drumming, participants hit two drums with both hands at the same time following verbal (e.g., "up" and "down"), visual (e.g., video…

Time dependence of breakdown in a global fiber-bundle model with continuous damage.

PubMed

Moral, L; Moreno, Y; Gómez, J B; Pacheco, A F

2001-06-01

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.

On the relationship of steady states of continuous and discrete models arising from biology.

PubMed

Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka

2012-12-01

For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.

Model documentation for relations between continuous real-time and discrete water-quality constituents in Cheney Reservoir near Cheney, Kansas, 2001--2009

USGS Publications Warehouse

Stone, Mandy L.; Graham, Jennifer L.; Gatotho, Jackline W.

2013-01-01

Cheney Reservoir, located in south-central Kansas, is one of the primary water supplies for the city of Wichita, Kansas. The U.S. Geological Survey has operated a continuous real-time water-quality monitoring station in Cheney Reservoir since 2001; continuously measured physicochemical properties include specific conductance, pH, water temperature, dissolved oxygen, turbidity, fluorescence (wavelength range 650 to 700 nanometers; estimate of total chlorophyll), and reservoir elevation. Discrete water-quality samples were collected during 2001 through 2009 and analyzed for sediment, nutrients, taste-and-odor compounds, cyanotoxins, phytoplankton community composition, actinomycetes bacteria, and other water-quality measures. Regression models were developed to establish relations between discretely sampled constituent concentrations and continuously measured physicochemical properties to compute concentrations of constituents that are not easily measured in real time. The water-quality information in this report is important to the city of Wichita because it allows quantification and characterization of potential constituents of concern in Cheney Reservoir. This report updates linear regression models published in 2006 that were based on data collected during 2001 through 2003. The update uses discrete and continuous data collected during May 2001 through December 2009. Updated models to compute dissolved solids, sodium, chloride, and suspended solids were similar to previously published models. However, several other updated models changed substantially from previously published models. In addition to updating relations that were previously developed, models also were developed for four new constituents, including magnesium, dissolved phosphorus, actinomycetes bacteria, and the cyanotoxin microcystin. In addition, a conversion factor of 0.74 was established to convert the Yellow Springs Instruments (YSI) model 6026 turbidity sensor measurements to the newer YSI model 6136 sensor at the Cheney Reservoir site. Because a high percentage of geosmin and microcystin data were below analytical detection thresholds (censored data), multiple logistic regression was used to develop models that best explained the probability of geosmin and microcystin concentrations exceeding relevant thresholds. The geosmin and microcystin models are particularly important because geosmin is a taste-and-odor compound and microcystin is a cyanotoxin.

Timing Processes Are Correlated when Tasks Share a Salient Event

ERIC Educational Resources Information Center

Zelaznik, Howard N.; Rosenbaum, David A.

2010-01-01

Event timing is manifested when participants make discrete movements such as repeatedly tapping a key. Emergent timing is manifested when participants make continuous movements such as repeatedly drawing a circle. Here we pursued the possibility that providing salient perceptual events to mark the completion of time intervals could allow circle…

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

An alternative to traditional goodness-of-fit tests for discretely measured continuous data

Treesearch

KaDonna C. Randolph; Bill Seaver

2007-01-01

Traditional goodness-of-fit tests such as the Kolmogorov-Smirnov and x2 tests are easily applied to data of the continuous or discrete type, respectively. Occasionally, however, the case arises when continuous data are recorded into discrete categories due to an imprecise measurement system. In this instance, the traditional goodness-of-fit...

Flow Control and Routing in an Integrated Voice and Data Communication Network

DTIC Science & Technology

1981-08-01

require continuous and almost real - time delivery; they are very sensitive to delay. Data conversations, on the other hand, are generally intolerant of...packets arrive in time to be delivered to the sink. However, this is not the solution we seek. We have noted that voice conversations require almost real ...by long messages that require continuous real - time delivery; e.g. voice facsimile, video. Class II: characterized by short discrete messages that

Discrete Deterministic and Stochastic Petri Nets

NASA Technical Reports Server (NTRS)

Zijal, Robert; Ciardo, Gianfranco

1996-01-01

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

Hybrid stochastic simplifications for multiscale gene networks.

PubMed

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-09-07

Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

Groundwater-level data from an earthen dam site in southern Westchester County, New York

USGS Publications Warehouse

Noll, Michael L.; Chu, Anthony

2018-05-01

In 2005, the U.S. Geological Survey began a cooperative study with New York City Department of Environmental Protection to characterize the local groundwater-flow system and identify potential sources of seeps on the southern embankment of the Hillview Reservoir in Westchester County, New York. Groundwater levels were collected at 49 wells at Hillview Reservoir, and 1 well in northern Bronx County, from April 2005 through November 2016. Groundwater levels were measured discretely with a chalked steel or electric tape, or continuously with a digital pressure transducer, or both, in accordance with U.S. Geological Survey groundwatermeasurement standards. These groundwater-level data were plotted as time series and are presented in this report as hydrographs. Twenty-eight of the 50 hydrographs have continuous record and discrete field groundwater-level measurements, 22 of the hydrographs contain only discrete measurements.

Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong

2016-06-01

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.

The partition function of the Bures ensemble as the τ-function of BKP and DKP hierarchies: continuous and discrete

NASA Astrophysics Data System (ADS)

Hu, Xing-Biao; Li, Shi-Hao

2017-07-01

The relationship between matrix integrals and integrable systems was revealed more than 20 years ago. As is known, matrix integrals over a Gaussian ensemble used in random matrix theory could act as the τ-function of several hierarchies of integrable systems. In this article, we will show that the time-dependent partition function of the Bures ensemble, whose measure has many interesting geometric properties, could act as the τ-function of BKP and DKP hierarchies. In addition, if discrete time variables are introduced, then this partition function could act as the τ-function of discrete BKP and DKP hierarchies. In particular, there are some links between the partition function of the Bures ensemble and Toda-type equations.

Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sudip; Swamy, Aravind Krishna; Daniel, Jo S.

2012-08-01

This paper presents a simple and practical approach to obtain the continuous relaxation and retardation spectra of asphalt concrete directly from the complex (dynamic) modulus test data. The spectra thus obtained are continuous functions of relaxation and retardation time. The major advantage of this method is that the continuous form is directly obtained from the master curves which are readily available from the standard characterization tests of linearly viscoelastic behavior of asphalt concrete. The continuous spectrum method offers efficient alternative to the numerical computation of discrete spectra and can be easily used for modeling viscoelastic behavior. In this research, asphalt concrete specimens have been tested for linearly viscoelastic characterization. The linearly viscoelastic test data have been used to develop storage modulus and storage compliance master curves. The continuous spectra are obtained from the fitted sigmoid function of the master curves via the inverse integral transform. The continuous spectra are shown to be the limiting case of the discrete distributions. The continuous spectra and the time-domain viscoelastic functions (relaxation modulus and creep compliance) computed from the spectra matched very well with the approximate solutions. It is observed that the shape of the spectra is dependent on the master curve parameters. The continuous spectra thus obtained can easily be implemented in material mix design process. Prony-series coefficients can be easily obtained from the continuous spectra and used in numerical analysis such as finite element analysis.

Metastability of Reversible Random Walks in Potential Fields

NASA Astrophysics Data System (ADS)

Landim, C.; Misturini, R.; Tsunoda, K.

2015-09-01

Let be an open and bounded subset of , and let be a twice continuously differentiable function. Denote by the discretization of , , and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.

Utilization of Historic Information in an Optimisation Task

NASA Technical Reports Server (NTRS)

Boesser, T.

1984-01-01

One of the basic components of a discrete model of motor behavior and decision making, which describes tracking and supervisory control in unitary terms, is assumed to be a filtering mechanism which is tied to the representational principles of human memory for time-series information. In a series of experiments subjects used the time-series information with certain significant limitations: there is a range-effect; asymmetric distributions seem to be recognized, but it does not seem to be possible to optimize performance based on skewed distributions. Thus there is a transformation of the displayed data between the perceptual system and representation in memory involving a loss of information. This rules out a number of representational principles for time-series information in memory and fits very well into the framework of a comprehensive discrete model for control of complex systems, modelling continuous control (tracking), discrete responses, supervisory behavior and learning.

Models for discrete-time self-similar vector processes with application to network traffic

NASA Astrophysics Data System (ADS)

Lee, Seungsin; Rao, Raghuveer M.; Narasimha, Rajesh

2003-07-01

The paper defines self-similarity for vector processes by employing the discrete-time continuous-dilation operation which has successfully been used previously by the authors to define 1-D discrete-time stochastic self-similar processes. To define self-similarity of vector processes, it is required to consider the cross-correlation functions between different 1-D processes as well as the autocorrelation function of each constituent 1-D process in it. System models to synthesize self-similar vector processes are constructed based on the definition. With these systems, it is possible to generate self-similar vector processes from white noise inputs. An important aspect of the proposed models is that they can be used to synthesize various types of self-similar vector processes by choosing proper parameters. Additionally, the paper presents evidence of vector self-similarity in two-channel wireless LAN data and applies the aforementioned systems to simulate the corresponding network traffic traces.

Hydra effects in discrete-time models of stable communities.

PubMed

Cortez, Michael H

2016-12-21

A species exhibits a hydra effect when, counter-intuitively, increased mortality of the species causes an increase in its abundance. Hydra effects have been studied in many continuous time (differential equation) multispecies models, but only rarely have hydra effects been observed in or studied with discrete time (difference equation) multispecies models. In addition most discrete time theory focuses on single-species models. Thus, it is unclear what unifying characteristics determine when hydra effects arise in discrete time models. Here, using discrete time multispecies models (where total abundance is the single variable describing each population), I show that a species exhibits a hydra effect in a stable system only when fixing that species' density at its equilibrium density destabilizes the system. This general characteristic is referred to as subsystem instability. I apply this result to two-species models and identify specific mechanisms that cause hydra effects in stable communities, e.g., in host--parasitoid models, host Allee effects and saturating parasitoid functional responses can cause parasitoid hydra effects. I discuss how the general characteristic can be used to identify mechanisms causing hydra effects in communities with three or more species. I also show that the condition for hydra effects at stable equilibria implies the system is reactive (i.e., density perturbations can grow before ultimately declining). This study extends previous work on conditions for hydra effects in single-species models by identifying necessary conditions for stable systems and sufficient conditions for cyclic systems. In total, these results show that hydra effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models. Copyright © 2016 Elsevier Ltd. All rights reserved.

Logistic and linear regression model documentation for statistical relations between continuous real-time and discrete water-quality constituents in the Kansas River, Kansas, July 2012 through June 2015

USGS Publications Warehouse

Foster, Guy M.; Graham, Jennifer L.

2016-04-06

The Kansas River is a primary source of drinking water for about 800,000 people in northeastern Kansas. Source-water supplies are treated by a combination of chemical and physical processes to remove contaminants before distribution. Advanced notification of changing water-quality conditions and cyanobacteria and associated toxin and taste-and-odor compounds provides drinking-water treatment facilities time to develop and implement adequate treatment strategies. The U.S. Geological Survey (USGS), in cooperation with the Kansas Water Office (funded in part through the Kansas State Water Plan Fund), and the City of Lawrence, the City of Topeka, the City of Olathe, and Johnson County Water One, began a study in July 2012 to develop statistical models at two Kansas River sites located upstream from drinking-water intakes. Continuous water-quality monitors have been operated and discrete-water quality samples have been collected on the Kansas River at Wamego (USGS site number 06887500) and De Soto (USGS site number 06892350) since July 2012. Continuous and discrete water-quality data collected during July 2012 through June 2015 were used to develop statistical models for constituents of interest at the Wamego and De Soto sites. Logistic models to continuously estimate the probability of occurrence above selected thresholds were developed for cyanobacteria, microcystin, and geosmin. Linear regression models to continuously estimate constituent concentrations were developed for major ions, dissolved solids, alkalinity, nutrients (nitrogen and phosphorus species), suspended sediment, indicator bacteria (Escherichia coli, fecal coliform, and enterococci), and actinomycetes bacteria. These models will be used to provide real-time estimates of the probability that cyanobacteria and associated compounds exceed thresholds and of the concentrations of other water-quality constituents in the Kansas River. The models documented in this report are useful for characterizing changes in water-quality conditions through time, characterizing potentially harmful cyanobacterial events, and indicating changes in water-quality conditions that may affect drinking-water treatment processes.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Discrete-continuous variable structural synthesis using dual methods

NASA Technical Reports Server (NTRS)

Schmit, L. A.; Fleury, C.

1980-01-01

Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.

A Multiple Items EPQ/EOQ Model for a Vendor and Multiple Buyers System with Considering Continuous and Discrete Demand Simultaneously

NASA Astrophysics Data System (ADS)

Jonrinaldi; Rahman, T.; Henmaidi; Wirdianto, E.; Zhang, D. Z.

2018-03-01

This paper proposed a mathematical model for multiple items Economic Production and Order Quantity (EPQ/EOQ) with considering continuous and discrete demand simultaneously in a system consisting of a vendor and multiple buyers. This model is used to investigate the optimal production lot size of the vendor and the number of shipments policy of orders to multiple buyers. The model considers the multiple buyers’ holding cost as well as transportation cost, which minimize the total production and inventory costs of the system. The continuous demand from any other customers can be fulfilled anytime by the vendor while the discrete demand from multiple buyers can be fulfilled by the vendor using the multiple delivery policy with a number of shipments of items in the production cycle time. A mathematical model is developed to illustrate the system based on EPQ and EOQ model. Solution procedures are proposed to solve the model using a Mixed Integer Non Linear Programming (MINLP) and algorithm methods. Then, the numerical example is provided to illustrate the system and results are discussed.

Discrete Li-occupation versus pseudo-continuous Na-occupation and their relationship with structural change behaviors in Fe₂(MoO₄)₃

DOE PAGES

Yue, Ji-Li; Zhou, Yong-Ning; Shi, Si-Qi; ...

2015-03-06

The key factors governing the single-phase or multi-phase structural change behaviors during the intercalation/deintercalation of guest ions have not been well studied and understood yet. Through systematic studies of orthorhombic Fe₂(MoO₄)₃ electrode, two distinct guest ion occupation paths, namely discrete one for Li and pseudo-continuous one for Na, as well as their relationship with single-phase and two-phase modes for Na⁺ and Li⁺, respectively during the intercalation/deintercalation process have been demonstrated. For the first time, the direct atomic-scale observation of biphasic domains (discrete occupation) in partially lithiated Fe₂(MoO₄)₃ and the one by one Na occupation (pseudo-continuous occupation) at 8d sites inmore » partially sodiated Fe₂(MoO₄)₃ are obtained during the discharge processes of Li/Fe₂(MoO₄)₃ and Na/Fe₂(MoO₄)₃ cells respectively. Our combined experimental and theoretical studies bring the new insights for the research and development of intercalation compounds as electrode materials for secondary batteries.« less

A study of MRI gradient echo signals from discrete magnetic particles with considerations of several parameters in simulations.

PubMed

Kokeny, Paul; Cheng, Yu-Chung N; Xie, He

2018-05-01

Modeling MRI signal behaviors in the presence of discrete magnetic particles is important, as magnetic particles appear in nanoparticle labeled cells, contrast agents, and other biological forms of iron. Currently, many models that take into account the discrete particle nature in a system have been used to predict magnitude signal decays in the form of R2* or R2' from one single voxel. Little work has been done for predicting phase signals. In addition, most calculations of phase signals rely on the assumption that a system containing discrete particles behaves as a continuous medium. In this work, numerical simulations are used to investigate MRI magnitude and phase signals from discrete particles, without diffusion effects. Factors such as particle size, number density, susceptibility, volume fraction, particle arrangements for their randomness, and field of view have been considered in simulations. The results are compared to either a ground truth model, theoretical work based on continuous mediums, or previous literature. Suitable parameters used to model particles in several voxels that lead to acceptable magnetic field distributions around particle surfaces and accurate MR signals are identified. The phase values as a function of echo time from a central voxel filled by particles can be significantly different from those of a continuous cubic medium. However, a completely random distribution of particles can lead to an R2' value which agrees with the prediction from the static dephasing theory. A sphere with a radius of at least 4 grid points used in simulations is found to be acceptable to generate MR signals equivalent from a larger sphere. Increasing number of particles with a fixed volume fraction in simulations reduces the resulting variance in the phase behavior, and converges to almost the same phase value for different particle numbers at each echo time. The variance of phase values is also reduced when increasing the number of particles in a fixed voxel. These results indicate that MRI signals from voxels containing discrete particles, even with a sufficient number of particles per voxel, cannot be properly modeled by a continuous medium with an equivalent susceptibility value in the voxel. Copyright © 2017 Elsevier Inc. All rights reserved.

Dynamic modeling and parameter estimation of a radial and loop type distribution system network

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

Jun Qui; Heng Chen; Girgis, A.A.

1993-05-01

This paper presents a new identification approach to three-phase power system modeling and model reduction taking power system network as multi-input, multi-output (MIMO) processes. The model estimate can be obtained in discrete-time input-output form, discrete- or continuous-time state-space variable form, or frequency-domain impedance transfer function matrix form. An algorithm for determining the model structure of this MIMO process is described. The effect of measurement noise on the approach is also discussed. This approach has been applied on a sample system and simulation results are also presented in this paper.

The exact fundamental solution for the Benes tracking problem

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2009-05-01

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

7 CFR 279.6 - Legal advice and extensions of time.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 4 2010-01-01 2010-01-01 false Legal advice and extensions of time. 279.6 Section 279.6 Agriculture Regulations of the Department of Agriculture (Continued) FOOD AND NUTRITION SERVICE... discretion, additional time is required for the firm to fully present information in support of its position...

Eigenvalue sensitivity of sampled time systems operating in closed loop

NASA Astrophysics Data System (ADS)

Bernal, Dionisio

2018-05-01

The use of feedback to create closed-loop eigenstructures with high sensitivity has received some attention in the Structural Health Monitoring field. Although practical implementation is necessarily digital, and thus in sampled time, work thus far has center on the continuous time framework, both in design and in checking performance. It is shown in this paper that the performance in discrete time, at typical sampling rates, can differ notably from that anticipated in the continuous time formulation and that discrepancies can be particularly large on the real part of the eigenvalue sensitivities; a consequence being important error on the (linear estimate) of the level of damage at which closed-loop stability is lost. As one anticipates, explicit consideration of the sampling rate poses no special difficulties in the closed-loop eigenstructure design and the relevant expressions are developed in the paper, including a formula for the efficient evaluation of the derivative of the matrix exponential based on the theory of complex perturbations. The paper presents an easily reproduced numerical example showing the level of error that can result when the discrete time implementation of the controller is not considered.

Search Parameter Optimization for Discrete, Bayesian, and Continuous Search Algorithms

DTIC Science & Technology

2017-09-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CONTINUOUS SEARCH ALGORITHMS by...to 09-22-2017 4. TITLE AND SUBTITLE SEARCH PARAMETER OPTIMIZATION FOR DISCRETE , BAYESIAN, AND CON- TINUOUS SEARCH ALGORITHMS 5. FUNDING NUMBERS 6...simple search and rescue acts to prosecuting aerial/surface/submersible targets on mission. This research looks at varying the known discrete and

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.

An empirically derived figure of merit for the quality of overall task performance

NASA Technical Reports Server (NTRS)

Lemay, Moira

1989-01-01

The need to develop an operationally relevant figure of merit for the quality of performance of a complex system such as an aircraft cockpit stems from a hypothesized dissociation between measures of performance and those of workload. Performance can be measured in terms of time, errors, or a combination of these. In most tasks performed by expert operators, errors are relatively rare and often corrected in time to avoid consequences. Moreover, perfect performance is seldom necessary to accomplish a particular task. Moreover, how well an expert performs a complex task consisting of a series of discrete cognitive tasks superimposed on a continuous task, such as flying an aircraft, does not depend on how well each discrete task is performed, but on their smooth sequencing. This makes the amount of time spent on each subtask of paramount importance in measuring overall performance, since smooth sequencing requires a minimum amount of time spent on each task. Quality consists in getting tasks done within a crucial time interval while maintaining acceptable continuous task performance. Thus, a figure of merit for overall quality of performance should be primarily a measure of time to perform discrete subtasks combined with a measure of basic vehicle control. Thus, the proposed figure of merit requires doing a task analysis on a series of performance, or runs, of a particular task, listing each discrete task and its associated time, and calculating the mean and standard deviation of these times, along with the mean and standard deviation of tracking error for the whole task. A set of simulator data on 30 runs of a landing task was obtained and a figure of merit will be calculated for each run. The figure of merit will be compared for voice and data link, so that the impact of this technology on total crew performance (not just communication performance) can be assessed. The effect of data link communication on other cockpit tasks will also be considered.

Stability analysis of the Euler discretization for SIR epidemic model

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

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

Automatic Methods and Tools for the Verification of Real Time Systems

DTIC Science & Technology

1997-11-30

We developed formal methods and tools for the verification of real - time systems . This was accomplished by extending techniques, based on automata...embedded real - time systems , we introduced hybrid automata, which equip traditional discrete automata with real-numbered clock variables and continuous... real - time systems , and we identified the exact boundary between decidability and undecidability of real-time reasoning.

Discrete photon statistics from continuous microwave measurements

NASA Astrophysics Data System (ADS)

Virally, Stéphane; Simoneau, Jean Olivier; Lupien, Christian; Reulet, Bertrand

2016-04-01

Photocount statistics are an important tool for the characterization of electromagnetic fields, especially for fields with an irrelevant phase. In the microwave domain, continuous rather than discrete measurements are the norm. Using a different approach, we recover discrete photon statistics from the cumulants of a continuous distribution of field quadrature measurements. The use of cumulants allows the separation between the signal of interest and experimental noise. Using a parametric amplifier as the first stage of the amplification chain, we extract useful data from up to the sixth cumulant of the continuous distribution of a coherent field, hence recovering up to the third moment of the discrete statistics associated with a signal with much less than one average photon.

Can spatial patterns along climatic gradients predict ecosystem responses to climate change? Experimenting with reaction-diffusion simulations.

PubMed

Roitberg, Elena; Shoshany, Maxim

2017-01-01

Following a predicted decline in water resources in the Mediterranean Basin, we used reaction-diffusion equations to gain a better understanding of expected changes in properties of vegetation patterns that evolve along the rainfall transition between semi-arid and arid rainfall regions. Two types of scenarios were investigated: the first, a discrete scenario, where the potential consequences of climate change are represented by patterns evolving at discrete rainfall levels along a rainfall gradient. This scenario concerns space-for-time substitutions characteristic of the rainfall gradient hypothesis. The second, a continuous scenario, represents explicitly the effect of rainfall decline on patterns which evolved at different rainfall levels along the rainfall gradient prior to the climate change. The eccentricity of patterns that emerge through these two scenarios was found to decrease with decreasing rainfall, while their solidity increased. Due to their inverse modes of change, their ratio was found to be a highly sensitive indicator for pattern response to rainfall decline. An eccentricity ratio versus rainfall (ER:R) line was generalized from the results of the discrete experiment, where ERs above this line represent developed (recovered) patterns and ERs below this line represent degraded patterns. For the rainfall range of 1.2 to 0.8 mm/day, the continuous rainfall decline experiment with ERs that lie above the ER:R line, yielded patterns less affected by rainfall decline than would be expected according to the discrete representation of ecosystems' response. Thus, for this range, space-for-time substitution represents an overestimation of the consequences of the expected rainfall decline. For rainfall levels below 0.8 mm/day, eccentricity ratios from the discrete and continuous experiments practically converge to the same trend of pattern change along the ER:R line. Thus, the rainfall gradient hypothesis may be valid for regions characterized by this important rainfall range, which typically include desert fringe ecosystems.

Fast and Accurate Learning When Making Discrete Numerical Estimates.

PubMed

Sanborn, Adam N; Beierholm, Ulrik R

2016-04-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.

Fast and Accurate Learning When Making Discrete Numerical Estimates

PubMed Central

Sanborn, Adam N.; Beierholm, Ulrik R.

2016-01-01

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155

Water quality monitoring and data collection in the Mississippi sound

USGS Publications Warehouse

Runner, Michael S.; Creswell, R.

2002-01-01

The United States Geological Survey and the Mississippi Department of Marine Resources are collecting data on the quality of the water in the Mississippi Sound of the Gulf of Mexico, and streamflow data for its tributaries. The U.S. Geological Survey is collecting continuous water-level data, continuous and discrete water-temperature data, continuous and discrete specific-conductance data, as well as chloride and salinity samples at two locations in the Mississippi Sound and three Corps of Engineers tidal gages. Continuous-discharge data are also being collected at two additional stations on tributaries. The Mississippi Department of Marine Resources collects water samples at 169 locations in the Gulf of Mexico. Between 1800 and 2000 samples are collected annually which are analyzed for turbidity and fecal coliform bacteria. The continuous data are made available real-time through the internet and are being used in conjunction with streamflow data, weather data, and sampling data for the monitoring and management of the oyster reefs, the shrimp fishery and other marine species and their habitats.

Principles of Discrete Time Mechanics

NASA Astrophysics Data System (ADS)

Jaroszkiewicz, George

2014-04-01

1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

PubMed Central

Kion-Crosby, Willow; Morozov, Alexandre V.

2015-01-01

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs. PMID:26646868

Loop transfer recovery for general nonminimum phase discrete time systems. I - Analysis

NASA Technical Reports Server (NTRS)

Chen, Ben M.; Saberi, Ali; Sannuti, Peddapullaiah; Shamash, Yacov

1992-01-01

A complete analysis of loop transfer recovery (LTR) for general nonstrictly proper, not necessarily minimum phase discrete time systems is presented. Three different observer-based controllers, namely, `prediction estimator' and full or reduced-order type `current estimator' based controllers, are used. The analysis corresponding to all these three controllers is unified into a single mathematical framework. The LTR analysis given here focuses on three fundamental issues: (1) the recoverability of a target loop when it is arbitrarily given, (2) the recoverability of a target loop while taking into account its specific characteristics, and (3) the establishment of necessary and sufficient conditions on the given system so that it has at least one recoverable target loop transfer function or sensitivity function. Various differences that arise in LTR analysis of continuous and discrete systems are pointed out.

Predicting Flood in Perlis Using Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Nadia Sabri, Syaidatul; Saian, Rizauddin

2017-06-01

Flood forecasting is widely being studied in order to reduce the effect of flood such as loss of property, loss of life and contamination of water supply. Usually flood occurs due to continuous heavy rainfall. This study used a variant of Ant Colony Optimization (ACO) algorithm named the Ant-Miner to develop the classification prediction model to predict flood. However, since Ant-Miner only accept discrete data, while rainfall data is a time series data, a pre-processing steps is needed to discretize the rainfall data initially. This study used a technique called the Symbolic Aggregate Approximation (SAX) to convert the rainfall time series data into discrete data. As an addition, Simple K-Means algorithm was used to cluster the data produced by SAX. The findings show that the predictive accuracy of the classification prediction model is more than 80%.

Robustness properties of discrete time regulators, LOG regulators and hybrid systems

NASA Technical Reports Server (NTRS)

Stein, G.; Athans, M.

1979-01-01

Robustness properites of sample-data LQ regulators are derived which show that these regulators have fundamentally inferior uncertainty tolerances when compared to their continuous-time counterparts. Results are also presented in stability theory, multivariable frequency domain analysis, LQG robustness, and mathematical representations of hybrid systems.

47 CFR 15.214 - Cordless telephones.

Code of Federal Regulations, 2010 CFR

2010-10-01

... discrete digital codes. Factory-set codes must be continuously varied over at least 256 possible codes as... readily select from among at least 256 possible discrete digital codes. The cordless telephone shall be... fixed code that is continuously varied among at least 256 discrete digital codes as each telephone is...

Boundaries, kinetic properties, and final domain structure of plane discrete uniform Poisson-Voronoi tessellations with von Neumann neighborhoods.

PubMed

Korobov, A

2009-03-01

Discrete random tessellations appear not infrequently in describing nucleation and growth transformations. Generally, several non-Euclidean metrics are possible in this case. Previously [A. Korobov, Phys. Rev. B 76, 085430 (2007)] continual analogs of such tessellations have been studied. Here one of the simplest discrete varieties of the Kolmogorov-Johnson-Mehl-Avrami model, namely, the model with von Neumann neighborhoods, has been examined per se, i.e., without continualization. The tessellation is uniform in the sense that domain boundaries consist of tiles. Similarities and distinctions between discrete and continual models are discussed.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

PubMed Central

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-01-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID:24829517

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

PubMed

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Hybrid stochastic simplifications for multiscale gene networks

PubMed Central

Crudu, Alina; Debussche, Arnaud; Radulescu, Ovidiu

2009-01-01

Background Stochastic simulation of gene networks by Markov processes has important applications in molecular biology. The complexity of exact simulation algorithms scales with the number of discrete jumps to be performed. Approximate schemes reduce the computational time by reducing the number of simulated discrete events. Also, answering important questions about the relation between network topology and intrinsic noise generation and propagation should be based on general mathematical results. These general results are difficult to obtain for exact models. Results We propose a unified framework for hybrid simplifications of Markov models of multiscale stochastic gene networks dynamics. We discuss several possible hybrid simplifications, and provide algorithms to obtain them from pure jump processes. In hybrid simplifications, some components are discrete and evolve by jumps, while other components are continuous. Hybrid simplifications are obtained by partial Kramers-Moyal expansion [1-3] which is equivalent to the application of the central limit theorem to a sub-model. By averaging and variable aggregation we drastically reduce simulation time and eliminate non-critical reactions. Hybrid and averaged simplifications can be used for more effective simulation algorithms and for obtaining general design principles relating noise to topology and time scales. The simplified models reproduce with good accuracy the stochastic properties of the gene networks, including waiting times in intermittence phenomena, fluctuation amplitudes and stationary distributions. The methods are illustrated on several gene network examples. Conclusion Hybrid simplifications can be used for onion-like (multi-layered) approaches to multi-scale biochemical systems, in which various descriptions are used at various scales. Sets of discrete and continuous variables are treated with different methods and are coupled together in a physically justified approach. PMID:19735554

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

NASA Astrophysics Data System (ADS)

Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.

2001-12-01

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.

The stochastic system approach for estimating dynamic treatments effect.

PubMed

Commenges, Daniel; Gégout-Petit, Anne

2015-10-01

The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.

Varieties of quantity estimation in children.

PubMed

Sella, Francesco; Berteletti, Ilaria; Lucangeli, Daniela; Zorzi, Marco

2015-06-01

In the number-to-position task, with increasing age and numerical expertise, children's pattern of estimates shifts from a biased (nonlinear) to a formal (linear) mapping. This widely replicated finding concerns symbolic numbers, whereas less is known about other types of quantity estimation. In Experiment 1, Preschool, Grade 1, and Grade 3 children were asked to map continuous quantities, discrete nonsymbolic quantities (numerosities), and symbolic (Arabic) numbers onto a visual line. Numerical quantity was matched for the symbolic and discrete nonsymbolic conditions, whereas cumulative surface area was matched for the continuous and discrete quantity conditions. Crucially, in the discrete condition children's estimation could rely either on the cumulative area or numerosity. All children showed a linear mapping for continuous quantities, whereas a developmental shift from a logarithmic to a linear mapping was observed for both nonsymbolic and symbolic numerical quantities. Analyses on individual estimates suggested the presence of two distinct strategies in estimating discrete nonsymbolic quantities: one based on numerosity and the other based on spatial extent. In Experiment 2, a non-spatial continuous quantity (shades of gray) and new discrete nonsymbolic conditions were added to the set used in Experiment 1. Results confirmed the linear patterns for the continuous tasks, as well as the presence of a subset of children relying on numerosity for the discrete nonsymbolic numerosity conditions despite the availability of continuous visual cues. Overall, our findings demonstrate that estimation of numerical and non-numerical quantities is based on different processing strategies and follow different developmental trajectories. (c) 2015 APA, all rights reserved).

A Method for Continuous (239)Pu Determinations in Arctic and Antarctic Ice Cores.

PubMed

Arienzo, M M; McConnell, J R; Chellman, N; Criscitiello, A S; Curran, M; Fritzsche, D; Kipfstuhl, S; Mulvaney, R; Nolan, M; Opel, T; Sigl, M; Steffensen, J P

2016-07-05

Atmospheric nuclear weapons testing (NWT) resulted in the injection of plutonium (Pu) into the atmosphere and subsequent global deposition. We present a new method for continuous semiquantitative measurement of (239)Pu in ice cores, which was used to develop annual records of fallout from NWT in ten ice cores from Greenland and Antarctica. The (239)Pu was measured directly using an inductively coupled plasma-sector field mass spectrometer, thereby reducing analysis time and increasing depth-resolution with respect to previous methods. To validate this method, we compared our one year averaged results to published (239)Pu records and other records of NWT. The (239)Pu profiles from the Arctic ice cores reflected global trends in NWT and were in agreement with discrete Pu profiles from lower latitude ice cores. The (239)Pu measurements in the Antarctic ice cores tracked low latitude NWT, consistent with previously published discrete records from Antarctica. Advantages of the continuous (239)Pu measurement method are (1) reduced sample preparation and analysis time; (2) no requirement for additional ice samples for NWT fallout determinations; (3) measurements are exactly coregistered with all other chemical, elemental, isotopic, and gas measurements from the continuous analytical system; and (4) the long half-life means the (239)Pu record is stable through time.

Quasi- and pseudo-maximum likelihood estimators for discretely observed continuous-time Markov branching processes

PubMed Central

Chen, Rui; Hyrien, Ollivier

2011-01-01

This article deals with quasi- and pseudo-likelihood estimation in a class of continuous-time multi-type Markov branching processes observed at discrete points in time. “Conventional” and conditional estimation are discussed for both approaches. We compare their properties and identify situations where they lead to asymptotically equivalent estimators. Both approaches possess robustness properties, and coincide with maximum likelihood estimation in some cases. Quasi-likelihood functions involving only linear combinations of the data may be unable to estimate all model parameters. Remedial measures exist, including the resort either to non-linear functions of the data or to conditioning the moments on appropriate sigma-algebras. The method of pseudo-likelihood may also resolve this issue. We investigate the properties of these approaches in three examples: the pure birth process, the linear birth-and-death process, and a two-type process that generalizes the previous two examples. Simulations studies are conducted to evaluate performance in finite samples. PMID:21552356

Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.

PubMed

Wang, Dongshu; Huang, Lihong

2014-03-01

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results. Copyright © 2013 Elsevier Ltd. All rights reserved.

Nonperturbative Treatment of non-Markovian Dynamics of Open Quantum Systems

NASA Astrophysics Data System (ADS)

Tamascelli, D.; Smirne, A.; Huelga, S. F.; Plenio, M. B.

2018-01-01

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments—one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (nonunitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, nonperturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open-system dynamics.

Robust model predictive control for constrained continuous-time nonlinear systems

NASA Astrophysics Data System (ADS)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

Evaluating sample allocation and effort in detecting population differentiation for discrete and continuously distributed individuals

Treesearch

Erin L. Landguth; Michael K. Schwartz

2014-01-01

One of the most pressing issues in spatial genetics concerns sampling. Traditionally, substructure and gene flow are estimated for individuals sampled within discrete populations. Because many species may be continuously distributed across a landscape without discrete boundaries, understanding sampling issues becomes paramount. Given large-scale, geographically broad...

Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes

NASA Astrophysics Data System (ADS)

Elliott, Thomas J.; Gu, Mile

2018-03-01

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine.

Continuous and discrete water-quality data collected at five sites on Lake Houston near Houston, Texas, 2006-08

USGS Publications Warehouse

Beussink, Amy M.; Burnich, Michael R.

2009-01-01

Lake Houston, a reservoir impounded in 1954 by the City of Houston, Texas, is a primary source of drinking water for Houston and surrounding areas. The U.S. Geological Survey, in cooperation with the City of Houston, developed a continuous water-quality monitoring network to track daily changes in water quality in the southwestern quadrant of Lake Houston beginning in 2006. Continuous water-quality data (the physiochemical properties water temperature, specific conductance, pH, dissolved oxygen concentration, and turbidity) were collected from Lake Houston to characterize the in-lake processes that affect water quality. Continuous data were collected hourly from mobile, multi-depth monitoring stations developed and constructed by the U.S. Geological Survey. Multi-depth monitoring stations were installed at five sites in three general locations in the southwestern quadrant of the lake. Discrete water-quality data (samples) were collected routinely (once or twice each month) at all sites to characterize the chemical and biological (phytoplankton and bacteria) response to changes in the continuous water-quality properties. Physiochemical properties (the five continuously monitored plus transparency) were measured in the field when samples were collected. In addition to the routine samples, discrete water-quality samples were collected synoptically (one or two times during the study period) at all sites to determine the presence and levels of selected constituents not analyzed in routine samples. Routine samples were measured or analyzed for acid neutralizing capacity; selected major ions and trace elements (calcium, silica, and manganese); nutrients (filtered and total ammonia nitrogen, filtered nitrate plus nitrite nitrogen, total nitrate nitrogen, filtered and total nitrite nitrogen, filtered and total orthophosphate phosphorus, total phosphorus, total nitrogen, total organic carbon); fecal indicator bacteria (total coliform and Escherichia coli); sediment (suspended-sediment concentration and loss-on-ignition); actinomycetes bacteria; taste-and-odor-causing compounds (2-methylisoborneol and geosmin); cyanobacterial toxins (total microcystins); and phytoplankton abundance, biovolume, and community composition (taxonomic identification to genus). Synoptic samples were analyzed for major ions, trace elements, wastewater indicators, pesticides, volatile organic compounds, and carbon. The analytical data are presented in tables by type (continuous, discrete routine, discrete synoptic) and listed by station number. Continuously monitored properties (except pH) also are displayed graphically.

A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2017-12-01

In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.

Stereo-hologram in discrete depth of field (Conference Presentation)

NASA Astrophysics Data System (ADS)

Lee, Kwanghoon; Park, Min-Chul

2017-05-01

In holographic space, continuous object space can be divided as several discrete spaces satisfied each of same depth of field (DoF). In the environment of wearable device using holography, specially, this concept can be applied to macroscopy filed in contrast of the field of microscopy. Since the former has not need to high depth resolution because perceiving power of eye in human visual system, it can distinguish clearly among the objects in depth space, has lower than optical power of microscopic field. Therefore continuous but discrete depth of field (DDoF) for whole object space can present the number of planes included sampled space considered its DoF. Each DoF plane has to consider the occlusion among the object's areas in its region to show the occluded phenomenon inducing by the visual axis around the eye field of view. It makes natural scene in recognition process even though the combined discontinuous DoF regions are altered to the continuous object space. Thus DDoF pull out the advantages such as saving consuming time of the calculation process making the hologram and the reconstruction. This approach deals mainly the properties of several factors required in stereo hologram HMD such as stereoscopic DoF according to the convergence, least number of DDoFs planes in normal visual circumstance (within to 10,000mm), the efficiency of saving time for taking whole holographic process under the our method compared to the existing. Consequently this approach would be applied directly to the stereo-hologram HMD field to embody a real-time holographic imaging.

Repelling, binding, and oscillating of two-particle discrete-time quantum walks

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

Wang, Qinghao; Li, Zhi-Jian, E-mail: zjli@sxu.edu.cn

In this paper, we investigate the effects of particle–particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle–particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.

Real-time frequency-to-time mapping based on spectrally-discrete chromatic dispersion.

PubMed

Dai, Yitang; Li, Jilong; Zhang, Ziping; Yin, Feifei; Li, Wangzhe; Xu, Kun

2017-07-10

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 10 4 -km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

Optimal Digital Controller Design for a Servo Motor Taking Account of Intersample Behavior

NASA Astrophysics Data System (ADS)

Akiyoshi, Tatsuro; Imai, Jun; Funabiki, Shigeyuki

A continuous-time plant with discretized continuous-time controller do not yield stability if the sampling rate is lower than some certain level. Thus far, high functioning electronic control has made use of high cost hardwares which are needed to implement discretized continuous-time controllers, while low cost hardwares generally do not have high enough sampling rate. This technical note presents results comparing performance indices with and without intersample behavior, and some answer to the question how a low specification device can control a plant effectively. We consider a machine simulating wafer handling robots at semiconductor factories, which is an electromechanical system driven by a direct drive motor. We illustrate controller design for the robot with and without intersample behavior, and simulations and experimental results by using these controllers. Taking intersample behavior into account proves to be effective to make control performance better and enables it to choose relatively long sampling period. By controller design via performance index with intersample behavior, we can cope with situation where short enough sampling period may not be employed, and freedom of controller design might be widened especially on choice of sampling period.

Implementation Strategies for Large-Scale Transport Simulations Using Time Domain Particle Tracking

NASA Astrophysics Data System (ADS)

Painter, S.; Cvetkovic, V.; Mancillas, J.; Selroos, J.

2008-12-01

Time domain particle tracking is an emerging alternative to the conventional random walk particle tracking algorithm. With time domain particle tracking, particles are moved from node to node on one-dimensional pathways defined by streamlines of the groundwater flow field or by discrete subsurface features. The time to complete each deterministic segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, a variety of kinetically controlled retention (sorption) processes, linear transformation, and temporal changes in groundwater velocities and sorption parameters. The simulation results in a set of arrival times at a monitoring location that can be post-processed with a kernel method to construct mass discharge (breakthrough) versus time. Implementation strategies differ for discrete flow (fractured media) systems and continuous porous media systems. The implementation strategy also depends on the scale at which hydraulic property heterogeneity is represented in the supporting flow model. For flow models that explicitly represent discrete features (e.g., discrete fracture networks), the sampling of residence times along segments is conceptually straightforward. For continuous porous media, such sampling needs to be related to the Lagrangian velocity field. Analytical or semi-analytical methods may be used to approximate the Lagrangian segment velocity distributions in aquifers with low-to-moderate variability, thereby capturing transport effects of subgrid velocity variability. If variability in hydraulic properties is large, however, Lagrangian velocity distributions are difficult to characterize and numerical simulations are required; in particular, numerical simulations are likely to be required for estimating the velocity integral scale as a basis for advective segment distributions. Aquifers with evolving heterogeneity scales present additional challenges. Large-scale simulations of radionuclide transport at two potential repository sites for high-level radioactive waste will be used to demonstrate the potential of the method. The simulations considered approximately 1000 source locations, multiple radionuclides with contrasting sorption properties, and abrupt changes in groundwater velocity associated with future glacial scenarios. Transport pathways linking the source locations to the accessible environment were extracted from discrete feature flow models that include detailed representations of the repository construction (tunnels, shafts, and emplacement boreholes) embedded in stochastically generated fracture networks. Acknowledgment The authors are grateful to SwRI Advisory Committee for Research, the Swedish Nuclear Fuel and Waste Management Company, and Posiva Oy for financial support.

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Continuous and difficult discrete cognitive tasks promote improved stability in older adults.

PubMed

Lajoie, Yves; Jehu, Deborah A; Richer, Natalie; Chan, Alan

2017-06-01

Directing attention away from postural control and onto a cognitive task affords the emergence of automatic control processes. Perhaps the continuous withdrawal of attention from the postural task facilitates an automatization of posture as opposed to only intermittent withdrawal; however this is unknown in the aging population. Twenty older adults (69.9±3.5years) stood with feet together on a force platform for 60s while performing randomly assigned discrete and continuous cognitive tasks. Participants were instructed to stand comfortably with their arms by their sides while verbally responding to the auditory stimuli as fast as possible during the discrete tasks, or mentally performing the continuous cognitive tasks. Participants also performed single-task standing. Results demonstrate significant reductions in sway amplitude and sway variability for the difficult discrete task as well as the continuous tasks relative to single-task standing. The continuous cognitive tasks also prompted greater frequency of sway in the anterior-posterior direction compared to single-standing and discrete tasks, and greater velocity in both directions compared to single-task standing, which could suggest ankle stiffening. No differences in the simple discrete condition were shown compared to single-task standing, perhaps due to the simplicity of the task. Therefore, we propose that the level of difficulty of the task, the specific neuropsychological process engaged during the cognitive task, and the type of task (discrete vs. continuous) influence postural control in older adults. Dual-tasking is a common activity of daily living; this work provides insight into the age-related changes in postural stability and attention demand. Copyright © 2017 Elsevier B.V. All rights reserved.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Modeling of wastewater treatment system of car parks from petroleum products

NASA Astrophysics Data System (ADS)

Savdur, S. N.; Stepanova, Yu V.; Kodolova, I. A.; Fesina, E. L.

2018-05-01

The paper discusses the technological complex of wastewater treatment of car parks from petroleum products. Based on the review of the main modeling methods of discrete-continuous chemical and engineering processes, it substantiates expediency of using the theory of Petri nets (PN) for modeling the process of wastewater treatment of car parks from petroleum products. It is proposed to use a modification of Petri nets which is focused on modeling and analysis of discrete-continuous chemical and engineering processes by prioritizing transitions, timing marks in positions and transitions. A model in the form of modified Petri nets (MPN) is designed. A software package to control the process for wastewater treatment is designed by means of SCADA TRACE MODE.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (CDC VERSION)

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1989. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

ORACLS- OPTIMAL REGULATOR ALGORITHMS FOR THE CONTROL OF LINEAR SYSTEMS (DEC VAX VERSION)

NASA Technical Reports Server (NTRS)

Frisch, H.

1994-01-01

This control theory design package, called Optimal Regulator Algorithms for the Control of Linear Systems (ORACLS), was developed to aid in the design of controllers and optimal filters for systems which can be modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, currently referred to as the Linear-Quadratic-Gaussian (LQG) problem, has become the most widely accepted method of determining optimal control policy. Within this theory, the infinite duration time-invariant problems, which lead to constant gain feedback control laws and constant Kalman-Bucy filter gains for reconstruction of the system state, exhibit high tractability and potential ease of implementation. A variety of new and efficient methods in the field of numerical linear algebra have been combined into the ORACLS program, which provides for the solution to time-invariant continuous or discrete LQG problems. The ORACLS package is particularly attractive to the control system designer because it provides a rigorous tool for dealing with multi-input and multi-output dynamic systems in both continuous and discrete form. The ORACLS programming system is a collection of subroutines which can be used to formulate, manipulate, and solve various LQG design problems. The ORACLS program is constructed in a manner which permits the user to maintain considerable flexibility at each operational state. This flexibility is accomplished by providing primary operations, analysis of linear time-invariant systems, and control synthesis based on LQG methodology. The input-output routines handle the reading and writing of numerical matrices, printing heading information, and accumulating output information. The basic vector-matrix operations include addition, subtraction, multiplication, equation, norm construction, tracing, transposition, scaling, juxtaposition, and construction of null and identity matrices. The analysis routines provide for the following computations: the eigenvalues and eigenvectors of real matrices; the relative stability of a given matrix; matrix factorization; the solution of linear constant coefficient vector-matrix algebraic equations; the controllability properties of a linear time-invariant system; the steady-state covariance matrix of an open-loop stable system forced by white noise; and the transient response of continuous linear time-invariant systems. The control law design routines of ORACLS implement some of the more common techniques of time-invariant LQG methodology. For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation. For the discrete version of this problem, the method of backwards differencing is applied to find the solutions to the discrete Riccati equation. A routine is also included to solve the steady-state Riccati equation by the Newton algorithms described by Klein, for continuous problems, and by Hewer, for discrete problems. Another routine calculates the prefilter gain to eliminate control state cross-product terms in the quadratic performance index and the weighting matrices for the sampled data optimal linear regulator problem. For cases with measurement noise, duality theory and optimal regulator algorithms are used to calculate solutions to the continuous and discrete Kalman-Bucy filter problems. Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory. These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model. In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output. There are three versions of ORACLS source code available for implementation: CDC, IBM, and DEC. The CDC version has been implemented on a CDC 6000 series computer with a central memory of approximately 13K (octal) of 60 bit words. The CDC version is written in FORTRAN IV, was developed in 1978, and last updated in 1986. The IBM version has been implemented on an IBM 370 series computer with a central memory requirement of approximately 300K of 8 bit bytes. The IBM version is written in FORTRAN IV and was generated in 1981. The DEC version has been implemented on a VAX series computer operating under VMS. The VAX version is written in FORTRAN 77 and was generated in 1986.

Path integrals and large deviations in stochastic hybrid systems.

PubMed

Bressloff, Paul C; Newby, Jay M

2014-04-01

We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

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

Guo, Z.; Department of Applied Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083; Lin, P.

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy lawmore » (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.« less

ECS: efficient communication scheduling for underwater sensor networks.

PubMed

Hong, Lu; Hong, Feng; Guo, Zhongwen; Li, Zhengbao

2011-01-01

TDMA protocols have attracted a lot of attention for underwater acoustic sensor networks (UWSNs), because of the unique characteristics of acoustic signal propagation such as great energy consumption in transmission, long propagation delay and long communication range. Previous TDMA protocols all allocated transmission time to nodes based on discrete time slots. This paper proposes an efficient continuous time scheduling TDMA protocol (ECS) for UWSNs, including the continuous time based and sender oriented conflict analysis model, the transmission moment allocation algorithm and the distributed topology maintenance algorithm. Simulation results confirm that ECS improves network throughput by 20% on average, compared to existing MAC protocols.

Wavelet transforms as solutions of partial differential equations

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

Zweig, G.

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). Wavelet transforms are useful in representing transients whose time and frequency structure reflect the dynamics of an underlying physical system. Speech sound, pressure in turbulent fluid flow, or engine sound in automobiles are excellent candidates for wavelet analysis. This project focused on (1) methods for choosing the parent wavelet for a continuous wavelet transform in pattern recognition applications and (2) the more efficient computation of continuous wavelet transforms by understanding the relationship between discrete wavelet transforms and discretized continuousmore » wavelet transforms. The most interesting result of this research is the finding that the generalized wave equation, on which the continuous wavelet transform is based, can be used to understand phenomena that relate to the process of hearing.« less

Discrete Emotion Effects on Lexical Decision Response Times

PubMed Central

Briesemeister, Benny B.; Kuchinke, Lars; Jacobs, Arthur M.

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account. PMID:21887307

Discrete emotion effects on lexical decision response times.

PubMed

Briesemeister, Benny B; Kuchinke, Lars; Jacobs, Arthur M

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account.

The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation

NASA Astrophysics Data System (ADS)

Zhang, Liangyin; Chen, Michael Z. Q.; Li, Chanying

2017-07-01

In this paper, two new pairs of dual continuous-time algebraic Riccati equations (CAREs) and dual discrete-time algebraic Riccati equations (DAREs) are proposed. The dual DAREs are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix. Then, in the case of singular matrices, a generalised inverse is introduced to deal with the dual DARE problem. These dual AREs can easily lead us to an iterative procedure for finding the anti-stabilising solutions, especially to DARE, by means of that for the stabilising solutions. Furthermore, we provide the counterpart results on the set of all solutions to DARE inspired by the results for CARE. Two examples are presented to illustrate the theoretical results.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Development of Proportional Reasoning: Where Young Children Go Wrong

PubMed Central

Boyer, Ty W.; Levine, Susan C.; Huttenlocher, Janellen

2008-01-01

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10- to 12-years of age, but can solve parallel problems involving continuous quantities by 6-years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A computerized proportional equivalence choice task was administered to kindergartners through fourth-graders in Study 1, and to first- and third-graders in Study 2. Both studies involved four between-subjects conditions that were formed by pairing continuous and discrete target proportions with continuous and discrete choice alternatives. In Study 1, target and choice alternatives were presented simultaneously and in Study 2 target and choice alternatives were presented sequentially. In both studies, children performed significantly worse when both the target and choice alternatives were represented with discrete quantities than when either or both of the proportions involved continuous quantities. Taken together, these findings indicate that children go astray on proportional reasoning problems involving discrete units only when a numerical match is possible, suggesting that their difficulty is due to an overextension of numerical equivalence concepts to proportional equivalence problems. PMID:18793078

Prompting children to reason proportionally: Processing discrete units as continuous amounts.

PubMed

Boyer, Ty W; Levine, Susan C

2015-05-01

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests whether performance on discrete unit problems might be improved by prompting intuitive reasoning with continuous-format problems. Participants were kindergarten, second-grade, and fourth-grade students (N = 194) assigned to either an experimental condition, where they were given continuous amount proportion problems before discrete unit proportion problems, or a control condition, where they were given all discrete unit problems. Results of a three-way mixed-model analysis of variance examining school grade, experimental condition, and block of trials indicated that fourth-grade students in the experimental condition outperformed those in the control condition on discrete unit problems in the second half of the experiment, but kindergarten and second-grade students did not differ by condition. This suggests that older children can be prompted to use intuitive strategies to reason proportionally. (c) 2015 APA, all rights reserved).

Revisiting "The evolution of reciprocity in sizable groups": continuous reciprocity in the repeated n-person prisoner's dilemma.

PubMed

Takezawa, Masanori; Price, Michael E

2010-05-21

For many years in evolutionary science, the consensus view has been that while reciprocal altruism can evolve in dyadic interactions, it is unlikely to evolve in sizable groups. This view had been based on studies which have assumed cooperation to be discrete rather than continuous (i.e., individuals can either fully cooperate or else fully defect, but they cannot continuously vary their level of cooperation). In real world cooperation, however, cooperation is often continuous. In this paper, we re-examine the evolution of reciprocity in sizable groups by presenting a model of the n-person prisoner's dilemma that assumes continuous rather than discrete cooperation. This model shows that continuous reciprocity has a dramatically wider basin of attraction than discrete reciprocity, and that this basin's size increases with efficiency of cooperation (marginal per capita return). Further, we find that assortative interaction interacts synergistically with continuous reciprocity to a much greater extent than it does with discrete reciprocity. These results suggest that previous models may have underestimated reciprocity's adaptiveness in groups. However, we also find that the invasion of continuous reciprocators into a population of unconditional defectors becomes realistic only within a narrow parameter space in which the efficiency of cooperation is close to its maximum bound. Therefore our model suggests that continuous reciprocity can evolve in large groups more easily than discrete reciprocity only under unusual circumstances. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

The multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test: I

NASA Astrophysics Data System (ADS)

Santini, Paolo Maria

2010-01-01

We propose an algorithmic procedure (i) to study the 'distance' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, (ii) to test the (asymptotic) integrability properties of such discretization. This method should provide, in particular, useful and concrete information on how good is any numerical scheme used to integrate a given integrable PDE. The procedure, illustrated on a fairly general ten-parameter family of discretizations of the nonlinear Schrödinger equation, consists of the following three steps: (i) the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in epsilon, following Degasperis et al (1997 Physica D 100 187-211) (ii) the application, to such an expansion, of the Degasperis-Procesi (DP) integrability test (Degasperis A and Procesi M 1999 Asymptotic integrability Symmetry and Perturbation Theory, SPT98, ed A Degasperis and G Gaeta (Singapore: World Scientific) pp 23-37 Degasperis A 2001 Multiscale expansion and integrability of dispersive wave equations Lectures given at the Euro Summer School: 'What is integrability?' (Isaac Newton Institute, Cambridge, UK, 13-24 August); Integrability (Lecture Notes in Physics vol 767) ed A Mikhailov (Berlin: Springer)), to test the asymptotic integrability properties of the discrete system and its 'distance' from its continuous limit; (iii) the use of the main output of the DP test to construct infinitely many approximate symmetries and constants of motion of the discrete system, through novel and simple formulas.

Transitions between discrete and rhythmic primitives in a unimanual task

PubMed Central

Sternad, Dagmar; Marino, Hamal; Charles, Steven K.; Duarte, Marcos; Dipietro, Laura; Hogan, Neville

2013-01-01

Given the vast complexity of human actions and interactions with objects, we proposed that control of sensorimotor behavior may utilize dynamic primitives. However, greater computational simplicity may come at the cost of reduced versatility. Evidence for primitives may be garnered by revealing such limitations. This study tested subjects performing a sequence of progressively faster discrete movements in order to “stress” the system. We hypothesized that the increasing pace would elicit a transition to rhythmic movements, assumed to be computationally and neurally more efficient. Abrupt transitions between the two types of movements would support the hypothesis that rhythmic and discrete movements are distinct primitives. Ten subjects performed planar point-to-point arm movements paced by a metronome: starting at 2 s, the metronome intervals decreased by 36 ms per cycle to 200 ms, stayed at 200 ms for several cycles, then increased by similar increments. Instructions emphasized to insert explicit stops between each movement with a duration that equaled the movement time. The experiment was performed with eyes open and closed, and with short and long metronome sounds, the latter explicitly specifying the dwell duration. Results showed that subjects matched instructed movement times but did not preserve the dwell times. Rather, they progressively reduced dwell time to zero, transitioning to continuous rhythmic movements before movement times reached their minimum. The acceleration profiles showed an abrupt change between discrete and rhythmic profiles. The loss of dwell time occurred earlier with long auditory specification, when subjects also showed evidence of predictive control. While evidence for hysteresis was weak, taken together, the results clearly indicated a transition between discrete and rhythmic movements, supporting the proposal that representation is based on primitives rather than on veridical internal models. PMID:23888139

Critical thresholds for eventual extinction in randomly disturbed population growth models.

PubMed

Peckham, Scott D; Waymire, Edward C; De Leenheer, Patrick

2018-02-16

This paper considers several single species growth models featuring a carrying capacity, which are subject to random disturbances that lead to instantaneous population reduction at the disturbance times. This is motivated in part by growing concerns about the impacts of climate change. Our main goal is to understand whether or not the species can persist in the long run. We consider the discrete-time stochastic process obtained by sampling the system immediately after the disturbances, and find various thresholds for several modes of convergence of this discrete process, including thresholds for the absence or existence of a positively supported invariant distribution. These thresholds are given explicitly in terms of the intensity and frequency of the disturbances on the one hand, and the population's growth characteristics on the other. We also perform a similar threshold analysis for the original continuous-time stochastic process, and obtain a formula that allows us to express the invariant distribution for this continuous-time process in terms of the invariant distribution of the discrete-time process, and vice versa. Examples illustrate that these distributions can differ, and this sends a cautionary message to practitioners who wish to parameterize these and related models using field data. Our analysis relies heavily on a particular feature shared by all the deterministic growth models considered here, namely that their solutions exhibit an exponentially weighted averaging property between a function of the initial condition, and the same function applied to the carrying capacity. This property is due to the fact that these systems can be transformed into affine systems.

An error bound for a discrete reduced order model of a linear multivariable system

NASA Technical Reports Server (NTRS)

Al-Saggaf, Ubaid M.; Franklin, Gene F.

1987-01-01

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

Experiment and simulation for CSI: What are the missing links?

NASA Technical Reports Server (NTRS)

Belvin, W. Keith; Park, K. C.

1989-01-01

Viewgraphs on experiment and simulation for control structure interaction (CSI) are presented. Topics covered include: control structure interaction; typical control/structure interaction system; CSI problem classification; actuator/sensor models; modeling uncertainty; noise models; real-time computations; and discrete versus continuous.

Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.

PubMed

Griffith, Mark; Courtney, Tod; Peccoud, Jean; Sanders, William H

2006-11-15

The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Software and benchmark models used for this publication can be made available upon request from the authors.

Discrete-to-continuous transition in quantum phase estimation

NASA Astrophysics Data System (ADS)

Rządkowski, Wojciech; Demkowicz-Dobrzański, Rafał

2017-09-01

We analyze the problem of quantum phase estimation in which the set of allowed phases forms a discrete N -element subset of the whole [0 ,2 π ] interval, φn=2 π n /N , n =0 ,⋯,N -1 , and study the discrete-to-continuous transition N →∞ for various cost functions as well as the mutual information. We also analyze the relation between the problems of phase discrimination and estimation by considering a step cost function of a given width σ around the true estimated value. We show that in general a direct application of the theory of covariant measurements for a discrete subgroup of the U(1 ) group leads to suboptimal strategies due to an implicit requirement of estimating only the phases that appear in the prior distribution. We develop the theory of subcovariant measurements to remedy this situation and demonstrate truly optimal estimation strategies when performing a transition from discrete to continuous phase estimation.

Networked event-triggered control: an introduction and research trends

NASA Astrophysics Data System (ADS)

Mahmoud, Magdi S.; Sabih, Muhammad

2014-11-01

A physical system can be studied as either continuous time or discrete-time system depending upon the control objectives. Discrete-time control systems can be further classified into two categories based on the sampling: (1) time-triggered control systems and (2) event-triggered control systems. Time-triggered systems sample states and calculate controls at every sampling instant in a periodic fashion, even in cases when states and calculated control do not change much. This indicates unnecessary and useless data transmission and computation efforts of a time-triggered system, thus inefficiency. For networked systems, the transmission of measurement and control signals, thus, cause unnecessary network traffic. Event-triggered systems, on the other hand, have potential to reduce the communication burden in addition to reducing the computation of control signals. This paper provides an up-to-date survey on the event-triggered methods for control systems and highlights the potential research directions.

On a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong

2017-02-01

In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms.

Automatic Methods and Tools for the Verification of Real Time Systems

DTIC Science & Technology

1997-07-31

real - time systems . This was accomplished by extending techniques, based on automata theory and temporal logic, that have been successful for the verification of time-independent reactive systems. As system specification lanmaage for embedded real - time systems , we introduced hybrid automata, which equip traditional discrete automata with real-numbered clock variables and continuous environment variables. As requirements specification languages, we introduced temporal logics with clock variables for expressing timing constraints.

Theory and operational rules for the discrete Hankel transform.

PubMed

Baddour, Natalie; Chouinard, Ugo

2015-04-01

Previous definitions of a discrete Hankel transform (DHT) have focused on methods to approximate the continuous Hankel integral transform. In this paper, we propose and evaluate the theory of a DHT that is shown to arise from a discretization scheme based on the theory of Fourier-Bessel expansions. The proposed transform also possesses requisite orthogonality properties which lead to invertibility of the transform. The standard set of shift, modulation, multiplication, and convolution rules are derived. In addition to the theory of the actual manipulated quantities which stand in their own right, this DHT can be used to approximate the continuous forward and inverse Hankel transform in the same manner that the discrete Fourier transform is known to be able to approximate the continuous Fourier transform.

Robustness of quantum key distribution with discrete and continuous variables to channel noise

NASA Astrophysics Data System (ADS)

Lasota, Mikołaj; Filip, Radim; Usenko, Vladyslav C.

2017-06-01

We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for continuous-variable quantum key distribution, to the discrete-variable case. Then we perform a comparison of the bounds on the tolerable channel noise between these two kinds of protocols using the same noise parametrization, in the case of implementation which is perfect otherwise. Obtained results show that continuous-variable protocols can exhibit similar robustness to the channel noise when the transmittance of the channel is relatively high. However, for strong loss discrete-variable protocols are superior and can overcome even the infinite-squeezing continuous-variable protocol while using limited nonclassical resources. The requirement on the probability of a single-photon production which would have to be fulfilled by a practical source of photons in order to demonstrate such superiority is feasible thanks to the recent rapid development in this field.

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.

Counting and classifying attractors in high dimensional dynamical systems.

PubMed

Bagley, R J; Glass, L

1996-12-07

Randomly connected Boolean networks have been used as mathematical models of neural, genetic, and immune systems. A key quantity of such networks is the number of basins of attraction in the state space. The number of basins of attraction changes as a function of the size of the network, its connectivity and its transition rules. In discrete networks, a simple count of the number of attractors does not reveal the combinatorial structure of the attractors. These points are illustrated in a reexamination of dynamics in a class of random Boolean networks considered previously by Kauffman. We also consider comparisons between dynamics in discrete networks and continuous analogues. A continuous analogue of a discrete network may have a different number of attractors for many different reasons. Some attractors in discrete networks may be associated with unstable dynamics, and several different attractors in a discrete network may be associated with a single attractor in the continuous case. Special problems in determining attractors in continuous systems arise when there is aperiodic dynamics associated with quasiperiodicity of deterministic chaos.

Optimization and quantization in gradient symbol systems: a framework for integrating the continuous and the discrete in cognition.

PubMed

Smolensky, Paul; Goldrick, Matthew; Mathis, Donald

2014-08-01

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization-Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. Copyright © 2013 Cognitive Science Society, Inc.

Beta oscillations define discrete perceptual cycles in the somatosensory domain.

PubMed

Baumgarten, Thomas J; Schnitzler, Alfons; Lange, Joachim

2015-09-29

Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8-20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain.

Nonlocal continuous models for forced vibration analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes

NASA Astrophysics Data System (ADS)

Kiani, Keivan

2014-06-01

Novel nonlocal discrete and continuous models are proposed for dynamic analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes (SWCNTs). The generated extra van der Waals forces between adjacent SWCNTs due to their lateral motions are evaluated via Lennard-Jones potential function. Using a nonlocal Rayleigh beam model, the discrete and continuous models are developed for both two- and three-dimensional ensembles of SWCNTs acted upon by transverse dynamic loads. The capabilities of the proposed continuous models in capturing the vibration behavior of SWCNTs ensembles are then examined through various numerical simulations. A reasonably good agreement between the results of the continuous models and those of the discrete ones is also reported. The effects of the applied load frequency, intertube spaces, and small-scale parameter on the transverse dynamic responses of both two- and three-dimensional ensembles of SWCNTs are explained. The proposed continuous models would be very useful for dynamic analyses of large populated ensembles of SWCNTs whose discrete models suffer from both computational efforts and labor costs.

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

NASA Technical Reports Server (NTRS)

Childs, A. G.

1971-01-01

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Discrete transparent boundary conditions for the mixed KDV-BBM equation

NASA Astrophysics Data System (ADS)

Besse, Christophe; Noble, Pascal; Sanchez, David

2017-09-01

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) and Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data.

Hesitations in continuous tracking induced by a concurrent discrete task

NASA Technical Reports Server (NTRS)

Klapp, S. T.; Kelly, P. A.; Netick, A.

1985-01-01

Subjects performed a continuous visually-guided pursuit tracking task with the right hand. From time to time (intervals averaging 30 sec) an auditory tone appeared signaling the subjects to perform a discrete response with the left hand. The presence of this tone was frequently associated with a hesitation in right-hand tracking which lasted 1/3 sec or longer. The rate of occurrence of these hesitations was about the same when the left-hand response involved a choice between competing responses as when the left hand responded in a predetermined direction. Hesitations occurred for three different mechanical tracking manipulanda using different controlling muscles, and appeared to be due to freezing rather than to relaxation of muscular action. The rate of occurrence of hesitations declined with practice, and this improvement in right-hand performance was accompanied by an improvement in performance of the concurrent left-hand response. The presence of hesitations, and their reduction with practice, can be interpreted within several viewpoints.

Robotic path-finding in inverse treatment planning for stereotactic radiosurgery with continuous dose delivery

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

Vandewouw, Marlee M., E-mail: marleev@mie.utoronto

Purpose: Continuous dose delivery in radiation therapy treatments has been shown to decrease total treatment time while improving the dose conformity and distribution homogeneity over the conventional step-and-shoot approach. The authors develop an inverse treatment planning method for Gamma Knife® Perfexion™ that continuously delivers dose along a path in the target. Methods: The authors’ method is comprised of two steps: find a path within the target, then solve a mixed integer optimization model to find the optimal collimator configurations and durations along the selected path. Robotic path-finding techniques, specifically, simultaneous localization and mapping (SLAM) using an extended Kalman filter, aremore » used to obtain a path that travels sufficiently close to selected isocentre locations. SLAM is novelly extended to explore a 3D, discrete environment, which is the target discretized into voxels. Further novel extensions are incorporated into the steering mechanism to account for target geometry. Results: The SLAM method was tested on seven clinical cases and compared to clinical, Hamiltonian path continuous delivery, and inverse step-and-shoot treatment plans. The SLAM approach improved dose metrics compared to the clinical plans and Hamiltonian path continuous delivery plans. Beam-on times improved over clinical plans, and had mixed performance compared to Hamiltonian path continuous plans. The SLAM method is also shown to be robust to path selection inaccuracies, isocentre selection, and dose distribution. Conclusions: The SLAM method for continuous delivery provides decreased total treatment time and increased treatment quality compared to both clinical and inverse step-and-shoot plans, and outperforms existing path methods in treatment quality. It also accounts for uncertainty in treatment planning by accommodating inaccuracies.« less

ECS: Efficient Communication Scheduling for Underwater Sensor Networks

PubMed Central

Hong, Lu; Hong, Feng; Guo, Zhongwen; Li, Zhengbao

2011-01-01

TDMA protocols have attracted a lot of attention for underwater acoustic sensor networks (UWSNs), because of the unique characteristics of acoustic signal propagation such as great energy consumption in transmission, long propagation delay and long communication range. Previous TDMA protocols all allocated transmission time to nodes based on discrete time slots. This paper proposes an efficient continuous time scheduling TDMA protocol (ECS) for UWSNs, including the continuous time based and sender oriented conflict analysis model, the transmission moment allocation algorithm and the distributed topology maintenance algorithm. Simulation results confirm that ECS improves network throughput by 20% on average, compared to existing MAC protocols. PMID:22163775

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

Consensus Algorithms for Networks of Systems with Second- and Higher-Order Dynamics

NASA Astrophysics Data System (ADS)

Fruhnert, Michael

This thesis considers homogeneous networks of linear systems. We consider linear feedback controllers and require that the directed graph associated with the network contains a spanning tree and systems are stabilizable. We show that, in continuous-time, consensus with a guaranteed rate of convergence can always be achieved using linear state feedback. For networks of continuous-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Hurwitz. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. Based on the conditions found, methods to compute feedback gains are proposed. We show that gains can be chosen such that consensus is achieved robustly over a variety of communication structures and system dynamics. We also consider the use of static output feedback. For networks of discrete-time second-order systems, we provide a new and simple derivation of the conditions for a second-order polynomials with complex coefficients to be Schur. We apply this result to obtain necessary and sufficient conditions to achieve consensus with networks whose graph Laplacian matrix may have complex eigenvalues. We show that consensus can always be achieved for marginally stable systems and discretized systems. Simple conditions for consensus achieving controllers are obtained when the Laplacian eigenvalues are all real. For networks of continuous-time time-variant higher-order systems, we show that uniform consensus can always be achieved if systems are quadratically stabilizable. In this case, we provide a simple condition to obtain a linear feedback control. For networks of discrete-time higher-order systems, we show that constant gains can be chosen such that consensus is achieved for a variety of network topologies. First, we develop simple results for networks of time-invariant systems and networks of time-variant systems that are given in controllable canonical form. Second, we formulate the problem in terms of Linear Matrix Inequalities (LMIs). The condition found simplifies the design process and avoids the parallel solution of multiple LMIs. The result yields a modified Algebraic Riccati Equation (ARE) for which we present an equivalent LMI condition.

The effect of haptic guidance and visual feedback on learning a complex tennis task.

PubMed

Marchal-Crespo, Laura; van Raai, Mark; Rauter, Georg; Wolf, Peter; Riener, Robert

2013-11-01

While haptic guidance can improve ongoing performance of a motor task, several studies have found that it ultimately impairs motor learning. However, some recent studies suggest that the haptic demonstration of optimal timing, rather than movement magnitude, enhances learning in subjects trained with haptic guidance. Timing of an action plays a crucial role in the proper accomplishment of many motor skills, such as hitting a moving object (discrete timing task) or learning a velocity profile (time-critical tracking task). The aim of the present study is to evaluate which feedback conditions-visual or haptic guidance-optimize learning of the discrete and continuous elements of a timing task. The experiment consisted in performing a fast tennis forehand stroke in a virtual environment. A tendon-based parallel robot connected to the end of a racket was used to apply haptic guidance during training. In two different experiments, we evaluated which feedback condition was more adequate for learning: (1) a time-dependent discrete task-learning to start a tennis stroke and (2) a tracking task-learning to follow a velocity profile. The effect that the task difficulty and subject's initial skill level have on the selection of the optimal training condition was further evaluated. Results showed that the training condition that maximizes learning of the discrete time-dependent motor task depends on the subjects' initial skill level. Haptic guidance was especially suitable for less-skilled subjects and in especially difficult discrete tasks, while visual feedback seems to benefit more skilled subjects. Additionally, haptic guidance seemed to promote learning in a time-critical tracking task, while visual feedback tended to deteriorate the performance independently of the task difficulty and subjects' initial skill level. Haptic guidance outperformed visual feedback, although additional studies are needed to further analyze the effect of other types of feedback visualization on motor learning of time-critical tasks.

Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Boyle, Richard D.

2014-01-01

Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

NASA Technical Reports Server (NTRS)

Sadovsky, Alexander V.; Davis, Damek; Isaacson, Douglas R.

2012-01-01

A class of problems in air traffic management asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures, but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs, hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the Fully Routed Nominal Problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively finite, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.

Comparing the Discrete and Continuous Logistic Models

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory

DTIC Science & Technology

2016-05-12

valued times series from a sample. (A practical algorithm to compute the estimator is a work in progress.) Third, finitely-valued spatial processes...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 mathematical statistics; time series ; Markov chains; random...proved. Second, a statistical method is developed to estimate the memory depth of discrete- time and continuously-valued times series from a sample. (A

Adolescents with Developmental Dyscalculia Do Not Have a Generalized Magnitude Deficit - Processing of Discrete and Continuous Magnitudes.

PubMed

McCaskey, Ursina; von Aster, Michael; O'Gorman Tuura, Ruth; Kucian, Karin

2017-01-01

The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD.

Adolescents with Developmental Dyscalculia Do Not Have a Generalized Magnitude Deficit – Processing of Discrete and Continuous Magnitudes

PubMed Central

McCaskey, Ursina; von Aster, Michael; O’Gorman Tuura, Ruth; Kucian, Karin

2017-01-01

The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD. PMID:28373834

40 CFR Appendix E to Part 403 - Sampling Procedures

Code of Federal Regulations, 2010 CFR

2010-07-01

... done manually or automatically, and discretely or continuously. If discrete sampling is employed, at least 12 aliquots should be composited. Discrete sampling may be flow proportioned either by varying the...

Educational Aspirations: Markov and Poisson Models. Rural Industrial Development Project Working Paper Number 14, August 1971.

ERIC Educational Resources Information Center

Kayser, Brian D.

The fit of educational aspirations of Illinois rural high school youths to 3 related one-parameter mathematical models was investigated. The models used were the continuous-time Markov chain model, the discrete-time Markov chain, and the Poisson distribution. The sample of 635 students responded to questionnaires from 1966 to 1969 as part of an…

Real-Time Control of an Ensemble of Heterogeneous Resources

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

Bernstein, Andrey; Bouman, Niek J.; Le Boudec, Jean-Yves

This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimizationmore » problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.« less

Distributed Optimal Consensus Control for Multiagent Systems With Input Delay.

PubMed

Zhang, Huaipin; Yue, Dong; Zhao, Wei; Hu, Songlin; Dou, Chunxia; Huaipin Zhang; Dong Yue; Wei Zhao; Songlin Hu; Chunxia Dou; Hu, Songlin; Zhang, Huaipin; Dou, Chunxia; Yue, Dong; Zhao, Wei

2018-06-01

This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

Inferring network structure in non-normal and mixed discrete-continuous genomic data.

PubMed

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2018-03-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.

Inferring network structure in non-normal and mixed discrete-continuous genomic data

PubMed Central

Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

2017-01-01

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. PMID:28437848

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

LMI designmethod for networked-based PID control

NASA Astrophysics Data System (ADS)

Souza, Fernando de Oliveira; Mozelli, Leonardo Amaral; de Oliveira, Maurício Carvalho; Palhares, Reinaldo Martinez

2016-10-01

In this paper, we propose a methodology for the design of networked PID controllers for second-order delayed processes using linear matrix inequalities. The proposed procedure takes into account time-varying delay on the plant, time-varying delays induced by the network and packed dropouts. The design is carried on entirely using a continuous-time model of the closed-loop system where time-varying delays are used to represent sampling and holding occurring in a discrete-time digital PID controller.

Piagetian conservation of discrete quantities in bonobos (Pan paniscus), chimpanzees (Pan troglodytes), and orangutans (Pongo pygmaeus).

PubMed

Suda, Chikako; Call, Josep

2005-10-01

This study investigated whether physical discreteness helps apes to understand the concept of Piagetian conservation (i.e. the invariance of quantities). Subjects were four bonobos, three chimpanzees, and five orangutans. Apes were tested on their ability to conserve discrete/continuous quantities in an over-conservation procedure in which two unequal quantities of edible rewards underwent various transformations in front of subjects. Subjects were examined to determine whether they could track the larger quantity of reward after the transformation. Comparison between the two types of conservation revealed that tests with bonobos supported the discreteness hypothesis. Bonobos, but neither chimpanzees nor orangutans, performed significantly better with discrete quantities than with continuous ones. The results suggest that at least bonobos could benefit from the discreteness of stimuli in their acquisition of conservation skills.

Rational Number Learning in the Early Years: What is Possible?

ERIC Educational Resources Information Center

Hunting, Robert P.

This report describes an investigation of how young children respond to two types of tasks: (1) finding one-half of a continuous and a discrete material; and (2) attempting to share continuous and discrete material equally between two dolls. Continuous material, such as string, paper, or liquid, is quantified by adults using measurement units. A…

Spectrum Control through Discrete Frequency Diffraction in the Presence of Photonic Gauge Potentials

NASA Astrophysics Data System (ADS)

Qin, Chengzhi; Zhou, Feng; Peng, Yugui; Sounas, Dimitrios; Zhu, Xuefeng; Wang, Bing; Dong, Jianji; Zhang, Xinliang; Alù; , Andrea; Lu, Peixiang

2018-03-01

By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

A continuous-discrete approach for evaluation of natural frequencies and mode shapes of high-rise buildings

NASA Astrophysics Data System (ADS)

Malekinejad, Mohsen; Rahgozar, Reza; Malekinejad, Ali; Rahgozar, Peyman

2016-09-01

In this paper, a continuous-discrete approach based on the concept of lumped mass and equivalent continuous approach is proposed for free vibration analysis of combined system of framed tube, shear core and outrigger-belt truss in high-rise buildings. This system is treated as a continuous system (i.e., discrete beams and columns are replaced with equivalent continuous membranes) and a discrete system (or lumped mass system) at different stages of dynamic analysis. The structure is discretized at each floor of the building as a series of lumped masses placed at the center of shear core. Each mass has two transitional degrees of freedom (lateral and axial( and one rotational. The effect of shear core and outrigger-belt truss on framed tube system is modeled as a rotational spring placed at the location of outrigger-belt truss system along structure's height. By solving the resulting eigen problem, natural frequencies and mode-shapes are obtained. Numerical examples are presented to show acceptable accuracy of the procedure in estimating the fundamental frequencies and corresponding mode shapes of the combined system as compared to finite element analysis of the complete structure. The simplified proposed method is much faster and should be more suitable for rapid interactive design.

Financial Data Analysis by means of Coupled Continuous-Time Random Walk in Rachev-Rűschendorf Model

NASA Astrophysics Data System (ADS)

Jurlewicz, A.; Wyłomańska, A.; Żebrowski, P.

2008-09-01

We adapt the continuous-time random walk formalism to describe asset price evolution. We expand the idea proposed by Rachev and Rűschendorf who analyzed the binomial pricing model in the discrete time with randomization of the number of price changes. As a result, in the framework of the proposed model we obtain a mixture of the Gaussian and a generalized arcsine laws as the limiting distribution of log-returns. Moreover, we derive an European-call-option price that is an extension of the Black-Scholes formula. We apply the obtained theoretical results to model actual financial data and try to show that the continuous-time random walk offers alternative tools to deal with several complex issues of financial markets.

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

Bykova, Nadezda A; Favorov, Alexander V; Mironov, Andrey A

2013-01-01

The problem of reconstruction of ancestral states given a phylogeny and data from extant species arises in a wide range of biological studies. The continuous-time Markov model for the discrete states evolution is generally used for the reconstruction of ancestral states. We modify this model to account for a case when the states of the extant species are uncertain. This situation appears, for example, if the states for extant species are predicted by some program and thus are known only with some level of reliability; it is common for bioinformatics field. The main idea is formulation of the problem as a hidden Markov model on a tree (tree HMM, tHMM), where the basic continuous-time Markov model is expanded with the introduction of emission probabilities of observed data (e.g. prediction scores) for each underlying discrete state. Our tHMM decoding algorithm allows us to predict states at the ancestral nodes as well as to refine states at the leaves on the basis of quantitative comparative genomics. The test on the simulated data shows that the tHMM approach applied to the continuous variable reflecting the probabilities of the states (i.e. prediction score) appears to be more accurate then the reconstruction from the discrete states assignment defined by the best score threshold. We provide examples of applying our model to the evolutionary analysis of N-terminal signal peptides and transcription factor binding sites in bacteria. The program is freely available at http://bioinf.fbb.msu.ru/~nadya/tHMM and via web-service at http://bioinf.fbb.msu.ru/treehmmweb.

A VLF-based technique in applications to digital control of nonlinear hybrid multirate systems

NASA Astrophysics Data System (ADS)

Vassilyev, Stanislav; Ulyanov, Sergey; Maksimkin, Nikolay

2017-01-01

In this paper, a technique for rigorous analysis and design of nonlinear multirate digital control systems on the basis of the reduction method and sublinear vector Lyapunov functions is proposed. The control system model under consideration incorporates continuous-time dynamics of the plant and discrete-time dynamics of the controller and takes into account uncertainties of the plant, bounded disturbances, nonlinear characteristics of sensors and actuators. We consider a class of multirate systems where the control update rate is slower than the measurement sampling rates and periodic non-uniform sampling is admitted. The proposed technique does not use the preliminary discretization of the system, and, hence, allows one to eliminate the errors associated with the discretization and improve the accuracy of analysis. The technique is applied to synthesis of digital controller for a flexible spacecraft in the fine stabilization mode and decentralized controller for a formation of autonomous underwater vehicles. Simulation results are provided to validate the good performance of the designed controllers.

Numerical method for accessing the universal scaling function for a multiparticle discrete time asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-11-01

In the universality class of the one-dimensional Kardar-Parisi-Zhang (KPZ) surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since and Derrida and Lebowitz’s original publication [Phys. Rev. Lett. 80, 209 (1998)] this universality has been verified for a variety of continuous-time, periodic-boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large-system-size limit (N→∞) of a single-particle discrete time system, even in the case of very small system sizes (N⩽22) . This fact allows us to not only verify that the DLSF properly characterizes multiple-particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open-boundary ASEP.

Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems

NASA Astrophysics Data System (ADS)

Mahdi Alavi, S. M.; Saif, Mehrdad

2013-12-01

This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.

Experimental confirmation of a PDE-based approach to design of feedback controls

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.; Brown, D. E.; Silcox, R. J.; Metcalf, Vern L.

1995-01-01

Issues regarding the experimental implementation of partial differential equation based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.

Second-order discrete Kalman filtering equations for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith; Alvin, Kenneth F.

1991-01-01

A general form for the first-order representation of the continuous, second-order linear structural dynamics equations is introduced in order to derive a corresponding form of first-order Kalman filtering equations (KFE). Time integration of the resulting first-order KFE is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete KFE involving only symmetric, N x N solution matrix.

A new spatial multiple discrete-continuous modeling approach to land use change analysis.

DOT National Transportation Integrated Search

2013-09-01

This report formulates a multiple discrete-continuous probit (MDCP) land-use model within a : spatially explicit economic structural framework for land-use change decisions. The spatial : MDCP model is capable of predicting both the type and intensit...

Combined visual illusion effects on the perceived index of difficulty and movement outcomes in discrete and continuous fitts' tapping.

PubMed

Alphonsa, Sushma; Dai, Boyi; Benham-Deal, Tami; Zhu, Qin

2016-01-01

The speed-accuracy trade-off is a fundamental movement problem that has been extensively investigated. It has been established that the speed at which one can move to tap targets depends on how large the targets are and how far they are apart. These spatial properties of the targets can be quantified by the index of difficulty (ID). Two visual illusions are known to affect the perception of target size and movement amplitude: the Ebbinghaus illusion and Muller-Lyer illusion. We created visual images that combined these two visual illusions to manipulate the perceived ID, and then examined people's visual perception of the targets in illusory context as well as their performance in tapping those targets in both discrete and continuous manners. The findings revealed that the combined visual illusions affected the perceived ID similarly in both discrete and continuous judgment conditions. However, the movement outcomes were affected by the combined visual illusions according to the tapping mode. In discrete tapping, the combined visual illusions affected both movement accuracy and movement amplitude such that the effective ID resembled the perceived ID. In continuous tapping, none of the movement outcomes were affected by the combined visual illusions. Participants tapped the targets with higher speed and accuracy in all visual conditions. Based on these findings, we concluded that distinct visual-motor control mechanisms were responsible for execution of discrete and continuous Fitts' tapping. Although discrete tapping relies on allocentric information (object-centered) to plan for action, continuous tapping relies on egocentric information (self-centered) to control for action. The planning-control model for rapid aiming movements is supported.

Detecting dynamical changes in time series by using the Jensen Shannon divergence

NASA Astrophysics Data System (ADS)

Mateos, D. M.; Riveaud, L. E.; Lamberti, P. W.

2017-08-01

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult because they have a common wide band power spectrum, a delta like autocorrelation function, and share other features as well. In general, signals are presented as continuous records and require to be discretized for being analyzed. In this work, we introduce different schemes for discretizing and for detecting dynamical changes in time series. One of the main motivations is to detect transitions between the chaotic and random regime. The tools here used here originate from the Information Theory. The schemes proposed are applied to simulated and real life signals, showing in all cases a high proficiency for detecting changes in the dynamics of the associated time series.

Spherical harmonics and rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Celeghini, E.; Gadella, M.; del Olmo, M. A.

2018-05-01

This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis.

Inaccurate Color Discrimination by Pollinators Promotes Evolution of Discrete Color Polymorphism in Food-Deceptive Flowers.

PubMed

Kagawa, Kotaro; Takimoto, Gaku

2016-02-01

Many plant species employing a food-deceptive pollination strategy show discrete or continuous floral polymorphism within their populations. Previous studies have suggested that negative frequency-dependent selection (NFDS) caused by the learning behavior of pollinators was responsible for the maintenance of floral polymorphism. However, NFDS alone does not explain why and when discrete or continuous polymorphism evolves. In this study, we use an evolutionary simulation model to propose that inaccurate discrimination of flower colors by pollinators results in evolution of discrete flower color polymorphism. Simulations showed that associative learning based on inaccurate discrimination in pollinators caused disruptive selection of flower colors. The degree of inaccuracy determined the number of discrete flower colors that evolved. Our results suggest that animal behavior based on inaccurate discrimination may be a general cause of disruptive selection that promotes discrete trait polymorphism.

Comparisons of discrete and integrative sampling accuracy in estimating pulsed aquatic exposures.

PubMed

Morrison, Shane A; Luttbeg, Barney; Belden, Jason B

2016-11-01

Most current-use pesticides have short half-lives in the water column and thus the most relevant exposure scenarios for many aquatic organisms are pulsed exposures. Quantifying exposure using discrete water samples may not be accurate as few studies are able to sample frequently enough to accurately determine time-weighted average (TWA) concentrations of short aquatic exposures. Integrative sampling methods that continuously sample freely dissolved contaminants over time intervals (such as integrative passive samplers) have been demonstrated to be a promising measurement technique. We conducted several modeling scenarios to test the assumption that integrative methods may require many less samples for accurate estimation of peak 96-h TWA concentrations. We compared the accuracies of discrete point samples and integrative samples while varying sampling frequencies and a range of contaminant water half-lives (t 50  = 0.5, 2, and 8 d). Differences the predictive accuracy of discrete point samples and integrative samples were greatest at low sampling frequencies. For example, when the half-life was 0.5 d, discrete point samples required 7 sampling events to ensure median values > 50% and no sampling events reporting highly inaccurate results (defined as < 10% of the true 96-h TWA). Across all water half-lives investigated, integrative sampling only required two samples to prevent highly inaccurate results and measurements resulting in median values > 50% of the true concentration. Regardless, the need for integrative sampling diminished as water half-life increased. For an 8-d water half-life, two discrete samples produced accurate estimates and median values greater than those obtained for two integrative samples. Overall, integrative methods are the more accurate method for monitoring contaminants with short water half-lives due to reduced frequency of extreme values, especially with uncertainties around the timing of pulsed events. However, the acceptability of discrete sampling methods for providing accurate concentration measurements increases with increasing aquatic half-lives. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Understanding Rasch Measurement: Rasch Models Overview.

ERIC Educational Resources Information Center

Wright, Benjamin D.; Mok, Magdalena

2000-01-01

Presents an overview of Rasch measurement models that begins with a conceptualization of continuous experiences often captured as discrete observations. Discusses the mathematical properties of the Rasch family of models that allow the transformation of discrete deterministic counts into continuous probabilistic abstractions. Also discusses six of…

THE STATISTICAL ANALYSIS OF DISCRETE AND CONTINUOUS OUTCOMES USING DESIRABILITY FUNCTIONS.

EPA Science Inventory

Multiple types of outcomes are sometimes measured on each animal in toxicology dose-response experiments. In this paper we introduce a method of deriving a composite score for a dose-response experiment that combines information from discrete and continuous outcomes through the ...

Discrete-continuous duality of protein structure space.

PubMed

Sadreyev, Ruslan I; Kim, Bong-Hyun; Grishin, Nick V

2009-06-01

Recently, the nature of protein structure space has been widely discussed in the literature. The traditional discrete view of protein universe as a set of separate folds has been criticized in the light of growing evidence that almost any arrangement of secondary structures is possible and the whole protein space can be traversed through a path of similar structures. Here we argue that the discrete and continuous descriptions are not mutually exclusive, but complementary: the space is largely discrete in evolutionary sense, but continuous geometrically when purely structural similarities are quantified. Evolutionary connections are mainly confined to separate structural prototypes corresponding to folds as islands of structural stability, with few remaining traceable links between the islands. However, for a geometric similarity measure, it is usually possible to find a reasonable cutoff that yields paths connecting any two structures through intermediates.

Evolution of Particle Size Distributions in Fragmentation Over Time

NASA Astrophysics Data System (ADS)

Charalambous, C. A.; Pike, W. T.

2013-12-01

We present a new model of fragmentation based on a probabilistic calculation of the repeated fracture of a particle population. The resulting continuous solution, which is in closed form, gives the evolution of fragmentation products from an initial block, through a scale-invariant power-law relationship to a final comminuted powder. Models for the fragmentation of particles have been developed separately in mainly two different disciplines: the continuous integro-differential equations of batch mineral grinding (Reid, 1965) and the fractal analysis of geophysics (Turcotte, 1986) based on a discrete model with a single probability of fracture. The first gives a time-dependent development of the particle-size distribution, but has resisted a closed-form solution, while the latter leads to the scale-invariant power laws, but with no time dependence. Bird (2009) recently introduced a bridge between these two approaches with a step-wise iterative calculation of the fragmentation products. The development of the particle-size distribution occurs with discrete steps: during each fragmentation event, the particles will repeatedly fracture probabilistically, cascading down the length scales to a final size distribution reached after all particles have failed to further fragment. We have identified this process as the equivalent to a sequence of trials for each particle with a fixed probability of fragmentation. Although the resulting distribution is discrete, it can be reformulated as a continuous distribution in maturity over time and particle size. In our model, Turcotte's power-law distribution emerges at a unique maturation index that defines a regime boundary. Up to this index, the fragmentation is in an erosional regime with the initial particle size setting the scaling. Fragmentation beyond this index is in a regime of comminution with rebreakage of the particles down to the size limit of fracture. The maturation index can increment continuously, for example under grinding conditions, or as discrete steps, such as with impact events. In both cases our model gives the energy associated with the fragmentation in terms of the developing surface area of the population. We show the agreement of our model to the evolution of particle size distributions associated with episodic and continuous fragmentation and how the evolution of some popular fractals may be represented using this approach. C. A. Charalambous and W. T. Pike (2013). Multi-Scale Particle Size Distributions of Mars, Moon and Itokawa based on a time-maturation dependent fragmentation model. Abstract Submitted to the AGU 46th Fall Meeting. Bird, N. R. A., Watts, C. W., Tarquis, A. M., & Whitmore, A. P. (2009). Modeling dynamic fragmentation of soil. Vadose Zone Journal, 8(1), 197-201. Reid, K. J. (1965). A solution to the batch grinding equation. Chemical Engineering Science, 20(11), 953-963. Turcotte, D. L. (1986). Fractals and fragmentation. Journal of Geophysical Research: Solid Earth 91(B2), 1921-1926.

A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics

NASA Astrophysics Data System (ADS)

Bertin, N.; Upadhyay, M. V.; Pradalier, C.; Capolungo, L.

2015-09-01

In this paper, we propose a novel full-field approach based on the fast Fourier transform (FFT) technique to compute mechanical fields in periodic discrete dislocation dynamics (DDD) simulations for anisotropic materials: the DDD-FFT approach. By coupling the FFT-based approach to the discrete continuous model, the present approach benefits from the high computational efficiency of the FFT algorithm, while allowing for a discrete representation of dislocation lines. It is demonstrated that the computational time associated with the new DDD-FFT approach is significantly lower than that of current DDD approaches when large number of dislocation segments are involved for isotropic and anisotropic elasticity, respectively. Furthermore, for fine Fourier grids, the treatment of anisotropic elasticity comes at a similar computational cost to that of isotropic simulation. Thus, the proposed approach paves the way towards achieving scale transition from DDD to mesoscale plasticity, especially due to the method’s ability to incorporate inhomogeneous elasticity.

Linear system theory

NASA Technical Reports Server (NTRS)

Callier, Frank M.; Desoer, Charles A.

1991-01-01

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Variable Structure PID Control to Prevent Integrator Windup

NASA Technical Reports Server (NTRS)

Hall, C. E.; Hodel, A. S.; Hung, J. Y.

1999-01-01

PID controllers are frequently used to control systems requiring zero steady-state error while maintaining requirements for settling time and robustness (gain/phase margins). PID controllers suffer significant loss of performance due to short-term integrator wind-up when used in systems with actuator saturation. We examine several existing and proposed methods for the prevention of integrator wind-up in both continuous and discrete time implementations.

Discrete factor approximations in simultaneous equation models: estimating the impact of a dummy endogenous variable on a continuous outcome.

PubMed

Mroz, T A

1999-10-01

This paper contains a Monte Carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models. When the true model has bivariate normal disturbances, estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias; these approximation estimators dominate all the other estimators examined when the disturbances are non-normal. The experiments also indicate that one should liberally add points of support to the discrete factor distribution. The paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages.

Relaxation Processes and Time Scale Transformation.

DTIC Science & Technology

1982-03-01

the response function may be immediately recognized as being 14 of the Kubo - Green type in the classical regime. Given this general framework, it is now...discussions of the master equation, 2and has recently been applied in cumulative damage models with discrete time parameter .3 However, it does not seem to...development parameter is taken tG be a positive, cumulative function that increases from an origin monotonically. Consider two continuous time scales e and t

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

PubMed

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Continuous-flow water sampler for real-time isotopic water measurements

NASA Astrophysics Data System (ADS)

Carter, J.; Dennis, K.

2013-12-01

Measuring the stable isotopes of liquid water (δ18O and δD) is a tool familiar to many Earth scientists, but most current techniques require discrete sampling. For example, isotope ratio mass spectrometry requires the collection of aliquots of water that are then converted to CO2, CO or H2 for analysis. Similarly, laser-based techniques, such as Cavity Ring-Down Spectroscopy (CRDS) convert discrete samples (typically < 2μL) of liquid water to water vapor using a flash vaporization process. By requiring the use of discrete samples fine-scale spatial and temporal studies of changes in δ18O and δD are limited. Here we present a continuous-flow water sampler that will enable scientists to probe isotopic changes in real-time, with applications including, but not limited to, quantification of the 'amount effect' (Dansgaard, 1964) during an individual precipitation event or storm track, real-time mixing of water in river systems, and shipboard continuous water measurements (Munksgaard et al., 2012). Due to the inherent ability of CRDS to measure a continuous flow of water vapor it is an ideal candidate for interfacing with a continuous water sampling system. Here we present results from the first commercially available continuous-flow water sampler, developed by engineers at Picarro. This peripheral device is compatible with Picarro CRDS isotopic water analyzers, allowing real-time, continuous isotopic measurements of liquid water. The new device, which expands upon the design of Munskgaard et al. (2011), utilizes expanded polytetrafluoroethylene (ePTFE) membrane technology to continuously generate gas-phase water, while liquid water is pumped through the system. The water vapor subsequently travels to the CRDS analyzer where the isotopic ratios are measured and recorded. The generation of water vapor using membrane technology is sensitive to environmental conditions, which if not actively control, lead to sustainable experimental noise and drift. Consequently, our continuous-flow water sample employs active control for all pertinent parameters, significantly increasing its stability and usability. We will present data from controlled laboratory experiments demonstrating sample-to-sample precision and long-term stability. We will also show experimental data that highlights the instrumental sample-to-sample memory, which we have decreased significantly from previous implementations of this technology. Additionally, we will present field results from the Sacramento River, CA. Dansgaard, W. (1964) 'Stable isotopes in precipitation', Tellus, 16(4), p. 436-468. Munksgaard, N.C., Wurster, C.M., Bass, A., Zagorskis, I., and Bird, M.I. (2012) 'First continuous shipboard d18O and dD measurements in seawater by diffusion sampling--cavity ring-down spectrometry', Environmental Chemistry Letters, 10, p.301-307. Munksgaard, N.C., Wurster, C.M., and Bird, M.I., (2011), 'Continuous analysis of δ18O and δD values of water by diffusion sampling cavity ring-down spectrometry: a novel sampling device for unattended field monitoring of precipitation, ground and surface waters', Rapid Communications in Mass Spectrometry, 25, p. 3706-3712.

Evidence for the Continuous Latent Structure of Mania in the Epidemiologic Catchment Area from Multiple Latent Structure and Construct Validation Methodologies

PubMed Central

Prisciandaro, James J.; Roberts, John E.

2011-01-01

Background Although psychiatric diagnostic systems have conceptualized mania as a discrete phenomenon, appropriate latent structure investigations testing this conceptualization are lacking. In contrast to these diagnostic systems, several influential theories of mania have suggested a continuous conceptualization. The present study examined whether mania has a continuous or discrete latent structure using a comprehensive approach including taxometric, information-theoretic latent distribution modeling (ITLDM), and predictive validity methodologies in the Epidemiologic Catchment Area (ECA) study. Methods Eight dichotomous manic symptom items were submitted to a variety of latent structural analyses; including factor analyses, taxometric procedures, and ITLDM; in 10,105 ECA community participants. Additionally, a variety of continuous and discrete models of mania were compared in terms of their relative abilities to predict outcomes (i.e., health service utilization, internalizing and externalizing disorders, and suicidal behavior). Results Taxometric and ITLDM analyses consistently supported a continuous conceptualization of mania. In ITLDM analyses, a continuous model of mania demonstrated 6:52:1 odds over the best fitting latent class model of mania. Factor analyses suggested that the continuous structure of mania was best represented by a single latent factor. Predictive validity analyses demonstrated a consistent superior ability of continuous models of mania relative to discrete models. Conclusions The present study provided three independent lines of support for a continuous conceptualization of mania. The implications of a continuous model of mania are discussed. PMID:20507671

Discrete-state representation of ion permeation coupled to fast gating in a model of ClC chloride channels: comparison to multi-ion continuous space Brownian dynamics simulations.

PubMed

Coalson, Rob D; Cheng, Mary Hongying

2010-01-28

A discrete-state model of chloride ion motion in a ClC chloride channel is constructed, following a previously developed multi-ion continuous space model of the same system (Cheng, M. H.; Mamonov, A. B.; Dukes, J. W.; Coalson, R. D. J. Phys. Chem. B 2007, 111, 5956) that included a simplistic representation of the fast gate in this channel. The reducibility of the many-body continuous space to the eight discrete-state model considered in the present work is examined in detail by performing three-dimensional Brownian dynamics simulations of each allowed state-to-state transition in order to extract the appropriate rate constant for this process, and then inserting the pairwise rate constants thereby obtained into an appropriate set of kinetic master equations. Experimental properties of interest, including the rate of Cl(-) ion permeation through the open channel and the average rate of closing of the fast gate as a function of bulk Cl(-) ion concentrations in the intracellular and extracellular electrolyte reservoirs are computed. Good agreement is found between the results obtained via the eight discrete-state model versus the multi-ion continuous space model, thereby encouraging continued development of the discrete-state model to include more complex behaviors observed experimentally in these channels.

Continuous distribution of emission states from single CdSe/ZnS quantum dots.

PubMed

Zhang, Kai; Chang, Hauyee; Fu, Aihua; Alivisatos, A Paul; Yang, Haw

2006-04-01

The photoluminescence dynamics of colloidal CdSe/ZnS/streptavidin quantum dots were studied using time-resolved single-molecule spectroscopy. Statistical tests of the photon-counting data suggested that the simple "on/off" discrete state model is inconsistent with experimental results. Instead, a continuous emission state distribution model was found to be more appropriate. Autocorrelation analysis of lifetime and intensity fluctuations showed a nonlinear correlation between them. These results were consistent with the model that charged quantum dots were also emissive, and that time-dependent charge migration gave rise to the observed photoluminescence dynamics.

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

On-Line Control of Metal Processing. Report of the Committee on On-Line Control of Metal Processing

DTIC Science & Technology

1989-02-01

Materials Engineering. His work has concentrated on the electroprocessing of metals in molten salts . He is a member of TMS, AIME, ES, Canadian Institute...continuous ingot casting process with three 32 discrete control loops Figure 4-2 Controller incorporating process model 36 Figure 4-3 Real-time molten ...and others while providing a controlled macrostructure and solidification substructure. In this process, molten metal continuously flows from a

Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

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

Korn, P., E-mail: peter.korn@mpimet.mpg.de; Danilov, S.; A.M. Obukhov Institute of Atmospheric Physics, Moscow

2017-02-01

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noisemore » in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics.« less

Virtualized Traffic: reconstructing traffic flows from discrete spatiotemporal data.

PubMed

Sewall, Jason; van den Berg, Jur; Lin, Ming C; Manocha, Dinesh

2011-01-01

We present a novel concept, Virtualized Traffic, to reconstruct and visualize continuous traffic flows from discrete spatiotemporal data provided by traffic sensors or generated artificially to enhance a sense of immersion in a dynamic virtual world. Given the positions of each car at two recorded locations on a highway and the corresponding time instances, our approach can reconstruct the traffic flows (i.e., the dynamic motions of multiple cars over time) between the two locations along the highway for immersive visualization of virtual cities or other environments. Our algorithm is applicable to high-density traffic on highways with an arbitrary number of lanes and takes into account the geometric, kinematic, and dynamic constraints on the cars. Our method reconstructs the car motion that automatically minimizes the number of lane changes, respects safety distance to other cars, and computes the acceleration necessary to obtain a smooth traffic flow subject to the given constraints. Furthermore, our framework can process a continuous stream of input data in real time, enabling the users to view virtualized traffic events in a virtual world as they occur. We demonstrate our reconstruction technique with both synthetic and real-world input. © 2011 IEEE Published by the IEEE Computer Society

How Mathematics Propels the Development of Physical Knowledge

ERIC Educational Resources Information Center

Schwartz, Daniel L.; Martin, Taylor; Pfaffman, Jay

2005-01-01

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of…

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.

Functional linear models to test for differences in prairie wetland hydraulic gradients

USGS Publications Warehouse

Greenwood, Mark C.; Sojda, Richard S.; Preston, Todd M.; Swayne, David A.; Yang, Wanhong; Voinov, A.A.; Rizzoli, A.; Filatova, T.

2010-01-01

Functional data analysis provides a framework for analyzing multiple time series measured frequently in time, treating each series as a continuous function of time. Functional linear models are used to test for effects on hydraulic gradient functional responses collected from three types of land use in Northeastern Montana at fourteen locations. Penalized regression-splines are used to estimate the underlying continuous functions based on the discretely recorded (over time) gradient measurements. Permutation methods are used to assess the statistical significance of effects. A method for accommodating missing observations in each time series is described. Hydraulic gradients may be an initial and fundamental ecosystem process that responds to climate change. We suggest other potential uses of these methods for detecting evidence of climate change.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

1997-01-01

Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

Extinction dynamics of a discrete population in an oasis.

PubMed

Berti, Stefano; Cencini, Massimo; Vergni, Davide; Vulpiani, Angelo

2015-07-01

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.

Summary and interpretation of discrete and continuous water-quality monitoring data, Mattawoman Creek, Charles County, Maryland, 2000-11

USGS Publications Warehouse

Chanat, Jeffrey G.; Miller, Cherie V.; Bell, Joseph M.; Majedi, Brenda Feit; Brower, David P.

2013-01-01

Discrete samples and continuous (15-minute interval) water-quality data were collected at Mattawoman Creek (U.S. Geological Survey station number 01658000) from October 2000 through January 2011, in cooperation with the Charles County (Maryland) Department of Planning and Growth Management, the Maryland Department of the Environment, and the Maryland Geological Survey. Mattawoman Creek is a fourth-order Maryland tributary to the tidal freshwater Potomac River; the creek’s watershed is experiencing development pressure due to its proximity to Washington, D.C. Data were analyzed for the purpose of describing ambient water quality, identifying potential contaminant sources, and quantifying nutrient and sediment loads to the tidal freshwater Mattawoman estuary. Continuous data, collected at 15-minute intervals, included discharge, derived from stage measurements made using a pressure transducer, as well as water temperature, pH, specific conductance, dissolved oxygen, and turbidity, all measured using a water-quality sonde. In addition to the continuous data, a total of 360 discrete water-quality samples, representative of monthly low-flow and targeted storm conditions, were analyzed for suspended sediment and nutrients. Continuous observations gathered by a second water-quality sonde, which was temporarily deployed in 2011 for quality-control purposes, indicated substantial lateral water-quality gradients due to inflow from a nearby tributary, representing about 10 percent of the total gaged area upstream of the sampling location. These lateral gradients introduced a time-varying bias into both the continuous and discrete data, resulting in observations that were at some times representative of water-quality conditions in the main channel and at other times biased towards conditions in the tributary. Despite this limitation, both the continuous and discrete data provided insight into the watershed-scale factors that influence water quality in Mattawoman Creek. Annual precipitation over the study period was representative of the long-term record for southern Maryland. The median value of continuously measured discharge was 25 cubic feet per second (ft3/s), and the maximum observed value was 3,210 ft3/s; there were 498 days, or about 15 percent of the study period, when flow was zero or too low to measure. Continuously measured water temperature followed a seasonal trend characteristic of the geographic setting; the trend in dissolved oxygen was inverted relative to temperature, and reflected nearly saturated conditions year round. Relations between discharge and both pH and specific conductance indicate that stream water can be conceptualized as a mixture of acidic, dilute precipitation with pH-neutral groundwater of higher conductance. Specific conductance data showed a pronounced winter peak in both median and extreme measurements, indicating the influence of road salt. However, this influence is minor relative to that observed in the Northeast Branch Anacostia River (U.S. Geological Survey station number 01649500), a nearby, more heavily urbanized comparison basin. The median suspended-sediment concentration in discrete samples was 24 milligrams per liter (mg/L), with minimum and maximum concentrations of 1 mg/L and 2,890 mg/L, respectively. Total nitrogen ranged from 0.21 mg/L to 4.09 mg/L, with a median of 0.69 mg/L; total phosphorus ranged from less than 0.01 mg/L to 0.98 mg/L, with a median of 0.07 mg/L. Total nitrogen was dominated by the dissolved organic fraction (49 percent based on median species concentrations); total phosphorus was predominantly particulate (70 percent). Seasonal trends in suspended-sediment concentration indicate a supply subsidy in late winter and spring; this could be linked to flood-plain interaction, mobilization of sediment from the channel or banks, or anthropogenic input. Seasonal trends for both total phosphorus and total nitrogen generally corresponded to seasonal trends for suspended sediment, indicating a common underlying physical control, likely acting in synchrony with seasonal biological controls on total nutrient concentrations. Speciation of phosphorus, including proportional concentration of the biologically available dissolved inorganic fraction, did not vary seasonally. The speciation of nitrogen reflected demand for inorganic nitrogen and associated transformation into organic nitrogen during the growing season. Stepwise regression models were developed, using continuous data corresponding to collection times for discrete samples as candidate surrogates for suspended sediment, total phosphorus, and total nitrogen. Turbidity and discharge were both included in the model for suspended sediment (R2 = 0.76, n = 185); only turbidity was selected as a robust predictor of total phosphorus and nitrogen (R2 = 0.68 and 0.61, respectively, n = 186 for both). Loads of sediment and nutrients to the downstream Mattawoman estuary were computed using the U.S. Geological Survey computer program LOADEST. Load estimation included comparison of a routinely applied seven-parameter regression model based on time, season, and discharge, with an eight-parameter model that also includes turbidity. Adding turbidity decreased total load estimates, based on hourly data for a fixed 2-month period, by 21, 8, and 3 percent for suspended sediment, total phosphorus, and total nitrogen, respectively, in addition to decreasing the standard error of prediction for all three constituents. The seasonal pattern in specific conductance, reflecting road salt application, is the strongest evidence of the effect of upstream development on water quality at Mattawoman Creek. Accordingly, ongoing continuous monitoring for trends in specific conductance would be the most reliable means of detecting further degradation associated with increased development.

Application of Markov Models for Analysis of Development of Psychological Characteristics

ERIC Educational Resources Information Center

Kuravsky, Lev S.; Malykh, Sergey B.

2004-01-01

A technique to study combined influence of environmental and genetic factors on the base of changes in phenotype distributions is presented. Histograms are exploited as base analyzed characteristics. A continuous time, discrete state Markov process with piece-wise constant interstate transition rates is associated with evolution of each histogram.…

29 CFR 1987.108 - Role of Federal agencies.

Code of Federal Regulations, 2014 CFR

2014-07-01

... (CONTINUED) PROCEDURES FOR HANDLING RETALIATION COMPLAINTS UNDER SECTION 402 OF THE FDA FOOD SAFETY...) The FDA, if interested in a proceeding, may participate as amicus curiae at any time in the proceeding, at the FDA's discretion. At the request of the FDA, copies of all documents in a case must be sent to...

Discrete wavelet transform and energy eigen value for rotor bars fault detection in variable speed field-oriented control of induction motor drive.

PubMed

Ameid, Tarek; Menacer, Arezki; Talhaoui, Hicham; Azzoug, Youness

2018-05-03

This paper presents a methodology for the broken rotor bars fault detection is considered when the rotor speed varies continuously and the induction machine is controlled by Field-Oriented Control (FOC). The rotor fault detection is obtained by analyzing a several mechanical and electrical quantities (i.e., rotor speed, stator phase current and output signal of the speed regulator) by the Discrete Wavelet Transform (DWT) in variable speed drives. The severity of the fault is obtained by stored energy calculation for active power signal. Hence, it can be a useful solution as fault indicator. The FOC is implemented in order to preserve a good performance speed control; to compensate the broken rotor bars effect in the mechanical speed and to ensure the operation continuity and to investigate the fault effect in the variable speed. The effectiveness of the technique is evaluated in simulation and in a real-time implementation by using Matlab/Simulink with the real-time interface (RTI) based on dSpace 1104 board. Copyright © 2018. Published by Elsevier Ltd.

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Ewald Electrostatics for Mixtures of Point and Continuous Line Charges.

PubMed

Antila, Hanne S; Tassel, Paul R Van; Sammalkorpi, Maria

2015-10-15

Many charged macro- or supramolecular systems, such as DNA, are approximately rod-shaped and, to the lowest order, may be treated as continuous line charges. However, the standard method used to calculate electrostatics in molecular simulation, the Ewald summation, is designed to treat systems of point charges. We extend the Ewald concept to a hybrid system containing both point charges and continuous line charges. We find the calculated force between a point charge and (i) a continuous line charge and (ii) a discrete line charge consisting of uniformly spaced point charges to be numerically equivalent when the separation greatly exceeds the discretization length. At shorter separations, discretization induces deviations in the force and energy, and point charge-point charge correlation effects. Because significant computational savings are also possible, the continuous line charge Ewald method presented here offers the possibility of accurate and efficient electrostatic calculations.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions

DTIC Science & Technology

2014-10-09

problems for stochastic partial differential equations driven by fractional Brownian motions are explicitly solved. For the control of a continuous time...linear systems with Brownian motion or a discrete time linear system with a white Gaussian noise and costs 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 stochastic optimal control, fractional Brownian motion , stochastic

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

NASA Astrophysics Data System (ADS)

Delay, Frederick; Badri, Hamid; Fahs, Marwan; Ackerer, Philippe

2017-12-01

Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays

NASA Astrophysics Data System (ADS)

Churilov, Alexander N.; Medvedev, Alexander; Zhusubaliyev, Zhanybai T.

A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis.

The effects of voice and manual control mode on dual task performance

NASA Technical Reports Server (NTRS)

Wickens, C. D.; Zenyuh, J.; Culp, V.; Marshak, W.

1986-01-01

Two fundamental principles of human performance, compatibility and resource competition, are combined with two structural dichotomies in the human information processing system, manual versus voice output, and left versus right cerebral hemisphere, in order to predict the optimum combination of voice and manual control with either hand, for time-sharing performance of a dicrete and continuous task. Eight right handed male subjected performed a discrete first-order tracking task, time-shared with an auditorily presented Sternberg Memory Search Task. Each task could be controlled by voice, or by the left or right hand, in all possible combinations except for a dual voice mode. When performance was analyzed in terms of a dual-task decrement from single task control conditions, the following variables influenced time-sharing efficiency in diminishing order of magnitude, (1) the modality of control, (discrete manual control of tracking was superior to discrete voice control of tracking and the converse was true with the memory search task), (2) response competition, (performance was degraded when both tasks were responded manually), (3) hemispheric competition, (performance degraded whenever two tasks were controlled by the left hemisphere) (i.e., voice or right handed control). The results confirm the value of predictive models invoice control implementation.

Discrete particle swarm optimization to solve multi-objective limited-wait hybrid flow shop scheduling problem

NASA Astrophysics Data System (ADS)

Santosa, B.; Siswanto, N.; Fiqihesa

2018-04-01

This paper proposes a discrete Particle Swam Optimization (PSO) to solve limited-wait hybrid flowshop scheduing problem with multi objectives. Flow shop schedulimg represents the condition when several machines are arranged in series and each job must be processed at each machine with same sequence. The objective functions are minimizing completion time (makespan), total tardiness time, and total machine idle time. Flow shop scheduling model always grows to cope with the real production system accurately. Since flow shop scheduling is a NP-Hard problem then the most suitable method to solve is metaheuristics. One of metaheuristics algorithm is Particle Swarm Optimization (PSO), an algorithm which is based on the behavior of a swarm. Originally, PSO was intended to solve continuous optimization problems. Since flow shop scheduling is a discrete optimization problem, then, we need to modify PSO to fit the problem. The modification is done by using probability transition matrix mechanism. While to handle multi objectives problem, we use Pareto Optimal (MPSO). The results of MPSO is better than the PSO because the MPSO solution set produced higher probability to find the optimal solution. Besides the MPSO solution set is closer to the optimal solution

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Finite State Models of Manned Systems: Validation, Simplification, and Extension.

DTIC Science & Technology

1979-11-01

model a time set is needed. A time set is some set T together with a binary relation defined on T which linearly orders the set. If "model time" is...discrete, so is T ; continuous time is represented by a set corresponding to a subset of the non-negative real numbers. In the following discussion time...defined as sequences, over time, of input and outIut values. The notion of sequences or trajectories is formalized as: AT = xx: T -- Al BT = tyIy: T -4BJ AT

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

On the design of henon and logistic map-based random number generator

NASA Astrophysics Data System (ADS)

Magfirawaty; Suryadi, M. T.; Ramli, Kalamullah

2017-10-01

The key sequence is one of the main elements in the cryptosystem. True Random Number Generators (TRNG) method is one of the approaches to generating the key sequence. The randomness source of the TRNG divided into three main groups, i.e. electrical noise based, jitter based and chaos based. The chaos based utilizes a non-linear dynamic system (continuous time or discrete time) as an entropy source. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. The principle of the design consists of combining 2D and 1D chaotic systems. A mathematical model is implemented for numerical simulations. We used comparator process as a harvester method to obtain the series of random bits. Without any post processing, the proposed design generated random bit sequence with high entropy value and passed all NIST 800.22 statistical tests.

Entropy production of doubly stochastic quantum channels

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

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less

A discrete Markov metapopulation model for persistence and extinction of species.

PubMed

Thompson, Colin J; Shtilerman, Elad; Stone, Lewi

2016-09-07

A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. Copyright © 2016 Elsevier Ltd. All rights reserved.

A new discrete dipole kernel for quantitative susceptibility mapping.

PubMed

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

Task Space Angular Velocity Blending for Real-Time Trajectory Generation

NASA Technical Reports Server (NTRS)

Volpe, Richard A. (Inventor)

1997-01-01

The invention is embodied in a method of controlling a robot manipulator moving toward a target frame F(sub 0) with a target velocity v(sub 0) including a linear target velocity v and an angular target velocity omega(sub 0) to smoothly and continuously divert the robot manipulator to a subsequent frame F(sub 1) by determining a global transition velocity v(sub 1), the global transition velocity including a linear transition velocity v(sub 1) and an angular transition velocity omega(sub 1), defining a blend time interval 2(tau)(sub 0) within which the global velocity of the robot manipulator is to be changed from a global target velocity v(sub 0) to the global transition velocity v(sub 1) and dividing the blend time interval 2(tau)(sub 0) into discrete time segments (delta)t. During each one of the discrete time segments delta t of the blend interval 2(tau)(sub 0), a blended global velocity v of the manipulator is computed as a blend of the global target velocity v(sub 0) and the global transition velocity v(sub 1), the blended global velocity v including a blended angular velocity omega and a blended linear velocity v, and then, the manipulator is rotated by an incremental rotation corresponding to an integration of the blended angular velocity omega over one discrete time segment (delta)t.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Opening up closure. Semiotics across scales

PubMed

Lemke

2000-01-01

The dynamic emergence of new levels of organization in complex systems is related to the semiotic reorganization of discrete/continuous variety at the level below as continuous/discrete meaning for the level above. In this view both the semiotic and the dynamic closure of system levels is reopened to allow the development and evolution of greater complexity.

Discrete-State and Continuous Models of Recognition Memory: Testing Core Properties under Minimal Assumptions

ERIC Educational Resources Information Center

Kellen, David; Klauer, Karl Christoph

2014-01-01

A classic discussion in the recognition-memory literature concerns the question of whether recognition judgments are better described by continuous or discrete processes. These two hypotheses are instantiated by the signal detection theory model (SDT) and the 2-high-threshold model, respectively. Their comparison has almost invariably relied on…

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Distinguishing Continuous and Discrete Approaches to Multilevel Mixture IRT Models: A Model Comparison Perspective

ERIC Educational Resources Information Center

Zhu, Xiaoshu

2013-01-01

The current study introduced a general modeling framework, multilevel mixture IRT (MMIRT) which detects and describes characteristics of population heterogeneity, while accommodating the hierarchical data structure. In addition to introducing both continuous and discrete approaches to MMIRT, the main focus of the current study was to distinguish…

Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation.

PubMed

Leverrier, Anthony; Grangier, Philippe

2009-05-08

We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.

Estimating the proportion of true null hypotheses when the statistics are discrete.

PubMed

Dialsingh, Isaac; Austin, Stefanie R; Altman, Naomi S

2015-07-15

In high-dimensional testing problems π0, the proportion of null hypotheses that are true is an important parameter. For discrete test statistics, the P values come from a discrete distribution with finite support and the null distribution may depend on an ancillary statistic such as a table margin that varies among the test statistics. Methods for estimating π0 developed for continuous test statistics, which depend on a uniform or identical null distribution of P values, may not perform well when applied to discrete testing problems. This article introduces a number of π0 estimators, the regression and 'T' methods that perform well with discrete test statistics and also assesses how well methods developed for or adapted from continuous tests perform with discrete tests. We demonstrate the usefulness of these estimators in the analysis of high-throughput biological RNA-seq and single-nucleotide polymorphism data. implemented in R. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Conceptual structure and the procedural affordances of rational numbers: relational reasoning with fractions and decimals.

PubMed

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

2015-02-01

The standard number system includes several distinct types of notations, which differ conceptually and afford different procedures. Among notations for rational numbers, the bipartite format of fractions (a/b) enables them to represent 2-dimensional relations between sets of discrete (i.e., countable) elements (e.g., red marbles/all marbles). In contrast, the format of decimals is inherently 1-dimensional, expressing a continuous-valued magnitude (i.e., proportion) but not a 2-dimensional relation between sets of countable elements. Experiment 1 showed that college students indeed view these 2-number notations as conceptually distinct. In a task that did not involve mathematical calculations, participants showed a strong preference to represent partitioned displays of discrete objects with fractions and partitioned displays of continuous masses with decimals. Experiment 2 provided evidence that people are better able to identify and evaluate ratio relationships using fractions than decimals, especially for discrete (or discretized) quantities. Experiments 3 and 4 found a similar pattern of performance for a more complex analogical reasoning task. When solving relational reasoning problems based on discrete or discretized quantities, fractions yielded greater accuracy than decimals; in contrast, when quantities were continuous, accuracy was lower for both symbolic notations. Whereas previous research has established that decimals are more effective than fractions in supporting magnitude comparisons, the present study reveals that fractions are relatively advantageous in supporting relational reasoning with discrete (or discretized) concepts. These findings provide an explanation for the effectiveness of natural frequency formats in supporting some types of reasoning, and have implications for teaching of rational numbers.

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

PubMed

Frasca, Mattia; Sharkey, Kieran J

2016-06-21

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Imaging Through Random Discrete-Scatterer Dispersive Media

DTIC Science & Technology

2015-08-27

to that of a conventional, continuous, linear - frequency-modulated chirped signal [3]. Chirped train signals are a particular realization of a class of...continuous chirp signals, characterized by linear frequency modulation [3], we assume the time instances tn to be given by 1 tn = τg ( 1− βg n 2Ng ) n...kernel Dn(z) [9] by sincN (z) = (N + 1)−1DN/2(2πz/N). DISTRIBUTION A: Distribution approved for public release. 4 We use the elementary identity5 π sin

The graphical brain: Belief propagation and active inference

PubMed Central

Friston, Karl J.; Parr, Thomas; de Vries, Bert

2018-01-01

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium. Author Summary This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain. PMID:29417960

Non-verbal numerical cognition: from reals to integers.

PubMed

Gallistel; Gelman

2000-02-01

Data on numerical processing by verbal (human) and non-verbal (animal and human) subjects are integrated by the hypothesis that a non-verbal counting process represents discrete (countable) quantities by means of magnitudes with scalar variability. These appear to be identical to the magnitudes that represent continuous (uncountable) quantities such as duration. The magnitudes representing countable quantity are generated by a discrete incrementing process, which defines next magnitudes and yields a discrete ordering. In the case of continuous quantities, the continuous accumulation process does not define next magnitudes, so the ordering is also continuous ('dense'). The magnitudes representing both countable and uncountable quantity are arithmetically combined in, for example, the computation of the income to be expected from a foraging patch. Thus, on the hypothesis presented here, the primitive machinery for arithmetic processing works with real numbers (magnitudes).

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

DOE PAGES

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

2016-10-20

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of timemore » integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.« less

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

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

Carlberg, Kevin Thomas; Barone, Matthew F.; Antil, Harbir

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. Furthermore, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated with residual minimization at the time-continuous level, while LSPG techniques do so at the time-discrete level. This work provides a detailed theoretical and computational comparison of the two techniques for two common classes of timemore » integrators: linear multistep schemes and Runge–Kutta schemes. We present a number of new findings, including conditions under which the LSPG ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and computationally that decreasing the time step does not necessarily decrease the error for the LSPG ROM; instead, the time step should be ‘matched’ to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible-flow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the LSPG reduced-order model by an order of magnitude.« less

21 CFR 862.2160 - Discrete photometric chemistry analyzer for clinical use.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Discrete photometric chemistry analyzer for... AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Laboratory Instruments § 862.2160 Discrete photometric chemistry analyzer for clinical use. (a...

21 CFR 862.2160 - Discrete photometric chemistry analyzer for clinical use.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Discrete photometric chemistry analyzer for... AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Laboratory Instruments § 862.2160 Discrete photometric chemistry analyzer for clinical use. (a...

21 CFR 862.2160 - Discrete photometric chemistry analyzer for clinical use.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Discrete photometric chemistry analyzer for... AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Laboratory Instruments § 862.2160 Discrete photometric chemistry analyzer for clinical use. (a...

21 CFR 862.2160 - Discrete photometric chemistry analyzer for clinical use.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Discrete photometric chemistry analyzer for... AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Laboratory Instruments § 862.2160 Discrete photometric chemistry analyzer for clinical use. (a...

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

Chen, Chuchu, E-mail: chenchuchu@lsec.cc.ac.cn; Hong, Jialin, E-mail: hjl@lsec.cc.ac.cn; Zhang, Liying, E-mail: lyzhang@lsec.cc.ac.cn

Stochastic Maxwell equations with additive noise are a system of stochastic Hamiltonian partial differential equations intrinsically, possessing the stochastic multi-symplectic conservation law. It is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic Maxwell equations with additive noise preserves the divergence in the sense of expectation. Moreover, we propose three novel stochastic multi-symplectic methods to discretize stochastic Maxwell equations in order to investigate the preservation of these properties numerically. We make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the correspondingmore » discrete version of the averaged divergence. Meanwhile, we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method. Especially, the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case. Numerical experiments are performed to verify our theoretical results.« less

Energy-modeled flight in a wind field

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

Feldman, M.A.; Cliff, E.M.

Optimal shaping of aerospace trajectories has provided the motivation for much modern study of optimization theory and algorithms. Current industrial practice favors approaches where the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP) by a discretization process. Two such formulations are implemented in the POST and the OTIS codes. In the present paper we use a discretization that is specially adapted to the flight problem of interest. Among the unique aspects of the present discretization are: a least-squares formulation for certain kinematic constraints; the use of an energy ideas to enforce Newton`s Laws; and, themore » inclusion of large magnitude horizontal winds. In the next section we shall provide a description of the flight problem and its NLP representation. Following this we provide some details of the constraint formulation. Finally, we present an overview of the NLP problem.« less

Cone penetrometer testing and discrete-depth ground water sampling techniques: A cost-effective method of site characterization in a multiple-aquifer setting

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

Zemo, D.A.; Pierce, Y.G.; Gallinatti, J.D.

Cone penetrometer testing (CPT), combined with discrete-depth ground water sampling methods, can significantly reduce the time and expense required to characterize large sites that have multiple aquifers. Results from the screening site characterization can then be used to design and install a cost-effective monitoring well network. At a site in northern California, it was necessary to characterize the stratigraphy and the distribution of volatile organic compounds (VOCs). To expedite characterization, a five-week field screening program was implemented that consisted of a shallow ground water survey, CPT soundings and pore-pressure measurements, and discrete-depth ground water sampling. Based on continuous lithologic informationmore » provided by the CPT soundings, four predominantly coarse-grained, water yielding stratigraphic packages were identified. Seventy-nine discrete-depth ground water samples were collected using either shallow ground water survey techniques, the BAT Enviroprobe, or the QED HydroPunch I, depending on subsurface conditions. Using results from these efforts, a 20-well monitoring network was designed and installed to monitor critical points within each stratigraphic package. Good correlation was found for hydraulic head and chemical results between discrete-depth screening data and monitoring well data. Understanding the vertical VOC distribution and concentrations produced substantial time and cost savings by minimizing the number of permanent monitoring wells and reducing the number of costly conductor casings that had to be installed. Additionally, significant long-term cost savings will result from reduced sampling costs, because fewer wells comprise the monitoring network. The authors estimate these savings to be 50% for site characterization costs, 65% for site characterization time, and 60% for long-term monitoring costs.« less

The Effects of Time Advance Mechanism on Simple Agent Behaviors in Combat Simulations

DTIC Science & Technology

2011-12-01

modeling packages that illustrate the differences between discrete-time simulation (DTS) and discrete-event simulation ( DES ) methodologies. Many combat... DES ) models , often referred to as “next-event” (Law and Kelton 2000) or discrete time simulation (DTS), commonly referred to as “time-step.” DTS...discrete-time simulation (DTS) and discrete-event simulation ( DES ) methodologies. Many combat models use DTS as their simulation time advance mechanism

Concentration and Velocity Measurements of Both Phases in Liquid-Solid Slurries

NASA Astrophysics Data System (ADS)

Altobelli, Stephen; Hill, Kimberly; Caprihan, Arvind

2007-03-01

Natural and industrial slurry flows abound. They are difficult to calculate and to measure. We demonstrate a simple technique for studying steady slurries. We previously used time-of-flight techniques to study pressure driven slurry flow in pipes. Only the continuous phase velocity and concentration fields were measured. The discrete phase concentration was inferred. In slurries composed of spherical, oil-filled pills and poly-methyl-siloxane oils, we were able to use inversion nulling to measure the concentration and velocity fields of both phases. Pills are available in 1-5mm diameter and silicone oils are available in a wide range of viscosities, so a range of flows can be studied. We demonstrated the technique in horizontal, rotating cylinder flows. We combined two tried and true methods to do these experiments. The first used the difference in T1 to select between phases. The second used gradient waveforms with controlled first moments to produce velocity dependent phase shifts. One novel processing method was developed that allows us to use static continuous phase measurements to reference both the continuous and discrete phase velocity images. ?

MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

PubMed

Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

2012-01-01

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

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

Khrennikov, Andrei; Volovich, Yaroslav

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (butmore » discrete time{exclamation_point}) dynamics is compatible with discrete energy levels.« less

Computing Science and Statistics. Volume 24. Graphics and Visualization

DTIC Science & Technology

1993-03-01

the dough , turbulent fluid flow, the time between drips of behavior changes radically when the population growth water from a faucet, Brownian motion... cookie which clearly is the discrete parameter analogue of continuous param- appropriate as after dinner fun. eter time series analysis". I strongly...methods. Your fortune cookie of the night reads: One problem that statisticians traditionally seem to "uYou have good friends who will come to your aid in

Mechanisms of chaos in billiards: dispersing, defocusing and nothing else

NASA Astrophysics Data System (ADS)

Bunimovich, Leonid A.

2018-02-01

We explain and justify that the only mechanisms of chaotic dynamics for billiards are dispersing and defocusing. We also introduce boomerang billiards which dynamics demonstrate that two rather broadly accepted views about some features of nonlinear dynamics are actually wrong. Namely correlations in billiards having focusing components of the boundary can decay exponentially, and continuous time correlations for a billiard flow may decay faster than discrete time correlations for a billiard map.

Discrete Latent Markov Models for Normally Distributed Response Data

ERIC Educational Resources Information Center

Schmittmann, Verena D.; Dolan, Conor V.; van der Maas, Han L. J.; Neale, Michael C.

2005-01-01

Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These…

School Psychology Crossroads in America: Discrepancies between Actual and Preferred Discrete Practices and Barriers to Preferred Practice

ERIC Educational Resources Information Center

Filter, Kevin J.; Ebsen, Sara; Dibos, Rebecca

2013-01-01

A nationally representative sample of American school psychology practitioners were surveyed to analyze discrepancies that they experience between their actual discrete practices and their preferred discrete practices relative to several domains of practice including assessment, intervention, meetings, and continuing education. Discrepancies were…

Current Density and Continuity in Discretized Models

ERIC Educational Resources Information Center

Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…

A Continuous Square Root in Formation Filter-Swoother with Discrete Data Update

NASA Technical Reports Server (NTRS)

Miller, J. K.

1994-01-01

A differential equation for the square root information matrix is derived and adapted to the problems of filtering and smoothing. The resulting continuous square root information filter (SRIF) performs the mapping of state and process noise by numerical integration of the SRIF matrix and admits data via a discrete least square update.

Prompting Children to Reason Proportionally: Processing Discrete Units as Continuous Amounts

ERIC Educational Resources Information Center

Boyer, Ty W.; Levine, Susan C.

2015-01-01

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests…

The Reliability and Validity of Discrete and Continuous Measures of Psychopathology: A Quantitative Review

ERIC Educational Resources Information Center

Markon, Kristian E.; Chmielewski, Michael; Miller, Christopher J.

2011-01-01

In 2 meta-analyses involving 58 studies and 59,575 participants, we quantitatively summarized the relative reliability and validity of continuous (i.e., dimensional) and discrete (i.e., categorical) measures of psychopathology. Overall, results suggest an expected 15% increase in reliability and 37% increase in validity through adoption of a…

Multisource Data Classification Using A Hybrid Semi-supervised Learning Scheme

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

Vatsavai, Raju; Bhaduri, Budhendra L; Shekhar, Shashi

2009-01-01

In many practical situations thematic classes can not be discriminated by spectral measurements alone. Often one needs additional features such as population density, road density, wetlands, elevation, soil types, etc. which are discrete attributes. On the other hand remote sensing image features are continuous attributes. Finding a suitable statistical model and estimation of parameters is a challenging task in multisource (e.g., discrete and continuous attributes) data classification. In this paper we present a semi-supervised learning method by assuming that the samples were generated by a mixture model, where each component could be either a continuous or discrete distribution. Overall classificationmore » accuracy of the proposed method is improved by 12% in our initial experiments.« less

Fast-slow asymptotics for a Markov chain model of fast sodium current

NASA Astrophysics Data System (ADS)

Starý, Tomáš; Biktashev, Vadim N.

2017-09-01

We explore the feasibility of using fast-slow asymptotics to eliminate the computational stiffness of discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a Markov chain model of fast sodium current, and investigate its asymptotic behaviour with respect to small parameters identified in different ways.

Cavity master equation for the continuous time dynamics of discrete-spin models.

PubMed

Aurell, E; Del Ferraro, G; Domínguez, E; Mulet, R

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Cavity master equation for the continuous time dynamics of discrete-spin models

NASA Astrophysics Data System (ADS)

Aurell, E.; Del Ferraro, G.; Domínguez, E.; Mulet, R.

2017-05-01

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Algorithms for Maneuvering Spacecraft Around Small Bodies

NASA Technical Reports Server (NTRS)

Acikmese, A. Bechet; Bayard, David

2006-01-01

A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.

Hybrid Markov-mass action law model for cell activation by rare binding events: Application to calcium induced vesicular release at neuronal synapses.

PubMed

Guerrier, Claire; Holcman, David

2016-10-18

Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Research and implementation of simulation for TDICCD remote sensing in vibration of optical axis

NASA Astrophysics Data System (ADS)

Liu, Zhi-hong; Kang, Xiao-jun; Lin, Zhe; Song, Li

2013-12-01

During the exposure time, the charge transfer speed in the push-broom direction and the line-by-lines canning speed of the sensor are required to match each other strictly for a space-borne TDICCD push-broom camera. However, as attitude disturbance of satellite and vibration of camera are inevitable, it is impossible to eliminate the speed mismatch, which will make the signal of different targets overlay each other and result in a decline of image resolution. The effects of velocity mismatch will be visually observed and analyzed by simulating the degradation of image quality caused by the vibration of the optical axis, and it is significant for the evaluation of image quality and design of the image restoration algorithm. How to give a model in time domain and space domain during the imaging time is the problem needed to be solved firstly. As vibration information for simulation is usually given by a continuous curve, the pixels of original image matrix and sensor matrix are discrete, as a result, they cannot always match each other well. The effect of simulation will also be influenced by the discrete sampling in integration time. In conclusion, it is quite significant for improving simulation accuracy and efficiency to give an appropriate discrete modeling and simulation method. The paper analyses discretization schemes in time domain and space domain and presents a method to simulate the quality of image of the optical system in the vibration of the line of sight, which is based on the principle of TDICCD sensor. The gray value of pixels in sensor matrix is obtained by a weighted arithmetic, which solves the problem of pixels dismatch. The result which compared with the experiment of hardware test indicate that this simulation system performances well in accuracy and reliability.

Modelling heat transfer during flow through a random packed bed of spheres

NASA Astrophysics Data System (ADS)

Burström, Per E. C.; Frishfelds, Vilnis; Ljung, Anna-Lena; Lundström, T. Staffan; Marjavaara, B. Daniel

2018-04-01

Heat transfer in a random packed bed of monosized iron ore pellets is modelled with both a discrete three-dimensional system of spheres and a continuous Computational Fluid Dynamics (CFD) model. Results show a good agreement between the two models for average values over a cross section of the bed for an even temperature profiles at the inlet. The advantage with the discrete model is that it captures local effects such as decreased heat transfer in sections with low speed. The disadvantage is that it is computationally heavy for larger systems of pellets. If averaged values are sufficient, the CFD model is an attractive alternative that is easy to couple to the physics up- and downstream the packed bed. The good agreement between the discrete and continuous model furthermore indicates that the discrete model may be used also on non-Stokian flow in the transitional region between laminar and turbulent flow, as turbulent effects show little influence of the overall heat transfer rates in the continuous model.

Patient flow improvement for an ophthalmic specialist outpatient clinic with aid of discrete event simulation and design of experiment.

PubMed

Pan, Chong; Zhang, Dali; Kon, Audrey Wan Mei; Wai, Charity Sue Lea; Ang, Woo Boon

2015-06-01

Continuous improvement in process efficiency for specialist outpatient clinic (SOC) systems is increasingly being demanded due to the growth of the patient population in Singapore. In this paper, we propose a discrete event simulation (DES) model to represent the patient and information flow in an ophthalmic SOC system in the Singapore National Eye Centre (SNEC). Different improvement strategies to reduce the turnaround time for patients in the SOC were proposed and evaluated with the aid of the DES model and the Design of Experiment (DOE). Two strategies for better patient appointment scheduling and one strategy for dilation-free examination are estimated to have a significant impact on turnaround time for patients. One of the improvement strategies has been implemented in the actual SOC system in the SNEC with promising improvement reported.

Implicit Incompressible SPH.

PubMed

Ihmsen, Markus; Cornelis, Jens; Solenthaler, Barbara; Horvath, Christopher; Teschner, Matthias

2013-07-25

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01% can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

Implicit incompressible SPH.

PubMed

Ihmsen, Markus; Cornelis, Jens; Solenthaler, Barbara; Horvath, Christopher; Teschner, Matthias

2014-03-01

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks.

PubMed

Deng, Zhimin; Tian, Tianhai

2014-07-29

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging. To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions. The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Efficient genetic algorithms using discretization scheduling.

PubMed

McLay, Laura A; Goldberg, David E

2005-01-01

In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling.

Decomposition of heterogeneous organic matterand its long-term stabilization in soils

USGS Publications Warehouse

Sierra, Carlos A.; Harmon, Mark E.; Perakis, Steven S.

2011-01-01

Soil organic matter is a complex mixture of material with heterogeneous biological, physical, and chemical properties. Decomposition models represent this heterogeneity either as a set of discrete pools with different residence times or as a continuum of qualities. It is unclear though, whether these two different approaches yield comparable predictions of organic matter dynamics. Here, we compare predictions from these two different approaches and propose an intermediate approach to study organic matter decomposition based on concepts from continuous models implemented numerically. We found that the disagreement between discrete and continuous approaches can be considerable depending on the degree of nonlinearity of the model and simulation time. The two approaches can diverge substantially for predicting long-term processes in soils. Based on our alternative approach, which is a modification of the continuous quality theory, we explored the temporal patterns that emerge by treating substrate heterogeneity explicitly. The analysis suggests that the pattern of carbon mineralization over time is highly dependent on the degree and form of nonlinearity in the model, mostly expressed as differences in microbial growth and efficiency for different substrates. Moreover, short-term stabilization and destabilization mechanisms operating simultaneously result in long-term accumulation of carbon characterized by low decomposition rates, independent of the characteristics of the incoming litter. We show that representation of heterogeneity in the decomposition process can lead to substantial improvements in our understanding of carbon mineralization and its long-term stability in soils.

How parasitism affects critical patch-size in a host-parasitoid model: application to the forest tent caterpillar.

PubMed

Cobbold, C A; Lewis, M A; Lutscher, F; Roland, J

2005-03-01

Habitat structure has broad impacts on many biological systems. In particular, habitat fragmentation can increase the probability of species extinction and on the other hand it can lead to population outbreaks in response to a decline in natural enemies. An extreme consequence of fragmentation is the isolation of small regions of suitable habitat surrounded by a large region of hostile matrix. This scenario can be interpreted as a critical patch-size problem, well studied in a continuous time framework, but relatively new to discrete time models. In this paper we present an integrodifference host-parasitoid model, discrete in time and continuous in space, to study how the critical habitat-size necessary for parasitoid survival changes in response to parasitoid life history traits, such as emergence time. We show that early emerging parasitoids may be able to persist in smaller habitats than late emerging species. The model predicts that these early emerging parasitoids lead to more severe host outbreaks. We hypothesise that promoting efficient late emerging parasitoids may be key in reducing outbreak severity, an approach requiring large continuous regions of suitable habitat. We parameterise the model for the host species of the forest tent caterpillar Malacosoma disstria Hbn., a pest insect for which fragmented landscape increases the severity of outbreaks. This host is known to have several parasitoids, due to paucity of data and as a first step in the modelling we consider a single generic parasitoid. The model findings are related to observations of the forest tent caterpillar offering insight into this host-parasitoid response to habitat structure.

Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data.

PubMed

de Haan-Rietdijk, Silvia; Voelkle, Manuel C; Keijsers, Loes; Hamaker, Ellen L

2017-01-01

The Experience Sampling Method is a common approach in psychological research for collecting intensive longitudinal data with high ecological validity. One characteristic of ESM data is that it is often unequally spaced, because the measurement intervals within a day are deliberately varied, and measurement continues over several days. This poses a problem for discrete-time (DT) modeling approaches, which are based on the assumption that all measurements are equally spaced. Nevertheless, DT approaches such as (vector) autoregressive modeling are often used to analyze ESM data, for instance in the context of affective dynamics research. There are equivalent continuous-time (CT) models, but they are more difficult to implement. In this paper we take a pragmatic approach and evaluate the practical relevance of the violated model assumption in DT AR(1) and VAR(1) models, for the N = 1 case. We use simulated data under an ESM measurement design to investigate the bias in the parameters of interest under four different model implementations, ranging from the true CT model that accounts for all the exact measurement times, to the crudest possible DT model implementation, where even the nighttime is treated as a regular interval. An analysis of empirical affect data illustrates how the differences between DT and CT modeling can play out in practice. We find that the size and the direction of the bias in DT (V)AR models for unequally spaced ESM data depend quite strongly on the true parameter in addition to data characteristics. Our recommendation is to use CT modeling whenever possible, especially now that new software implementations have become available.

Discrete- vs. Continuous-Time Modeling of Unequally Spaced Experience Sampling Method Data

PubMed Central

de Haan-Rietdijk, Silvia; Voelkle, Manuel C.; Keijsers, Loes; Hamaker, Ellen L.

2017-01-01

The Experience Sampling Method is a common approach in psychological research for collecting intensive longitudinal data with high ecological validity. One characteristic of ESM data is that it is often unequally spaced, because the measurement intervals within a day are deliberately varied, and measurement continues over several days. This poses a problem for discrete-time (DT) modeling approaches, which are based on the assumption that all measurements are equally spaced. Nevertheless, DT approaches such as (vector) autoregressive modeling are often used to analyze ESM data, for instance in the context of affective dynamics research. There are equivalent continuous-time (CT) models, but they are more difficult to implement. In this paper we take a pragmatic approach and evaluate the practical relevance of the violated model assumption in DT AR(1) and VAR(1) models, for the N = 1 case. We use simulated data under an ESM measurement design to investigate the bias in the parameters of interest under four different model implementations, ranging from the true CT model that accounts for all the exact measurement times, to the crudest possible DT model implementation, where even the nighttime is treated as a regular interval. An analysis of empirical affect data illustrates how the differences between DT and CT modeling can play out in practice. We find that the size and the direction of the bias in DT (V)AR models for unequally spaced ESM data depend quite strongly on the true parameter in addition to data characteristics. Our recommendation is to use CT modeling whenever possible, especially now that new software implementations have become available. PMID:29104554

Stabilization and robustness of non-linear unity-feedback system - Factorization approach

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Kabuli, M. G.

1988-01-01

The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.

Judgement of discrete and continuous quantity in adults: number counts!

PubMed

Nys, Julie; Content, Alain

2012-01-01

Three experiments involving a Stroop-like paradigm were conducted. In Experiment 1, adults received a number comparison task in which large sets of dots, orthogonally varying along a discrete dimension (number of dots) and a continuous dimension (cumulative area), were presented. Incongruent trials were processed more slowly and with less accuracy than congruent trials, suggesting that continuous dimensions such as cumulative area are automatically processed and integrated during a discrete quantity judgement task. Experiment 2, in which adults were asked to perform area comparison on the same stimuli, revealed the reciprocal interference from number on the continuous quantity judgements. Experiment 3, in which participants received both the number and area comparison tasks, confirmed the results of Experiments 1 and 2. Contrasting with earlier statements, the results support the view that number acts as a more salient cue than continuous dimensions in adults. Furthermore, the individual predisposition to automatically access approximate number representations was found to correlate significantly with adults' exact arithmetical skills.

Lindley frailty model for a class of compound Poisson processes

NASA Astrophysics Data System (ADS)

Kadilar, Gamze Özel; Ata, Nihal

2013-10-01

The Lindley distribution gain importance in survival analysis for the similarity of exponential distribution and allowance for the different shapes of hazard function. Frailty models provide an alternative to proportional hazards model where misspecified or omitted covariates are described by an unobservable random variable. Despite of the distribution of the frailty is generally assumed to be continuous, it is appropriate to consider discrete frailty distributions In some circumstances. In this paper, frailty models with discrete compound Poisson process for the Lindley distributed failure time are introduced. Survival functions are derived and maximum likelihood estimation procedures for the parameters are studied. Then, the fit of the models to the earthquake data set of Turkey are examined.

Sparse spikes super-resolution on thin grids II: the continuous basis pursuit

NASA Astrophysics Data System (ADS)

Duval, Vincent; Peyré, Gabriel

2017-09-01

This article analyzes the performance of the continuous basis pursuit (C-BP) method for sparse super-resolution. The C-BP has been recently proposed by Ekanadham, Tranchina and Simoncelli as a refined discretization scheme for the recovery of spikes in inverse problems regularization. One of the most well known discretization scheme, the basis pursuit (BP, also known as \

A Bell-Curved Based Algorithm for Mixed Continuous and Discrete Structural Optimization

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.; Weber, Michael; Sobieszczanski-Sobieski, Jaroslaw

2001-01-01

An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (mu + mu) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on 2-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).

A 24 km fiber-based discretely signaled continuous variable quantum key distribution system.

PubMed

Dinh Xuan, Quyen; Zhang, Zheshen; Voss, Paul L

2009-12-21

We report a continuous variable key distribution system that achieves a final secure key rate of 3.45 kilobits/s over a distance of 24.2 km of optical fiber. The protocol uses discrete signaling and post-selection to improve reconciliation speed and quantifies security by means of quantum state tomography. Polarization multiplexing and a frequency translation scheme permit transmission of a continuous wave local oscillator and suppression of noise from guided acoustic wave Brillouin scattering by more than 27 dB.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

The nexus between geopolitical uncertainty and crude oil markets: An entropy-based wavelet analysis

NASA Astrophysics Data System (ADS)

Uddin, Gazi Salah; Bekiros, Stelios; Ahmed, Ali

2018-04-01

The global financial crisis and the subsequent geopolitical turbulence in energy markets have brought increased attention to the proper statistical modeling especially of the crude oil markets. In particular, we utilize a time-frequency decomposition approach based on wavelet analysis to explore the inherent dynamics and the casual interrelationships between various types of geopolitical, economic and financial uncertainty indices and oil markets. Via the introduction of a mixed discrete-continuous multiresolution analysis, we employ the entropic criterion for the selection of the optimal decomposition level of a MODWT as well as the continuous-time coherency and phase measures for the detection of business cycle (a)synchronization. Overall, a strong heterogeneity in the revealed interrelationships is detected over time and across scales.

Identification of a core-periphery structure among participants of a business climate survey. An investigation based on the ZEW survey data

NASA Astrophysics Data System (ADS)

Stolzenburg, U.; Lux, T.

2011-12-01

Processes of social opinion formation might be dominated by a set of closely connected agents who constitute the cohesive `core' of a network and have a higher influence on the overall outcome of the process than those agents in the more sparsely connected `periphery'. Here we explore whether such a perspective could shed light on the dynamics of a well known economic sentiment index. To this end, we hypothesize that the respondents of the survey under investigation form a core-periphery network, and we identify those agents that define the core (in a discrete setting) or the proximity of each agent to the core (in a continuous setting). As it turns out, there is significant correlation between the so identified cores of different survey questions. Both the discrete and the continuous cores allow an almost perfect replication of the original series with a reduced data set of core members or weighted entries according to core proximity. Using a monthly time series on industrial production in Germany, we also compared experts' predictions with the real economic development. The core members identified in the discrete setting showed significantly better prediction capabilities than those agents assigned to the periphery of the network.

Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases

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

Conrady, Florian; Hnybida, Jeff; Department of Physics, University of Waterloo, Waterloo, Ontario

2011-01-15

We derive the matrix elements of generators of unitary irreducible representations of SL(2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1). This is done with regard to a discrete basis diagonalized by J{sup 3} and a continuous basis diagonalized by K{sup 1}, and for both the discrete and continuous series of SU(1,1). For completeness, we also treat the more conventional SU(2) decomposition as a fifth case. The derivation proceeds in a functional/differential framework and exploits the fact that state functions and differential operators have a similar structure in all five cases. The states aremore » defined explicitly and related to SU(1,1) and SU(2) matrix elements.« less

40 CFR 420.111 - Specialized definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... steel products such as coiled wire, rods, and tubes in discrete batches or bundles. (b) The term continuous means those alkaline cleaning operations which process steel products other than in discrete...

Prediction of flow dynamics using point processes

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; Stemler, Thomas; Eroglu, Deniz; Marwan, Norbert

2018-01-01

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

Construction of energy-stable Galerkin reduced order models.

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

Kalashnikova, Irina; Barone, Matthew Franklin; Arunajatesan, Srinivasan

2013-05-01

This report aims to unify several approaches for building stable projection-based reduced order models (ROMs). Attention is focused on linear time-invariant (LTI) systems. The model reduction procedure consists of two steps: the computation of a reduced basis, and the projection of the governing partial differential equations (PDEs) onto this reduced basis. Two kinds of reduced bases are considered: the proper orthogonal decomposition (POD) basis and the balanced truncation basis. The projection step of the model reduction can be done in two ways: via continuous projection or via discrete projection. First, an approach for building energy-stable Galerkin ROMs for linear hyperbolicmore » or incompletely parabolic systems of PDEs using continuous projection is proposed. The idea is to apply to the set of PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. The resulting ROM will be energy-stable for any choice of reduced basis. It is shown that, for many PDE systems, the desired transformation is induced by a special weighted L2 inner product, termed the %E2%80%9Csymmetry inner product%E2%80%9D. Attention is then turned to building energy-stable ROMs via discrete projection. A discrete counterpart of the continuous symmetry inner product, a weighted L2 inner product termed the %E2%80%9CLyapunov inner product%E2%80%9D, is derived. The weighting matrix that defines the Lyapunov inner product can be computed in a black-box fashion for a stable LTI system arising from the discretization of a system of PDEs in space. It is shown that a ROM constructed via discrete projection using the Lyapunov inner product will be energy-stable for any choice of reduced basis. Connections between the Lyapunov inner product and the inner product induced by the balanced truncation algorithm are made. Comparisons are also made between the symmetry inner product and the Lyapunov inner product. The performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.« less

Structure and Randomness of Continuous-Time, Discrete-Event Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2017-10-01

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ɛ -machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.

A brief review of models of DC-DC power electronic converters for analysis of their stability

NASA Astrophysics Data System (ADS)

Siewniak, Piotr; Grzesik, Bogusław

2014-10-01

A brief review of models of DC-DC power electronic converters (PECs) is presented in this paper. It contains the most popular, continuous-time and discrete-time models used for PEC simulation, design, stability analysis and other applications. Both large-signal and small-signal models are considered. Special attention is paid to models that are used in practice for the analysis of the global and local stability of PECs.

Regression Analysis of Mixed Recurrent-Event and Panel-Count Data with Additive Rate Models

PubMed Central

Zhu, Liang; Zhao, Hui; Sun, Jianguo; Leisenring, Wendy; Robison, Leslie L.

2015-01-01

Summary Event-history studies of recurrent events are often conducted in fields such as demography, epidemiology, medicine, and social sciences (Cook and Lawless, 2007; Zhao et al., 2011). For such analysis, two types of data have been extensively investigated: recurrent-event data and panel-count data. However, in practice, one may face a third type of data, mixed recurrent-event and panel-count data or mixed event-history data. Such data occur if some study subjects are monitored or observed continuously and thus provide recurrent-event data, while the others are observed only at discrete times and hence give only panel-count data. A more general situation is that each subject is observed continuously over certain time periods but only at discrete times over other time periods. There exists little literature on the analysis of such mixed data except that published by Zhu et al. (2013). In this paper, we consider the regression analysis of mixed data using the additive rate model and develop some estimating equation-based approaches to estimate the regression parameters of interest. Both finite sample and asymptotic properties of the resulting estimators are established, and the numerical studies suggest that the proposed methodology works well for practical situations. The approach is applied to a Childhood Cancer Survivor Study that motivated this study. PMID:25345405

Theoretical and experimental analysis of amplitude control ablation and bipolar ablation in creating linear lesion and discrete lesions for treating atrial fibrillation.

PubMed

Yan, Shengjie; Wu, Xiaomei; Wang, Weiqi

2017-09-01

Radiofrequency (RF) energy is often used to create a linear lesion or discrete lesions for blocking the accessory conduction pathways for treating atrial fibrillation. By using finite element analysis, we study the ablation effect of amplitude control ablation mode (AcM) and bipolar ablation mode (BiM) in creating a linear lesion and discrete lesions in a 5-mm-thick atrial wall; particularly, the characteristic of lesion shape has been investigated in amplitude control ablation. Computer models of multipolar catheter were developed to study the lesion dimensions in atrial walls created through AcM, BiM and special electrodes activated ablation methods in AcM and BiM. To validate the theoretical results in this study, an in vitro experiment with porcine cardiac tissue was performed. At 40 V/20 V root mean squared (RMS) of the RF voltage for AcM, the continuous and transmural lesion was created by AcM-15s, AcM-5s and AcM-ad-20V ablation in 5-mm-thick atrial wall. At 20 V RMS for BiM, the continuous but not transmural lesion was created. AcM ablation yielded asymmetrical and discrete lesions shape, whereas the lesion shape turned to more symmetrical and continuous as the electrodes alternative activated period decreased from 15 s to 5 s. Two discrete lesions were created when using AcM, AcM-ad-40V, BiM-ad-20V and BiM-ad-40V. The experimental and computational thermal lesion shapes created in cardiac tissue were in agreement. Amplitude control ablation technology and bipolar ablation technology are feasible methods to create continuous lesion or discrete for pulmonary veins isolation.

Continuous methane measurements from a late Holocene Greenland ice core: Atmospheric and in-situ signals

NASA Astrophysics Data System (ADS)

Rhodes, Rachael H.; Faïn, Xavier; Stowasser, Christopher; Blunier, Thomas; Chappellaz, Jérôme; McConnell, Joseph R.; Romanini, Daniele; Mitchell, Logan E.; Brook, Edward J.

2013-04-01

Ancient air trapped inside bubbles in ice cores can now be analysed for methane concentration utilising a laser spectrometer coupled to a continuous melter system. We present a new ultra-high resolution record of atmospheric methane variability over the last 1800 yr obtained from continuous analysis of a shallow ice core from the North Greenland Eemian project (NEEM-2011-S1) during a 4-week laboratory-based measurement campaign. Our record faithfully replicates the form and amplitudes of multi-decadal oscillations previously observed in other ice cores and demonstrates the detailed depth resolution (5.3 cm), rapid acquisition time (30 m day-1) and good long-term reproducibility (2.6%, 2σ) of the continuous measurement technique. In addition, we report the detection of high frequency ice core methane signals of non-atmospheric origin. Firstly, measurements of air from the firn-ice transition region and an interval of ice core dating from 1546-1560 AD (gas age) resolve apparently quasi-annual scale methane oscillations. Traditional gas chromatography measurements on discrete ice samples confirm these signals and indicate peak-to-peak amplitudes of ca. 22 parts per billion (ppb). We hypothesise that these oscillations result from staggered bubble close-off between seasonal layers of contrasting density during time periods of sustained multi-year atmospheric methane change. Secondly, we report the detection of abrupt (20-100 cm depth interval), high amplitude (35-80 ppb excess) methane spikes in the NEEM ice that are reproduced by discrete measurements. We show for the first time that methane spikes present in thin and infrequent layers in polar, glacial ice are accompanied by elevated concentrations of carbon- and nitrogen-based chemical impurities, and suggest that biological in-situ production may be responsible.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1990-01-01

The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

PubMed Central

Liu, Yu-Ying; Li, Shuang; Li, Fuxin; Song, Le; Rehg, James M.

2016-01-01

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset. PMID:27019571

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1992-01-01

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

8 CFR 241.4 - Continued detention of inadmissible, criminal, and other aliens beyond the removal period.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., Notice of Entry of Appearance as Attorney or Representative, at the time of the interview or prior to... Field Office may in his or her discretion schedule a personal or telephonic interview with the alien as... released and reasons therefore. (3) Personal interview. (i) If the HQPDU Director does not accept a panel's...

8 CFR 241.4 - Continued detention of inadmissible, criminal, and other aliens beyond the removal period.

Code of Federal Regulations, 2011 CFR

2011-01-01

..., Notice of Entry of Appearance as Attorney or Representative, at the time of the interview or prior to... Field Office may in his or her discretion schedule a personal or telephonic interview with the alien as... released and reasons therefore. (3) Personal interview. (i) If the HQPDU Director does not accept a panel's...

Velocity locking and pulsed invasions of fragmented habitats with seasonal growth

NASA Astrophysics Data System (ADS)

Korolev, Kirill; Wang, Ching-Hao

From crystal growth to epidemics, spatial spreading is a common mechanism of change in nature. Typically, spreading results from two processes: growth and dispersal in ecology or chemical reactions and diffusion in physics. These two processes combine to produce a reaction-diffusion wave, an invasion front advancing at a constant velocity. We show that the properties of these waves are remarkably different depending whether space and time are continuous, as they are for a chemical reaction, or discrete, as they are for a pest invading a patchy habitat in seasonal climates. For discrete space and time, we report a new type of expansions with velocities that can lock into specific values and become insensitive to changes in dispersal and growth, i.e. the dependence of the velocity on model parameters exhibits plateaus or pauses. As a result, the evolution and response to perturbations in locked expansions can be markedly different compared to the expectations based on continuous models. The phenomenon of velocity locking requires cooperative growth and does not occur when per capita growth rate decline monotonically with population density. We obtain both numerical and analytical results describing highly non-analytic properties of locked expansions.

Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity

NASA Astrophysics Data System (ADS)

Pin, Victor Gómez

In his book about the Categories (that is about the ultimate elements of classification and order), in the chapter concerning the quantity (IV, 20) Aristotle says that this concept recovers two kinds of modalities: the discrete quantity and the continuous quantity and he gives as examples the number for the first one; line, surface, solid, times and space for the second one. The main philosophical problem raised by this text is to determine which of the two modalities of the quantity has the ontological priority over the other (given two concepts A and B, we assume that A has ontological priority over B if every entity that possesses the quality B possesses necessarily the quality A). The problem is magnified by the fact that space, which in some part of Aristotle's Physics is mentioned not only as a category properly speaking but even as the main category whose power can be amazing, is in the evoked text of the Categories's Book reduced to expression of the continuum, and sharing this condition with time. In this matter the controversy is constant through the common history of Science and Philosophy.

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.

Partial reinforcement (acquisition) effects within subjects

PubMed Central

Amsel, Abram; MacKinnon, John R.; Rashotte, Michael E.; Surridge, C. Thomas

1964-01-01

Acquisition performance of 22 rats in a straight alley runway was examined. The animals were subjected to partial reinforcement when the alley was black (B±) and continuous reinforcement when it was white (W+). The results indicated (a) higher terminal performance, for partial as against continuous reinforcement conditions, for starting-time and running-time measures, and (b) lower terminal performance under partial conditions for a goal-entry-time measure. These results confirm within subjects an effect previously demonstrated, in the runway, only in between-groups tests, where one group is run under partial reinforcement and a separate group is run under continuous reinforcement in the presence of the same external stimuli. Differences between the runway situation, employing a discrete-trial procedure and performance measures at three points in the response chain, and the Skinner box situation, used in its free-operant mode with a single performance measure, are discussed in relation to the present findings. PMID:14130088

PARTIAL REINFORCEMENT (ACQUISITION) EFFECTS WITHIN SUBJECTS.

PubMed

AMSEL, A; MACKINNON, J R; RASHOTTE, M E; SURRIDGE, C T

1964-03-01

Acquisition performance of 22 rats in a straight alley runway was examined. The animals were subjected to partial reinforcement when the alley was black (B+/-) and continuous reinforcement when it was white (W+). The results indicated (a) higher terminal performance, for partial as against continuous reinforcement conditions, for starting-time and running-time measures, and (b) lower terminal performance under partial conditions for a goal-entry-time measure. These results confirm within subjects an effect previously demonstrated, in the runway, only in between-groups tests, where one group is run under partial reinforcement and a separate group is run under continuous reinforcement in the presence of the same external stimuli. Differences between the runway situation, employing a discrete-trial procedure and performance measures at three points in the response chain, and the Skinner box situation, used in its free-operant mode with a single performance measure, are discussed in relation to the present findings.

From empirical data to time-inhomogeneous continuous Markov processes.

PubMed

Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G

2016-03-01

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

Bound states of moving potential wells in discrete wave mechanics

NASA Astrophysics Data System (ADS)

Longhi, S.

2017-10-01

Discrete wave mechanics describes the evolution of classical or matter waves on a lattice, which is governed by a discretized version of the Schrödinger equation. While for a vanishing lattice spacing wave evolution of the continuous Schrödinger equation is retrieved, spatial discretization and lattice effects can deeply modify wave dynamics. Here we discuss implications of breakdown of exact Galilean invariance of the discrete Schrödinger equation on the bound states sustained by a smooth potential well which is uniformly moving on the lattice with a drift velocity v. While in the continuous limit the number of bound states does not depend on the drift velocity v, as one expects from the covariance of ordinary Schrödinger equation for a Galilean boost, lattice effects can lead to a larger number of bound states for the moving potential well as compared to the potential well at rest. Moreover, for a moving potential bound states on a lattice become rather generally quasi-bound (resonance) states.

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

NASA Technical Reports Server (NTRS)

Lakin, W. D.; Grosch, C. E.

1983-01-01

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Recognition of pornographic web pages by classifying texts and images.

PubMed

Hu, Weiming; Wu, Ou; Chen, Zhouyao; Fu, Zhouyu; Maybank, Steve

2007-06-01

With the rapid development of the World Wide Web, people benefit more and more from the sharing of information. However, Web pages with obscene, harmful, or illegal content can be easily accessed. It is important to recognize such unsuitable, offensive, or pornographic Web pages. In this paper, a novel framework for recognizing pornographic Web pages is described. A C4.5 decision tree is used to divide Web pages, according to content representations, into continuous text pages, discrete text pages, and image pages. These three categories of Web pages are handled, respectively, by a continuous text classifier, a discrete text classifier, and an algorithm that fuses the results from the image classifier and the discrete text classifier. In the continuous text classifier, statistical and semantic features are used to recognize pornographic texts. In the discrete text classifier, the naive Bayes rule is used to calculate the probability that a discrete text is pornographic. In the image classifier, the object's contour-based features are extracted to recognize pornographic images. In the text and image fusion algorithm, the Bayes theory is used to combine the recognition results from images and texts. Experimental results demonstrate that the continuous text classifier outperforms the traditional keyword-statistics-based classifier, the contour-based image classifier outperforms the traditional skin-region-based image classifier, the results obtained by our fusion algorithm outperform those by either of the individual classifiers, and our framework can be adapted to different categories of Web pages.

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

NASA Astrophysics Data System (ADS)

Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.

2017-06-01

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

40 CFR 420.91 - Specialized definitions.

Code of Federal Regulations, 2010 CFR

2010-07-01

... wire, rods, and tubes in discrete batches or bundles. (f) The term continuous means those pickling operations which process steel products other than in discrete batches or bundles. (g) The term acid recovery...

The seasonal timing of warming that controls onset of the growing season.

PubMed

Clark, James S; Melillo, Jerry; Mohan, Jacqueline; Salk, Carl

2014-04-01

Forecasting how global warming will affect onset of the growing season is essential for predicting terrestrial productivity, but suffers from conflicting evidence. We show that accurate estimates require ways to connect discrete observations of changing tree status (e.g., pre- vs. post budbreak) with continuous responses to fluctuating temperatures. By coherently synthesizing discrete observations with continuous responses to temperature variation, we accurately quantify how increasing temperature variation accelerates onset of growth. Application to warming experiments at two latitudes demonstrates that maximum responses to warming are concentrated in late winter, weeks ahead of the main budbreak period. Given that warming will not occur uniformly over the year, knowledge of when temperature variation has the most impact can guide prediction. Responses are large and heterogeneous, yet predictable. The approach has immediate application to forecasting effects of warming on growing season length, requiring only information that is readily available from weather stations and generated in climate models. © 2013 John Wiley & Sons Ltd.

Algorithms for optimization of branching gravity-driven water networks

NASA Astrophysics Data System (ADS)

Dardani, Ian; Jones, Gerard F.

2018-05-01

The design of a water network involves the selection of pipe diameters that satisfy pressure and flow requirements while considering cost. A variety of design approaches can be used to optimize for hydraulic performance or reduce costs. To help designers select an appropriate approach in the context of gravity-driven water networks (GDWNs), this work assesses three cost-minimization algorithms on six moderate-scale GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution which is mapped onto a discrete-diameter set. The backtracking algorithm finds the global optimum for all but the largest of cases tested, for which its long runtime makes it an infeasible option. The calculus-based algorithm's discrete-diameter solution produced slightly higher-cost results but was more scalable to larger network cases. Furthermore, the new calculus-based algorithm's continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. The genetic algorithm produced solutions even closer to the global optimum with consistently short run times, although slightly higher solution costs were seen for the larger network cases tested. The results of this study highlight the advantages and weaknesses of each GDWN design method including closeness to the global optimum, the ability to prune the solution space of infeasible and suboptimal candidates without missing the global optimum, and algorithm run time. We also extend an existing closed-form model of Jones (2011) to include minor losses and a more comprehensive two-part cost model, which realistically applies to pipe sizes that span a broad range typical of GDWNs of interest in this work, and for smooth and commercial steel roughness values.

A framework for longitudinal data analysis via shape regression

NASA Astrophysics Data System (ADS)

Fishbaugh, James; Durrleman, Stanley; Piven, Joseph; Gerig, Guido

2012-02-01

Traditional longitudinal analysis begins by extracting desired clinical measurements, such as volume or head circumference, from discrete imaging data. Typically, the continuous evolution of a scalar measurement is estimated by choosing a 1D regression model, such as kernel regression or fitting a polynomial of fixed degree. This type of analysis not only leads to separate models for each measurement, but there is no clear anatomical or biological interpretation to aid in the selection of the appropriate paradigm. In this paper, we propose a consistent framework for the analysis of longitudinal data by estimating the continuous evolution of shape over time as twice differentiable flows of deformations. In contrast to 1D regression models, one model is chosen to realistically capture the growth of anatomical structures. From the continuous evolution of shape, we can simply extract any clinical measurements of interest. We demonstrate on real anatomical surfaces that volume extracted from a continuous shape evolution is consistent with a 1D regression performed on the discrete measurements. We further show how the visualization of shape progression can aid in the search for significant measurements. Finally, we present an example on a shape complex of the brain (left hemisphere, right hemisphere, cerebellum) that demonstrates a potential clinical application for our framework.

The discrimination of discrete and continuous amounts in African grey parrots (Psittacus erithacus).

PubMed

Aïn, Syrina Al; Giret, Nicolas; Grand, Marion; Kreutzer, Michel; Bovet, Dalila

2009-01-01

A wealth of research in infants and animals demonstrates discrimination of quantities, in some cases nonverbal numerical perception, and even elementary calculation capacities. We investigated the ability of three African grey parrots (Psittacus erithacus) to select the largest amount of food between two sets, either discrete food items (experiment 1) or as volume of a food substance (experiment 2). The two amounts were presented simultaneously and were visible at the time of choice. Parrots were tested several times for all possible combinations between 1 and 5 seeds or 0.2 and 1 ml of food substance. In both conditions, subjects performed above chance for almost all combinations. Accuracy was negatively correlated with the ratio, that is performance improved with greater differences between amounts. Therefore, these results with both individual items and volume discrimination suggest that parrots use an analogue of magnitude, rather than object-file mechanisms to quantify items and substances.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Estimating the concordance probability in a survival analysis with a discrete number of risk groups.

PubMed

Heller, Glenn; Mo, Qianxing

2016-04-01

A clinical risk classification system is an important component of a treatment decision algorithm. A measure used to assess the strength of a risk classification system is discrimination, and when the outcome is survival time, the most commonly applied global measure of discrimination is the concordance probability. The concordance probability represents the pairwise probability of lower patient risk given longer survival time. The c-index and the concordance probability estimate have been used to estimate the concordance probability when patient-specific risk scores are continuous. In the current paper, the concordance probability estimate and an inverse probability censoring weighted c-index are modified to account for discrete risk scores. Simulations are generated to assess the finite sample properties of the concordance probability estimate and the weighted c-index. An application of these measures of discriminatory power to a metastatic prostate cancer risk classification system is examined.

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

NASA Astrophysics Data System (ADS)

Küchlin, Stephan; Jenny, Patrick

2018-06-01

Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Solutions of burnt-bridge models for molecular motor transport.

PubMed

Morozov, Alexander Yu; Pronina, Ekaterina; Kolomeisky, Anatoly B; Artyomov, Maxim N

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called "bridges"), is investigated theoretically by analyzing discrete-state stochastic "burnt-bridge" models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed ("burned") with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Finite size effects in epidemic spreading: the problem of overpopulated systems

NASA Astrophysics Data System (ADS)

Ganczarek, Wojciech

2013-12-01

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

Exact Solutions of Burnt-Bridge Models for Molecular Motor Transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander; Pronina, Ekaterina; Kolomeisky, Anatoly; Artyomov, Maxim

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called ``bridges''), is investigated theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (``burned'') with a probability p, creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For general case of p<1 a new theoretical method is developed, and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics, periodic and random distribution of bridges and different burning dynamics are analyzed and compared. Theoretical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

Solutions of burnt-bridge models for molecular motor transport

NASA Astrophysics Data System (ADS)

Morozov, Alexander Yu.; Pronina, Ekaterina; Kolomeisky, Anatoly B.; Artyomov, Maxim N.

2007-03-01

Transport of molecular motors, stimulated by interactions with specific links between consecutive binding sites (called “bridges”), is investigated theoretically by analyzing discrete-state stochastic “burnt-bridge” models. When an unbiased diffusing particle crosses the bridge, the link can be destroyed (“burned”) with a probability p , creating a biased directed motion for the particle. It is shown that for probability of burning p=1 the system can be mapped into a one-dimensional single-particle hopping model along the periodic infinite lattice that allows one to calculate exactly all dynamic properties. For the general case of p<1 a theoretical method is developed and dynamic properties are computed explicitly. Discrete-time and continuous-time dynamics for periodic distribution of bridges and different burning dynamics are analyzed and compared. Analytical predictions are supported by extensive Monte Carlo computer simulations. Theoretical results are applied for analysis of the experiments on collagenase motor proteins.

A continuous analog of run length distributions reflecting accumulated fractionation events.

PubMed

Yu, Zhe; Sankoff, David

2016-11-11

We propose a new, continuous model of the fractionation process (duplicate gene deletion after polyploidization) on the real line. The aim is to infer how much DNA is deleted at a time, based on segment lengths for alternating deleted (invisible) and undeleted (visible) regions. After deriving a number of analytical results for "one-sided" fractionation, we undertake a series of simulations that help us identify the distribution of segment lengths as a gamma with shape and rate parameters evolving over time. This leads to an inference procedure based on observed length distributions for visible and invisible segments. We suggest extensions of this mathematical and simulation work to biologically realistic discrete models, including two-sided fractionation.

Approximation of optimal filter for Ornstein-Uhlenbeck process with quantised discrete-time observation

NASA Astrophysics Data System (ADS)

Bania, Piotr; Baranowski, Jerzy

2018-02-01

Quantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker-Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein-Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

Searching for a Link Between Suprathermal Ions and Solar Wind Parameters During Quiet Times.

NASA Astrophysics Data System (ADS)

Nickell, J.; Desai, M. I.; Dayeh, M. A.

2017-12-01

The acceleration processes that suprathermal particles undergo are largely ambiguous. The two prevailing acceleration processes are: 1) Continuous acceleration in the IP space due to i) Bulk velocity fluctuations (e.g., Fahr et al. 2012), ii) magnetic compressions (e.g., Fisk and Gloeckler 2012), iii) magnetic field waves and turbulence (e.g., Zhang and Lee 2013), and iv) reconnection between magnetic islands (e.g., Drake et al. 2014) . 2) Discrete acceleration that occurs in discrete solar events such as CIRs, CME-driven shocks, and flares (e.g., Reames 1999, Desai et al. 2008). Using data from ACE/ULEIS during solar cycles 23 and 24 (1997-present), we examine the solar wind and magnetic field parameters during quiet-times (e.g., Dayeh et al. 2017) in an attempt to gain insights into the acceleration processes of the suprathermal particle population. In particular, we look for compression regions by performing comparative studies between solar wind and magnetic field parameters during quiet-times in the interplanetary space.

Input-output characterization of an ultrasonic testing system by digital signal analysis

NASA Technical Reports Server (NTRS)

Karaguelle, H.; Lee, S. S.; Williams, J., Jr.

1984-01-01

The input/output characteristics of an ultrasonic testing system used for stress wave factor measurements were studied. The fundamentals of digital signal processing are summarized. The inputs and outputs are digitized and processed in a microcomputer using digital signal processing techniques. The entire ultrasonic test system, including transducers and all electronic components, is modeled as a discrete-time linear shift-invariant system. Then the impulse response and frequency response of the continuous time ultrasonic test system are estimated by interpolating the defining points in the unit sample response and frequency response of the discrete time system. It is found that the ultrasonic test system behaves as a linear phase bandpass filter. Good results were obtained for rectangular pulse inputs of various amplitudes and durations and for tone burst inputs whose center frequencies are within the passband of the test system and for single cycle inputs of various amplitudes. The input/output limits on the linearity of the system are determined.

Observability under recurrent loss of data

NASA Technical Reports Server (NTRS)

Luck, Rogelio; Ray, Asok; Halevi, Yoram

1992-01-01

An account is given of the concept of extended observability in finite-dimensional linear time-invariant systems under recurrent loss of data, where the state vector has to be reconstructed from an ensemble of sensor data at nonconsecutive samples. An at once necessary and sufficient condition for extended observability that can be expressed via a recursive relation is presented, together with such conditions for this as may be related to the characteristic polynomial of the state transition matrix in a discrete-time setting, or of the system matrix in a continuous-time setting.

Excitation of Continuous and Discrete Modes in Incompressible Boundary Layers

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Reshotko, Eli

1998-01-01

This report documents the full details of the condensed journal article by Ashpis & Reshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited." A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wave-number plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.

Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks.

PubMed

Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue

2014-11-01

Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.

Discrete Sparse Coding.

PubMed

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

Global robust stability of bidirectional associative memory neural networks with multiple time delays.

PubMed

Senan, Sibel; Arik, Sabri

2007-10-01

This correspondence presents a sufficient condition for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point for bidirectional associative memory neural networks with discrete time delays. The results impose constraint conditions on the network parameters of the neural system independently of the delay parameter, and they are applicable to all bounded continuous nonmonotonic neuron activation functions. Some numerical examples are given to compare our results with the previous robust stability results derived in the literature.

Optimal Trajectories Generation in Robotic Fiber Placement Systems

NASA Astrophysics Data System (ADS)

Gao, Jiuchun; Pashkevich, Anatol; Caro, Stéphane

2017-06-01

The paper proposes a methodology for optimal trajectories generation in robotic fiber placement systems. A strategy to tune the parameters of the optimization algorithm at hand is also introduced. The presented technique transforms the original continuous problem into a discrete one where the time-optimal motions are generated by using dynamic programming. The developed strategy for the optimization algorithm tuning allows essentially reducing the computing time and obtaining trajectories satisfying industrial constraints. Feasibilities and advantages of the proposed methodology are confirmed by an application example.

Attitude estimation of earth orbiting satellites by decomposed linear recursive filters

NASA Technical Reports Server (NTRS)

Kou, S. R.

1975-01-01

Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.

Synchronization of Chaotic Systems without Direct Connections Using Reinforcement Learning

NASA Astrophysics Data System (ADS)

Sato, Norihisa; Adachi, Masaharu

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

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

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Non-smooth saddle-node bifurcations III: Strange attractors in continuous time

NASA Astrophysics Data System (ADS)

Fuhrmann, G.

2016-08-01

Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a non-smooth bifurcation. By a previous result on the occurrence of non-smooth bifurcations in forced discrete time dynamical systems, this yields that within the class of families of quasiperiodically driven differential equations, non-smooth saddle-node bifurcations occur in a set with non-empty C2-interior.

Adaptive model reduction for continuous systems via recursive rational interpolation

NASA Technical Reports Server (NTRS)

Lilly, John H.

1994-01-01

A method for adaptive identification of reduced-order models for continuous stable SISO and MIMO plants is presented. The method recursively finds a model whose transfer function (matrix) matches that of the plant on a set of frequencies chosen by the designer. The algorithm utilizes the Moving Discrete Fourier Transform (MDFT) to continuously monitor the frequency-domain profile of the system input and output signals. The MDFT is an efficient method of monitoring discrete points in the frequency domain of an evolving function of time. The model parameters are estimated from MDFT data using standard recursive parameter estimation techniques. The algorithm has been shown in simulations to be quite robust to additive noise in the inputs and outputs. A significant advantage of the method is that it enables a type of on-line model validation. This is accomplished by simultaneously identifying a number of models and comparing each with the plant in the frequency domain. Simulations of the method applied to an 8th-order SISO plant and a 10-state 2-input 2-output plant are presented. An example of on-line model validation applied to the SISO plant is also presented.

75 FR 6355 - Manufacturing Extension Partnership (MEP) Availability of Funds for Three Regions Including the...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-02-09

... continuation of manufacturing extension service within three discrete geographic areas located in Illinois... discrete geographic areas located in Illinois, Arizona and Central Pennsylvania. The three areas are...

On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space.

PubMed

Wu, Chase Q; Wang, Li

2017-10-10

Sensor networks have been used in a rapidly increasing number of applications in many fields. This work generalizes a sensor deployment problem to place a minimum set of wireless sensors at candidate locations in constrained 3D space to k -cover a given set of target objects. By exhausting the combinations of discreteness/continuousness constraints on either sensor locations or target objects, we formulate four classes of sensor deployment problems in 3D space: deploy sensors at Discrete/Continuous Locations (D/CL) to cover Discrete/Continuous Targets (D/CT). We begin with the design of an approximate algorithm for DLDT and then reduce DLCT, CLDT, and CLCT to DLDT by discretizing continuous sensor locations or target objects into a set of divisions without sacrificing sensing precision. Furthermore, we consider a connected version of each problem where the deployed sensors must form a connected network, and design an approximation algorithm to minimize the number of deployed sensors with connectivity guarantee. For performance comparison, we design and implement an optimal solution and a genetic algorithm (GA)-based approach. Extensive simulation results show that the proposed deployment algorithms consistently outperform the GA-based heuristic and achieve a close-to-optimal performance in small-scale problem instances and a significantly superior overall performance than the theoretical upper bound.

Comparative study of lesions created by high-intensity focused ultrasound using sequential discrete and continuous scanning strategies.

PubMed

Fan, Tingbo; Liu, Zhenbo; Zhang, Dong; Tang, Mengxing

2013-03-01

Lesion formation and temperature distribution induced by high-intensity focused ultrasound (HIFU) were investigated both numerically and experimentally via two energy-delivering strategies, i.e., sequential discrete and continuous scanning modes. Simulations were presented based on the combination of Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and bioheat equation. Measurements were performed on tissue-mimicking phantoms sonicated by a 1.12-MHz single-element focused transducer working at an acoustic power of 75 W. Both the simulated and experimental results show that, in the sequential discrete mode, obvious saw-tooth-like contours could be observed for the peak temperature distribution and the lesion boundaries, with the increasing interval space between two adjacent exposure points. In the continuous scanning mode, more uniform peak temperature distributions and lesion boundaries would be produced, and the peak temperature values would decrease significantly with the increasing scanning speed. In addition, compared to the sequential discrete mode, the continuous scanning mode could achieve higher treatment efficiency (lesion area generated per second) with a lower peak temperature. The present studies suggest that the peak temperature and tissue lesion resulting from the HIFU exposure could be controlled by adjusting the transducer scanning speed, which is important for improving the HIFU treatment efficiency.

Finsler Geometry of Nonlinear Elastic Solids with Internal Structure

DTIC Science & Technology

2017-01-01

should enable regularized numerical solutions with discretization -size independence for representation of materials demonstrating softening, e.g...additional possibility of a discrete larger void/cavity forming at the core of the sphere. In the second case, comparison with the classical...core of the domain. This hollow sphere physically represents a discrete cavity, while the constant field ξH physically represents a continuous

Variable Weight Fractional Collisions for Multiple Species Mixtures

DTIC Science & Technology

2017-08-28

DISTRIBUTION A: APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED; PA #17517 6 / 21 VARIABLE WEIGHTS FOR DYNAMIC RANGE Continuum to Discrete ...Representation: Many Particles →̃ Continuous Distribution Discretized VDF Yields Vlasov But Collision Integral Still a Problem Particle Methods VDF to Delta...Function Set Collisions between Discrete Velocities But Poorly Resolved Tail (Tail Critical to Inelastic Collisions) Variable Weights Permit Extra DOF in

Discrete structures in continuum descriptions of defective crystals

PubMed Central

2016-01-01

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of ‘plastic strain variables’, which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. PMID:27002070

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

Penetrating transmission zeros in the design of robust servomechanism systems

NASA Technical Reports Server (NTRS)

Wang, S. H.; Davison, E. J.

1981-01-01

In the design of a robust servomechanism system, it is well known that the system cannot track a reference signal whose frequency coincides with the transmission zeros of the system. This paper proposes a new design method for overcoming this difficulty. The controller to be used employs a sampler and holding device with exponential decay. It is shown that the transmission zeros of the discretized system can be shifted by changing the rate of the exponential decay of the holding device. Thus, it is possible to design a robust controller for the discretized system to track any reference signal of given frequency, even if the given frequency coincides with the transmission zeros of the original continuous-time system.

GEE-based SNP set association test for continuous and discrete traits in family-based association studies.

PubMed

Wang, Xuefeng; Lee, Seunggeun; Zhu, Xiaofeng; Redline, Susan; Lin, Xihong

2013-12-01

Family-based genetic association studies of related individuals provide opportunities to detect genetic variants that complement studies of unrelated individuals. Most statistical methods for family association studies for common variants are single marker based, which test one SNP a time. In this paper, we consider testing the effect of an SNP set, e.g., SNPs in a gene, in family studies, for both continuous and discrete traits. Specifically, we propose a generalized estimating equations (GEEs) based kernel association test, a variance component based testing method, to test for the association between a phenotype and multiple variants in an SNP set jointly using family samples. The proposed approach allows for both continuous and discrete traits, where the correlation among family members is taken into account through the use of an empirical covariance estimator. We derive the theoretical distribution of the proposed statistic under the null and develop analytical methods to calculate the P-values. We also propose an efficient resampling method for correcting for small sample size bias in family studies. The proposed method allows for easily incorporating covariates and SNP-SNP interactions. Simulation studies show that the proposed method properly controls for type I error rates under both random and ascertained sampling schemes in family studies. We demonstrate through simulation studies that our approach has superior performance for association mapping compared to the single marker based minimum P-value GEE test for an SNP-set effect over a range of scenarios. We illustrate the application of the proposed method using data from the Cleveland Family GWAS Study. © 2013 WILEY PERIODICALS, INC.

A two-phase model of resource allocation in visual working memory.

PubMed

Ye, Chaoxiong; Hu, Zhonghua; Li, Hong; Ristaniemi, Tapani; Liu, Qiang; Liu, Taosheng

2017-10-01

Two broad theories of visual working memory (VWM) storage have emerged from current research, a discrete slot-based theory and a continuous resource theory. However, neither the discrete slot-based theory or continuous resource theory clearly stipulates how the mental commodity for VWM (discrete slot or continuous resource) is allocated. Allocation may be based on the number of items via stimulus-driven factors, or it may be based on task demands via voluntary control. Previous studies have obtained conflicting results regarding the automaticity versus controllability of such allocation. In the current study, we propose a two-phase allocation model, in which the mental commodity could be allocated only by stimulus-driven factors in the early consolidation phase. However, when there is sufficient time to complete the early phase, allocation can enter the late consolidation phase, where it can be flexibly and voluntarily controlled according to task demands. In an orientation recall task, we instructed participants to store either fewer items at high-precision or more items at low-precision. In 3 experiments, we systematically manipulated memory set size and exposure duration. We did not find an effect of task demands when the set size was high and exposure duration was short. However, when we either decreased the set size or increased the exposure duration, we found a trade-off between the number and precision of VWM representations. These results can be explained by a two-phase model, which can also account for previous conflicting findings in the literature. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Well-posed and stable transmission problems

NASA Astrophysics Data System (ADS)

Nordström, Jan; Linders, Viktor

2018-07-01

We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability are analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to the coupling of fluid-acoustic models, multi-grid implementations, adaptive mesh refinements, multi-block formulations and numerical filtering.

High-speed photonically assisted analog-to-digital conversion using a continuous wave multiwavelength source and phase modulation.

PubMed

Bortnik, Bartosz J; Fetterman, Harold R

2008-10-01

A more simple photonically assisted analog-to-digital conversion system utilizing a cw multiwavelength source and phase modulation instead of a mode-locked laser is presented. The output of the cw multiwavelength source is launched into a dispersive device (such as a single-mode fiber). This fiber creates a pulse train, where the central wavelength of each pulse corresponds to a spectral line of the optical source. The pulses can then be either dispersed again to perform discrete wavelength time stretching or demultiplexed for continuous time analog-to-digital conversion. We experimentally demonstrate the operation of both time stretched and interleaved systems at 38 GHz. The potential of integrating this type of system on a monolithic chip is discussed.

Suitability of the echo-time-shift method as laboratory standard for thermal ultrasound dosimetry

NASA Astrophysics Data System (ADS)

Fuhrmann, Tina; Georg, Olga; Haller, Julian; Jenderka, Klaus-Vitold

2017-03-01

Ultrasound therapy is a promising, non-invasive application with potential to significantly improve cancer therapies like surgery, viro- or immunotherapy. This therapy needs faster, cheaper and more easy-to-handle quality assurance tools for therapy devices as well as possibilities to verify treatment plans and for dosimetry. This limits comparability and safety of treatments. Accurate spatial and temporal temperature maps could be used to overcome these shortcomings. In this contribution first results of suitability and accuracy investigations of the echo-time-shift method for two-dimensional temperature mapping during and after sonication are presented. The analysis methods used to calculate time-shifts were a discrete frame-to-frame and a discrete frame-to-base-frame algorithm as well as a sigmoid fit for temperature calculation. In the future accuracy could be significantly enhanced by using continuous methods for time-shift calculation. Further improvements can be achieved by improving filtering algorithms and interpolation of sampled diagnostic ultrasound data. It might be a comparatively accurate, fast and affordable method for laboratory and clinical quality control.

Self-assembled fibre optoelectronics with discrete translational symmetry

PubMed Central

Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel

2016-01-01

Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout. PMID:27698454

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Self-assembled fibre optoelectronics with discrete translational symmetry.

PubMed

Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F; Joannopoulos, John; Fink, Yoel

2016-10-04

Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼10 4 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.

On the form of ROCs constructed from confidence ratings.

PubMed

Malmberg, Kenneth J

2002-03-01

A classical question for memory researchers is whether memories vary in an all-or-nothing, discrete manner (e.g., stored vs. not stored, recalled vs. not recalled), or whether they vary along a continuous dimension (e.g., strength, similarity, or familiarity). For yes-no classification tasks, continuous- and discrete-state models predict nonlinear and linear receiver operating characteristics (ROCs), respectively (D. M. Green & J. A. Swets, 1966; N. A. Macmillan & C. D. Creelman, 1991). Recently, several authors have assumed that these predictions are generalizable to confidence ratings tasks (J. Qin, C. L. Raye, M. K. Johnson, & K. J. Mitchell, 2001; S. D. Slotnick, S. A. Klein, C. S. Dodson, & A. P. Shimamura, 2000, and A. P. Yonelinas, 1999). This assumption is shown to be unwarranted by showing that discrete-state ratings models predict both linear and nonlinear ROCs. The critical factor determining the form of the discrete-state ROC is the response strategy adopted by the classifier.

About the discrete-continuous nature of a hematopoiesis model for Chronic Myeloid Leukemia.

PubMed

Gaudiano, Marcos E; Lenaerts, Tom; Pacheco, Jorge M

2016-12-01

Blood of mammals is composed of a variety of cells suspended in a fluid medium known as plasma. Hematopoiesis is the biological process of birth, replication and differentiation of blood cells. Despite of being essentially a stochastic phenomenon followed by a huge number of discrete entities, blood formation has naturally an associated continuous dynamics, because the cellular populations can - on average - easily be described by (e.g.) differential equations. This deterministic dynamics by no means contemplates some important stochastic aspects related to abnormal hematopoiesis, that are especially significant for studying certain blood cancer deceases. For instance, by mere stochastic competition against the normal cells, leukemic cells sometimes do not reach the population thereshold needed to kill the organism. Of course, a pure discrete model able to follow the stochastic paths of billons of cells is computationally impossible. In order to avoid this difficulty, we seek a trade-off between the computationally feasible and the biologically realistic, deriving an equation able to size conveniently both the discrete and continuous parts of a model for hematopoiesis in terrestrial mammals, in the context of Chronic Myeloid Leukemia. Assuming the cancer is originated from a single stem cell inside of the bone marrow, we also deduce a theoretical formula for the probability of non-diagnosis as a function of the mammal average adult mass. In addition, this work cellular dynamics analysis may shed light on understanding Peto's paradox, which is shown here as an emergent property of the discrete-continuous nature of the system. Copyright © 2016 Elsevier Inc. All rights reserved.

Some applications of uncertainty relations in quantum information

NASA Astrophysics Data System (ADS)

Majumdar, A. S.; Pramanik, T.

2016-08-01

We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the Einstein, Podolsky and Rosen (EPR) paradox. Entropic uncertainty relations (EURs) are used to reveal quantum steering for non-Gaussian continuous variable states. EURs for discrete variables are studied in the context of quantum memory where fine-graining yields the optimum lower bound of uncertainty. The fine-grained uncertainty relation is used to obtain connections between uncertainty and the nonlocality of retrieval games for bipartite and tripartite systems. The Robertson-Schrödinger (RS) uncertainty relation is applied for distinguishing pure and mixed states of discrete variables.