Piecewise linear approximation for hereditary control problems

NASA Technical Reports Server (NTRS)

Propst, Georg

1987-01-01

Finite dimensional approximations are presented for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems when a quadratic cost integral has to be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in case the cost integral ranges over a finite time interval as well as in the case it ranges over an infinite time interval. The arguments in the latter case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense. This feature is established using a vector-component stability criterion in the state space R(n) x L(2) and the favorable eigenvalue behavior of the piecewise linear approximations.

Implicit Monte Carlo with a linear discontinuous finite element material solution and piecewise non-constant opacity

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

Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.

2016-02-23

Here, the non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examinemore » the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ~ 1/T 3, but we formulate and test a slight extension for opacities ~ 1/T 3.5, where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.« less

Canards in a minimal piecewise-linear square-wave burster

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

Desroches, M.; Krupa, M.; Fernández-García, S., E-mail: soledad@us.es

We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that itsmore » fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).« less

Robust Neighboring Optimal Guidance for the Advanced Launch System

NASA Technical Reports Server (NTRS)

Hull, David G.

1993-01-01

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

A structure-preserving split finite element discretization of the split 1D linear shallow-water equations

NASA Astrophysics Data System (ADS)

Bauer, Werner; Behrens, Jörn

2017-04-01

We present a locally conservative, low-order finite element (FE) discretization of the covariant 1D linear shallow-water equations written in split form (cf. tet{[1]}). The introduction of additional differential forms (DF) that build pairs with the original ones permits a splitting of these equations into topological momentum and continuity equations and metric-dependent closure equations that apply the Hodge-star. Our novel discretization framework conserves this geometrical structure, in particular it provides for all DFs proper FE spaces such that the differential operators (here gradient and divergence) hold in strong form. The discrete topological equations simply follow by trivial projections onto piecewise constant FE spaces without need to partially integrate. The discrete Hodge-stars operators, representing the discretized metric equations, are realized by nontrivial Galerkin projections (GP). Here they follow by projections onto either a piecewise constant (GP0) or a piecewise linear (GP1) space. Our framework thus provides essentially three different schemes with significantly different behavior. The split scheme using twice GP1 is unstable and shares the same discrete dispersion relation and similar second-order convergence rates as the conventional P1-P1 FE scheme that approximates both velocity and height variables by piecewise linear spaces. The split scheme that applies both GP1 and GP0 is stable and shares the dispersion relation of the conventional P1-P0 FE scheme that approximates the velocity by a piecewise linear and the height by a piecewise constant space with corresponding second- and first-order convergence rates. Exhibiting for both velocity and height fields second-order convergence rates, we might consider the split GP1-GP0 scheme though as stable versions of the conventional P1-P1 FE scheme. For the split scheme applying twice GP0, we are not aware of a corresponding conventional formulation to compare with. Though exhibiting larger absolute error values, it shows similar convergence rates as the other split schemes, but does not provide a satisfactory approximation of the dispersion relation as short waves are propagated much to fast. Despite this, the finding of this new scheme illustrates the potential of our discretization framework as a toolbox to find and to study new FE schemes based on new combinations of FE spaces. [1] Bauer, W. [2016], A new hierarchically-structured n-dimensional covariant form of rotating equations of geophysical fluid dynamics, GEM - International Journal on Geomathematics, 7(1), 31-101.

Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis

PubMed Central

Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel

2013-01-01

This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007

The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.

PubMed

Storace, Marco; Linaro, Daniele; de Lange, Enno

2008-09-01

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters. (c) 2008 American Institute of Physics.

Does transport time help explain the high trauma mortality rates in rural areas? New and traditional predictors assessed by new and traditional statistical methods

PubMed Central

Røislien, Jo; Lossius, Hans Morten; Kristiansen, Thomas

2015-01-01

Background Trauma is a leading global cause of death. Trauma mortality rates are higher in rural areas, constituting a challenge for quality and equality in trauma care. The aim of the study was to explore population density and transport time to hospital care as possible predictors of geographical differences in mortality rates, and to what extent choice of statistical method might affect the analytical results and accompanying clinical conclusions. Methods Using data from the Norwegian Cause of Death registry, deaths from external causes 1998–2007 were analysed. Norway consists of 434 municipalities, and municipality population density and travel time to hospital care were entered as predictors of municipality mortality rates in univariate and multiple regression models of increasing model complexity. We fitted linear regression models with continuous and categorised predictors, as well as piecewise linear and generalised additive models (GAMs). Models were compared using Akaike's information criterion (AIC). Results Population density was an independent predictor of trauma mortality rates, while the contribution of transport time to hospital care was highly dependent on choice of statistical model. A multiple GAM or piecewise linear model was superior, and similar, in terms of AIC. However, while transport time was statistically significant in multiple models with piecewise linear or categorised predictors, it was not in GAM or standard linear regression. Conclusions Population density is an independent predictor of trauma mortality rates. The added explanatory value of transport time to hospital care is marginal and model-dependent, highlighting the importance of exploring several statistical models when studying complex associations in observational data. PMID:25972600

Piecewise linear emulator of the nonlinear Schrödinger equation and the resulting analytic solutions for Bose-Einstein condensates.

PubMed

Theodorakis, Stavros

2003-06-01

We emulate the cubic term Psi(3) in the nonlinear Schrödinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a delta function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Psi(3) one. In particular, it can be used for the nonlinear Schrödinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions.

On the Modeling of the Residual Effects of the Clock Behavior and the Atmosphere Effects in the Analysis of VLBI Data

NASA Astrophysics Data System (ADS)

Bo, Zhang; Li, Jin-Ling; Wang, Guan-Gli

2002-01-01

We checked the dependence of the estimation of parameters on the choice of piecewise interval in the continuous piecewise linear modeling of the residual clock and atmosphere effects by single analysis of 27 VLBI experiments involving Shanghai station (Seshan 25m). The following are tentatively shown: (1) Different choices of the piecewise interval lead to differences in the estimation of station coordinates and in the weighted root mean squares ( wrms ) of the delay residuals, which can be of the order of centimeters or dozens of picoseconds respectively. So the choice of piecewise interval should not be arbitrary . (2) The piecewise interval should not be too long, otherwise the short - term variations in the residual clock and atmospheric effects can not be properly modeled. While in order to maintain enough degrees of freedom in parameter estimation, the interval can not be too short, otherwise the normal equation may become near or solely singular and the noises can not be constrained as well. Therefore the choice of the interval should be within some reasonable range. (3) Since the conditions of clock and atmosphere are different from experiment to experiment and from station to station, the reasonable range of the piecewise interval should be tested and chosen separately for each experiment as well as for each station by real data analysis. This is really arduous work in routine data analysis. (4) Generally speaking, with the default interval for clock as 60min, the reasonable range of piecewise interval for residual atmospheric effect modeling is between 10min to 40min, while with the default interval for atmosphere as 20min, that for residual clock behavior is between 20min to 100min.

Near constant-time optimal piecewise LDR to HDR inverse tone mapping

NASA Astrophysics Data System (ADS)

Chen, Qian; Su, Guan-Ming; Yin, Peng

2015-02-01

In a backward compatible HDR image/video compression, it is a general approach to reconstruct HDR from compressed LDR as a prediction to original HDR, which is referred to as inverse tone mapping. Experimental results show that 2- piecewise 2nd order polynomial has the best mapping accuracy than 1 piece high order or 2-piecewise linear, but it is also the most time-consuming method because to find the optimal pivot point to split LDR range to 2 pieces requires exhaustive search. In this paper, we propose a fast algorithm that completes optimal 2-piecewise 2nd order polynomial inverse tone mapping in near constant time without quality degradation. We observe that in least square solution, each entry in the intermediate matrix can be written as the sum of some basic terms, which can be pre-calculated into look-up tables. Since solving the matrix becomes looking up values in tables, computation time barely differs regardless of the number of points searched. Hence, we can carry out the most thorough pivot point search to find the optimal pivot that minimizes MSE in near constant time. Experiment shows that our proposed method achieves the same PSNR performance while saving 60 times computation time compared to the traditional exhaustive search in 2-piecewise 2nd order polynomial inverse tone mapping with continuous constraint.

Semilinear programming: applications and implementation

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

Mohan, S.

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

Limit cycles in planar piecewise linear differential systems with nonregular separation line

NASA Astrophysics Data System (ADS)

Cardin, Pedro Toniol; Torregrosa, Joan

2016-12-01

In this paper we deal with planar piecewise linear differential systems defined in two zones. We consider the case when the two linear zones are angular sectors of angles α and 2 π - α, respectively, for α ∈(0 , π) . We study the problem of determining lower bounds for the number of isolated periodic orbits in such systems using Melnikov functions. These limit cycles appear studying higher order piecewise linear perturbations of a linear center. It is proved that the maximum number of limit cycles that can appear up to a sixth order perturbation is five. Moreover, for these values of α, we prove the existence of systems with four limit cycles up to fifth order and, for α = π / 2, we provide an explicit example with five up to sixth order. In general, the nonregular separation line increases the number of periodic orbits in comparison with the case where the two zones are separated by a straight line.

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Parameterizations for ensemble Kalman inversion

NASA Astrophysics Data System (ADS)

Chada, Neil K.; Iglesias, Marco A.; Roininen, Lassi; Stuart, Andrew M.

2018-05-01

The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which lie in the linear span of the initial ensemble. Choice of the parameterization of the unknown field is thus a key component of the success of the method. We demonstrate how both geometric ideas and hierarchical ideas can be used to design effective parameterizations for a number of applied inverse problems arising in electrical impedance tomography, groundwater flow and source inversion. In particular we show how geometric ideas, including the level set method, can be used to reconstruct piecewise continuous fields, and we show how hierarchical methods can be used to learn key parameters in continuous fields, such as length-scales, resulting in improved reconstructions. Geometric and hierarchical ideas are combined in the level set method to find piecewise constant reconstructions with interfaces of unknown topology.

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

Optimal Design of Spring Characteristics of Damper for Subharmonic Vibration in Automatic Transmission Powertrain

NASA Astrophysics Data System (ADS)

Nakae, T.; Ryu, T.; Matsuzaki, K.; Rosbi, S.; Sueoka, A.; Takikawa, Y.; Ooi, Y.

2016-09-01

In the torque converter, the damper of the lock-up clutch is used to effectively absorb the torsional vibration. The damper is designed using a piecewise-linear spring with three stiffness stages. However, a nonlinear vibration, referred to as a subharmonic vibration of order 1/2, occurred around the switching point in the piecewise-linear restoring torque characteristics because of the nonlinearity. In the present study, we analyze vibration reduction for subharmonic vibration. The model used herein includes the torque converter, the gear train, and the differential gear. The damper is modeled by a nonlinear rotational spring of the piecewise-linear spring. We focus on the optimum design of the spring characteristics of the damper in order to suppress the subharmonic vibration. A piecewise-linear spring with five stiffness stages is proposed, and the effect of the distance between switching points on the subharmonic vibration is investigated. The results of our analysis indicate that the subharmonic vibration can be suppressed by designing a damper with five stiffness stages to have a small spring constant ratio between the neighboring springs. The distances between switching points must be designed to be large enough that the amplitude of the main frequency component of the systems does not reach the neighboring switching point.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing

2015-05-01

This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n-dimensional discontinuous neural networks with time-varying delays can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3(n) locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Resonant power processors. I - State plane analysis

NASA Technical Reports Server (NTRS)

Oruganti, R.; Lee, F. C.

1984-01-01

State-plane techniques in conjunction with piecewise-linear analysis is employed to study the steady-state and transient characteristics of a series resonant converter. With the direct viewing of the resonant tank energy and the device switching instants, the state portrayal provides unique insights into the complex behavior of the converter. Operation of the converter under both continuous and discontinuous current modes and at frequencies both below and above resonant frequency are discussed.

Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Piecewise polynomial representations of genomic tracks.

PubMed

Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

2012-01-01

Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.

Analysis of single-degree-of-freedom piezoelectric energy harvester with stopper by incremental harmonic balance method

NASA Astrophysics Data System (ADS)

Zhao, Dan; Wang, Xiaoman; Cheng, Yuan; Liu, Shaogang; Wu, Yanhong; Chai, Liqin; Liu, Yang; Cheng, Qianju

2018-05-01

Piecewise-linear structure can effectively broaden the working frequency band of the piezoelectric energy harvester, and improvement of its research can promote the practical process of energy collection device to meet the requirements for powering microelectronic components. In this paper, the incremental harmonic balance (IHB) method is introduced for the complicated and difficult analysis process of the piezoelectric energy harvester to solve these problems. After obtaining the nonlinear dynamic equation of the single-degree-of-freedom piecewise-linear energy harvester by mathematical modeling and the equation is solved based on the IHB method, the theoretical amplitude-frequency curve of open-circuit voltage is achieved. Under 0.2 g harmonic excitation, a piecewise-linear energy harvester is experimentally tested by unidirectional frequency-increasing scanning. The results demonstrate that the theoretical and experimental amplitudes have the same trend, and the width of the working band with high voltage output are 4.9 Hz and 4.7 Hz, respectively, and the relative error is 4.08%. The open-output peak voltage are 21.53 V and 18.25 V, respectively, and the relative error is 15.23%. Since the theoretical value is consistent with the experimental results, the theoretical model and the incremental harmonic balance method used in this paper are suitable for solving single-degree-of-freedom piecewise-linear piezoelectric energy harvester and can be applied to further parameter optimized design.

True orbit simulation of piecewise linear and linear fractional maps of arbitrary dimension using algebraic numbers

NASA Astrophysics Data System (ADS)

Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji

2015-06-01

We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.

Balance Contrast Enhancement using piecewise linear stretching

NASA Astrophysics Data System (ADS)

Rahavan, R. V.; Govil, R. C.

1993-04-01

Balance Contrast Enhancement is one of the techniques employed to produce color composites with increased color contrast. It equalizes the three images used for color composition in range and mean. This results in a color composite with large variation in hue. Here, it is shown that piecewise linear stretching can be used for performing the Balance Contrast Enhancement. In comparison with the Balance Contrast Enhancement Technique using parabolic segment as transfer function (BCETP), the method presented here is algorithmically simple, constraint-free and produces comparable results.

Tell a Piecewise Story

ERIC Educational Resources Information Center

Sinclair, Nathalie; Armstrong, Alayne

2011-01-01

Piecewise linear functions and story graphs are concepts usually associated with algebra, but in the authors' classroom, they found success teaching this topic in a distinctly geometrical manner. The focus of the approach was less on learning geometric concepts and more on using spatial and kinetic reasoning. It not only supports the learning of…

Towards enhancing and delaying disturbances in free shear flows

NASA Technical Reports Server (NTRS)

Criminale, W. O.; Jackson, T. L.; Lasseigne, D. G.

1994-01-01

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor.

PubMed

Du, Yuhuan; Guo, Yingqing

2016-07-15

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor

PubMed Central

Du, Yuhuan; Guo, Yingqing

2016-01-01

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter. PMID:27428976

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

NASA Technical Reports Server (NTRS)

Jenkins, Jerald M.

1987-01-01

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Filter-based multiscale entropy analysis of complex physiological time series.

PubMed

Xu, Yuesheng; Zhao, Liang

2013-08-01

Multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiological time series. We reinterpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce filter-based multiscale entropy (FME), which filters a time series to generate multiple frequency components, and then we compute the blockwise entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory, which suggests that the human heartbeat interval time series can be described in piecewise linear patterns, we propose piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. The numerical performance of the adaptive piecewise constant filter multiscale entropy without prior information is comparable to that of PLFME, whose design takes prior information into account.

Exact analytical formulae for linearly distributed vortex and source sheets in uence computation in 2D vortex methods

NASA Astrophysics Data System (ADS)

Kuzmina, K. S.; Marchevsky, I. K.; Ryatina, E. P.

2017-11-01

We consider the methodology of numerical schemes development for two-dimensional vortex method. We describe two different approaches to deriving integral equation for unknown vortex sheet intensity. We simulate the velocity of the surface line of an airfoil as the influence of attached vortex and source sheets. We consider a polygonal approximation of the airfoil and assume intensity distributions of free and attached vortex sheets and attached source sheet to be approximated with piecewise constant or piecewise linear (continuous or discontinuous) functions. We describe several specific numerical schemes that provide different accuracy and have a different computational cost. The study shows that a Galerkin-type approach to solving boundary integral equation requires computing several integrals and double integrals over the panels. We obtain exact analytical formulae for all the necessary integrals, which makes it possible to raise significantly the accuracy of vortex sheet intensity computation and improve the quality of velocity and vorticity field representation, especially in proximity to the surface line of the airfoil. All the formulae are written down in the invariant form and depend only on the geometric relationship between the positions of the beginnings and ends of the panels.

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

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

Rajpathak, Bhooshan, E-mail: bhooshan@ee.iitb.ac.in; Pillai, Harish K., E-mail: hp@ee.iitb.ac.in; Bandyopadhyay, Santanu, E-mail: santanu@me.iitb.ac.in

2015-10-15

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

DOE PAGES

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...

2015-11-12

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach

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

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less

Bilinear effect in complex systems

NASA Astrophysics Data System (ADS)

Lam, Lui; Bellavia, David C.; Han, Xiao-Pu; Alston Liu, Chih-Hui; Shu, Chang-Qing; Wei, Zhengjin; Zhou, Tao; Zhu, Jichen

2010-09-01

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.

Nonlinear Modeling by Assembling Piecewise Linear Models

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Analytical modelling of Halbach linear generator incorporating pole shifting and piece-wise spring for ocean wave energy harvesting

NASA Astrophysics Data System (ADS)

Tan, Yimin; Lin, Kejian; Zu, Jean W.

2018-05-01

Halbach permanent magnet (PM) array has attracted tremendous research attention in the development of electromagnetic generators for its unique properties. This paper has proposed a generalized analytical model for linear generators. The slotted stator pole-shifting and implementation of Halbach array have been combined for the first time. Initially, the magnetization components of the Halbach array have been determined using Fourier decomposition. Then, based on the magnetic scalar potential method, the magnetic field distribution has been derived employing specially treated boundary conditions. FEM analysis has been conducted to verify the analytical model. A slotted linear PM generator with Halbach PM has been constructed to validate the model and further improved using piece-wise springs to trigger full range reciprocating motion. A dynamic model has been developed to characterize the dynamic behavior of the slider. This analytical method provides an effective tool in development and optimization of Halbach PM generator. The experimental results indicate that piece-wise springs can be employed to improve generator performance under low excitation frequency.

Slope Estimation in Noisy Piecewise Linear Functions✩

PubMed Central

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2014-01-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure. PMID:25419020

Slope Estimation in Noisy Piecewise Linear Functions.

PubMed

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2015-03-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.

A refraction-corrected tomographic algorithm for immersion laser-ultrasonic imaging of solids with piecewise linear surface profile

NASA Astrophysics Data System (ADS)

Zarubin, V.; Bychkov, A.; Simonova, V.; Zhigarkov, V.; Karabutov, A.; Cherepetskaya, E.

2018-05-01

In this paper, a technique for reflection mode immersion 2D laser-ultrasound tomography of solid objects with piecewise linear 2D surface profiles is presented. Pulsed laser radiation was used for generation of short ultrasonic probe pulses, providing high spatial resolution. A piezofilm sensor array was used for detection of the waves reflected by the surface and internal inhomogeneities of the object. The original ultrasonic image reconstruction algorithm accounting for refraction of acoustic waves at the liquid-solid interface provided longitudinal resolution better than 100 μm in the polymethyl methacrylate sample object.

Adjusting for overdispersion in piecewise exponential regression models to estimate excess mortality rate in population-based research.

PubMed

Luque-Fernandez, Miguel Angel; Belot, Aurélien; Quaresma, Manuela; Maringe, Camille; Coleman, Michel P; Rachet, Bernard

2016-10-01

In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean). Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001). However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3) for non-flexible piecewise exponential models. We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.

A hybrid approach to modeling and control of vehicle height for electronically controlled air suspension

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Cai, Yingfeng; Wang, Shaohua; Liu, Yanling; Chen, Long

2016-01-01

The control problems associated with vehicle height adjustment of electronically controlled air suspension (ECAS) still pose theoretical challenges for researchers, which manifest themselves in the publications on this subject over the last years. This paper deals with modeling and control of a vehicle height adjustment system for ECAS, which is an example of a hybrid dynamical system due to the coexistence and coupling of continuous variables and discrete events. A mixed logical dynamical (MLD) modeling approach is chosen for capturing enough details of the vehicle height adjustment process. The hybrid dynamic model is constructed on the basis of some assumptions and piecewise linear approximation for components nonlinearities. Then, the on-off statuses of solenoid valves and the piecewise approximation process are described by propositional logic, and the hybrid system is transformed into the set of linear mixed-integer equalities and inequalities, denoted as MLD model, automatically by HYSDEL. Using this model, a hybrid model predictive controller (HMPC) is tuned based on online mixed-integer quadratic optimization (MIQP). Two different scenarios are considered in the simulation, whose results verify the height adjustment effectiveness of the proposed approach. Explicit solutions of the controller are computed to control the vehicle height adjustment system in realtime using an offline multi-parametric programming technology (MPT), thus convert the controller into an equivalent explicit piecewise affine form. Finally, bench experiments for vehicle height lifting, holding and lowering procedures are conducted, which demonstrate that the HMPC can adjust the vehicle height by controlling the on-off statuses of solenoid valves directly. This research proposes a new modeling and control method for vehicle height adjustment of ECAS, which leads to a closed-loop system with favorable dynamical properties.

Fault detection for piecewise affine systems with application to ship propulsion systems.

PubMed

Yang, Ying; Linlin, Li; Ding, Steven X; Qiu, Jianbin; Peng, Kaixiang

2017-09-09

In this paper, the design approach of non-synchronized diagnostic observer-based fault detection (FD) systems is investigated for piecewise affine processes via continuous piecewise Lyapunov functions. Considering that the dynamics of piecewise affine systems in different regions can be considerably different, the weighting matrices are used to weight the residual of each region, so as to optimize the fault detectability. A numerical example and a case study on a ship propulsion system are presented in the end to demonstrate the effectiveness of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Active distribution network planning considering linearized system loss

NASA Astrophysics Data System (ADS)

Li, Xiao; Wang, Mingqiang; Xu, Hao

2018-02-01

In this paper, various distribution network planning techniques with DGs are reviewed, and a new distribution network planning method is proposed. It assumes that the location of DGs and the topology of the network are fixed. The proposed model optimizes the capacities of DG and the optimal distribution line capacity simultaneously by a cost/benefit analysis and the benefit is quantified by the reduction of the expected interruption cost. Besides, the network loss is explicitly analyzed in the paper. For simplicity, the network loss is appropriately simplified as a quadratic function of difference of voltage phase angle. Then it is further piecewise linearized. In this paper, a piecewise linearization technique with different segment lengths is proposed. To validate its effectiveness and superiority, the proposed distribution network planning model with elaborate linearization technique is tested on the IEEE 33-bus distribution network system.

Chua's Equation was Proved to BE Chaotic in Two Years, Lorenz Equation in Thirty Six Years

NASA Astrophysics Data System (ADS)

Muthuswamy, Bharathwaj

2013-01-01

Although there are probably more publications on Chua's circuit than any other chaotic circuit, a tutorial with a historical emphasis is still lacking. Hence the goal of this chapter is to provide such a tutorial. This chapter will prove useful for a novice who is looking to understand the basics behind chaotic circuits without too much technical details. The chapter also includes a cookbook approach to a rigorous proof of chaos in piecewise-linear systems. The proof is a summary of the original piecewise-linear proof of chaos in Chua's circuit. The chapter concludes with a discussion of circuits derived from Chua's circuit.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

Roessler, O. E.; Kahiert, C.; Ughleke, B.

A piecewise-linear autonomous 3-variable ordinary differential equation is presented which permits analytical modeling of chaotic attractors. A once-differentiable system of equations is defined which consists of two linear half-systems which meet along a threshold plane. The trajectories described by each equation is thereby continuous along the divide, forming a one-parameter family of invariant tori. The addition of a damping term produces a system of equations for various chaotic attractors. Extension of the system by means of a 4-variable generalization yields hypertori and hyperchaos. It is noted that the hierarchy established is amenable to analysis by the use of Poincare half-maps. Applications of the systems of ordinary differential equations to modeling turbulent flows are discussed.

Lipschitz Metric for the Novikov Equation

NASA Astrophysics Data System (ADS)

Cai, Hong; Chen, Geng; Chen, Robin Ming; Shen, Yannan

2018-03-01

We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport metric which renders the solution map Lipschitz continuous on bounded sets of {H^1(R)\\cap W^{1,4}(R)} , although it is not Lipschitz continuous under the natural Sobolev metric from an energy law due to the finite time gradient blowup. By an application of Thom's transversality theorem, we also prove that when the initial data is in an open dense subset of {H^1(R)\\cap W^{1,4}(R)} , the solution is piecewise smooth. This generic regularity result helps us extend the Lipschitz continuous metric to the general weak solutions. Our method of constructing the metric can be used to treat other kinds of quasi-linear equations, provided a good knowledge about the energy concentration.

Longitudinal mathematics development of students with learning disabilities and students without disabilities: a comparison of linear, quadratic, and piecewise linear mixed effects models.

PubMed

Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz

2015-04-01

Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Improved Displacement Transfer Functions for Structure Deformed Shape Predictions Using Discretely Distributed Surface Strains

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2012-01-01

In the formulations of earlier Displacement Transfer Functions for structure shape predictions, the surface strain distributions, along a strain-sensing line, were represented with piecewise linear functions. To improve the shape-prediction accuracies, Improved Displacement Transfer Functions were formulated using piecewise nonlinear strain representations. Through discretization of an embedded beam (depth-wise cross section of a structure along a strain-sensing line) into multiple small domains, piecewise nonlinear functions were used to describe the surface strain distributions along the discretized embedded beam. Such piecewise approach enabled the piecewise integrations of the embedded beam curvature equations to yield slope and deflection equations in recursive forms. The resulting Improved Displacement Transfer Functions, written in summation forms, were expressed in terms of beam geometrical parameters and surface strains along the strain-sensing line. By feeding the surface strains into the Improved Displacement Transfer Functions, structural deflections could be calculated at multiple points for mapping out the overall structural deformed shapes for visual display. The shape-prediction accuracies of the Improved Displacement Transfer Functions were then examined in view of finite-element-calculated deflections using different tapered cantilever tubular beams. It was found that by using the piecewise nonlinear strain representations, the shape-prediction accuracies could be greatly improved, especially for highly-tapered cantilever tubular beams.

Identification of Piecewise Linear Uniform Motion Blur

NASA Astrophysics Data System (ADS)

Patanukhom, Karn; Nishihara, Akinori

A motion blur identification scheme is proposed for nonlinear uniform motion blurs approximated by piecewise linear models which consist of more than one linear motion component. The proposed scheme includes three modules that are a motion direction estimator, a motion length estimator and a motion combination selector. In order to identify the motion directions, the proposed scheme is based on a trial restoration by using directional forward ramp motion blurs along different directions and an analysis of directional information via frequency domain by using a Radon transform. Autocorrelation functions of image derivatives along several directions are employed for estimation of the motion lengths. A proper motion combination is identified by analyzing local autocorrelation functions of non-flat component of trial restored results. Experimental examples of simulated and real world blurred images are given to demonstrate a promising performance of the proposed scheme.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Changes in Clavicle Length and Maturation in Americans: 1840-1980.

PubMed

Langley, Natalie R; Cridlin, Sandra

2016-01-01

Secular changes refer to short-term biological changes ostensibly due to environmental factors. Two well-documented secular trends in many populations are earlier age of menarche and increasing stature. This study synthesizes data on maximum clavicle length and fusion of the medial epiphysis in 1840-1980 American birth cohorts to provide a comprehensive assessment of developmental and morphological change in the clavicle. Clavicles from the Hamann-Todd Human Osteological Collection (n = 354), McKern and Stewart Korean War males (n = 341), Forensic Anthropology Data Bank (n = 1,239), and the McCormick Clavicle Collection (n = 1,137) were used in the analysis. Transition analysis was used to evaluate fusion of the medial epiphysis (scored as unfused, fusing, or fused). Several statistical treatments were used to assess fluctuations in maximum clavicle length. First, Durbin-Watson tests were used to evaluate autocorrelation, and a local regression (LOESS) was used to identify visual shifts in the regression slope. Next, piecewise regression was used to fit linear regression models before and after the estimated breakpoints. Multiple starting parameters were tested in the range determined to contain the breakpoint, and the model with the smallest mean squared error was chosen as the best fit. The parameters from the best-fit models were then used to derive the piecewise models, which were compared with the initial simple linear regression models to determine which model provided the best fit for the secular change data. The epiphyseal union data indicate a decline in the age at onset of fusion since the early twentieth century. Fusion commences approximately four years earlier in mid- to late twentieth-century birth cohorts than in late nineteenth- and early twentieth-century birth cohorts. However, fusion is completed at roughly the same age across cohorts. The most significant decline in age at onset of epiphyseal union appears to have occurred since the mid-twentieth century. LOESS plots show a breakpoint in the clavicle length data around the mid-twentieth century in both sexes, and piecewise regression models indicate a significant decrease in clavicle length in the American population after 1940. The piecewise model provides a slightly better fit than the simple linear model. Since the model standard error is not substantially different from the piecewise model, an argument could be made to select the less complex linear model. However, we chose the piecewise model to detect changes in clavicle length that are overfitted with a linear model. The decrease in maximum clavicle length is in line with a documented narrowing of the American skeletal form, as shown by analyses of cranial and facial breadth and bi-iliac breadth of the pelvis. Environmental influences on skeletal form include increases in body mass index, health improvements, improved socioeconomic status, and elimination of infectious diseases. Secular changes in bony dimensions and skeletal maturation stipulate that medical and forensic standards used to deduce information about growth, health, and biological traits must be derived from modern populations.

Hurst Estimation of Scale Invariant Processes with Stationary Increments and Piecewise Linear Drift

NASA Astrophysics Data System (ADS)

Modarresi, N.; Rezakhah, S.

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first, we determine the scale intervals, their linear drifts and eliminate them. Then, a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion (fBm).

Payment contracts in a preventive health care system: a perspective from operations management.

PubMed

Yaesoubi, Reza; Roberts, Stephen D

2011-12-01

We consider a health care system consisting of two noncooperative parties: a health purchaser (payer) and a health provider, where the interaction between the two parties is governed by a payment contract. We determine the contracts that coordinate the health purchaser-health provider relationship; i.e. the contracts that maximize the population's welfare while allowing each entity to optimize its own objective function. We show that under certain conditions (1) when the number of customers for a preventive medical intervention is verifiable, there exists a gate-keeping contract and a set of concave piecewise linear contracts that coordinate the system, and (2) when the number of customers is not verifiable, there exists a contract of bounded linear form and a set of incentive-feasible concave piecewise linear contracts that coordinate the system. Copyright © 2011 Elsevier B.V. All rights reserved.

Characterization of intermittency in renewal processes: Application to earthquakes

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

Akimoto, Takuma; Hasumi, Tomohiro; Aizawa, Yoji

2010-03-15

We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the piecewise linear intermittent map. Thus, we provide a framework to understand a unified characterization of intermittency and also present the Lyapunov exponent for renewal processes. This method is applied to the occurrence of earthquakes using the Japan Meteorological Agency and the National Earthquake Information Center catalog. By analyzing the return map of interevent times, we find that interevent times are not independent and identically distributed random variablesmore » but that the conditional probability distribution functions in the tail obey the Weibull distribution.« less

Cubic Zig-Zag Enrichment of the Classical Kirchhoff Kinematics for Laminated and Sandwich Plates

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2012-01-01

A detailed anaylsis and examples are presented that show how to enrich the kinematics of classical Kirchhoff plate theory by appending them with a set of continuous piecewise-cubic functions. This analysis is used to obtain functions that contain the effects of laminate heterogeneity and asymmetry on the variations of the inplane displacements and transverse shearing stresses, for use with a {3, 0} plate theory in which these distributions are specified apriori. The functions used for the enrichment are based on the improved zig-zag plate theory presented recently by Tessler, Di Scuva, and Gherlone. With the approach presented herein, the inplane displacements are represented by a set of continuous piecewise-cubic functions, and the transverse shearing stresses and strains are represented by a set of piecewise-quadratic functions that are discontinuous at the ply interfaces.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

On the stability, storage capacity, and design of nonlinear continuous neural networks

NASA Technical Reports Server (NTRS)

Guez, Allon; Protopopsecu, Vladimir; Barhen, Jacob

1988-01-01

The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the post synaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3N equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. Moreover, it is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

Determination of pKa values of alendronate sodium in aqueous solution by piecewise linear regression based on acid-base potentiometric titration.

PubMed

Ke, Jing; Dou, Hanfei; Zhang, Ximin; Uhagaze, Dushimabararezi Serge; Ding, Xiali; Dong, Yuming

2016-12-01

As a mono-sodium salt form of alendronic acid, alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups. The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and pH value based on acid-base potentiometric titration reaction. The distribution curves of alendronate sodium were drawn according to the determined pKa values. There were 4 dissociation constants (pKa 1 =2.43, pKa 2 =7.55, pKa 3 =10.80, pKa 4 =11.99, respectively) of alendronate sodium, and 12 existing forms, of which 4 could be ignored, existing in different pH environments.

A generalized analog implementation of piecewise linear neuron models using CCII building blocks.

PubMed

Soleimani, Hamid; Ahmadi, Arash; Bavandpour, Mohammad; Sharifipoor, Ozra

2014-03-01

This paper presents a set of reconfigurable analog implementations of piecewise linear spiking neuron models using second generation current conveyor (CCII) building blocks. With the same topology and circuit elements, without W/L modification which is impossible after circuit fabrication, these circuits can produce different behaviors, similar to the biological neurons, both for a single neuron as well as a network of neurons just by tuning reference current and voltage sources. The models are investigated, in terms of analog implementation feasibility and costs, targeting large scale hardware implementations. Results show that, in order to gain the best performance, area and accuracy; these models can be compromised. Simulation results are presented for different neuron behaviors with CMOS 350 nm technology. Copyright © 2013 Elsevier Ltd. All rights reserved.

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

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

Ganapol, B.; Picca, P.; Previti, A.

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making usemore » of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)« less

Piecewise multivariate modelling of sequential metabolic profiling data.

PubMed

Rantalainen, Mattias; Cloarec, Olivier; Ebbels, Timothy M D; Lundstedt, Torbjörn; Nicholson, Jeremy K; Holmes, Elaine; Trygg, Johan

2008-02-19

Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints. A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS) models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted. The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA) for modelling and analysis of short time-series data.

Boundary element modelling of dynamic behavior of piecewise homogeneous anisotropic elastic solids

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Litvinchuk, S. Yu

2018-04-01

A traditional direct boundary integral equations method is applied to solve three-dimensional dynamic problems of piecewise homogeneous linear elastic solids. The materials of homogeneous parts are considered to be generally anisotropic. The technique used to solve the boundary integral equations is based on the boundary element method applied together with the Radau IIA convolution quadrature method. A numerical example of suddenly loaded 3D prismatic rod consisting of two subdomains with different anisotropic elastic properties is presented to verify the accuracy of the proposed formulation.

Filtrage Lineaire par Morceaux Avec Petit Bruit d’Observation (Piecewise Linear Filtering with Small Observation Noise)

DTIC Science & Technology

1990-11-19

stir divers exemple-s le comportement des filtres l)r0pose5 par ra.)pDort ceux du processus estliner et dti filtre optimal obtenu de fa~on approch6e...Piecewise monotone filtering with small observation noise, Siam J., Control Optim. 20, 261-285, 1989 . Vii [10 W.ll. Fleming and R.W. Rishel...Milbeiro, de Oliveira : Filtres approch~s pour un probl~me de filtrage non lin~aire discret avec petit bruit d’observation,rapport INVRIA, 1142. 1989

Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

NASA Astrophysics Data System (ADS)

Chunodkar, Apurva A.; Akella, Maruthi R.

2013-12-01

This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

A new weak Galerkin finite element method for elliptic interface problems

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

Mu, Lin; Wang, Junping; Ye, Xiu

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions.

PubMed

Liu, Qingshan; Wang, Jun

2011-04-01

This paper presents a one-layer recurrent neural network for solving a class of constrained nonsmooth optimization problems with piecewise-linear objective functions. The proposed neural network is guaranteed to be globally convergent in finite time to the optimal solutions under a mild condition on a derived lower bound of a single gain parameter in the model. The number of neurons in the neural network is the same as the number of decision variables of the optimization problem. Compared with existing neural networks for optimization, the proposed neural network has a couple of salient features such as finite-time convergence and a low model complexity. Specific models for two important special cases, namely, linear programming and nonsmooth optimization, are also presented. In addition, applications to the shortest path problem and constrained least absolute deviation problem are discussed with simulation results to demonstrate the effectiveness and characteristics of the proposed neural network.

Construction of Response Surface with Higher Order Continuity and Its Application to Reliability Engineering

NASA Technical Reports Server (NTRS)

Krishnamurthy, T.; Romero, V. J.

2002-01-01

The usefulness of piecewise polynomials with C1 and C2 derivative continuity for response surface construction method is examined. A Moving Least Squares (MLS) method is developed and compared with four other interpolation methods, including kriging. First the selected methods are applied and compared with one another in a two-design variables problem with a known theoretical response function. Next the methods are tested in a four-design variables problem from a reliability-based design application. In general the piecewise polynomial with higher order derivative continuity methods produce less error in the response prediction. The MLS method was found to be superior for response surface construction among the methods evaluated.

Integrate and fire neural networks, piecewise contractive maps and limit cycles.

PubMed

Catsigeras, Eleonora; Guiraud, Pierre

2013-09-01

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincaré map associated to the system. We show that for efficient interactions the Poincaré map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincaré map under study, but also to a wide class of general n-dimensional piecewise contractive maps.

An Ensemble of Neural Networks for Stock Trading Decision Making

NASA Astrophysics Data System (ADS)

Chang, Pei-Chann; Liu, Chen-Hao; Fan, Chin-Yuan; Lin, Jun-Lin; Lai, Chih-Ming

Stock turning signals detection are very interesting subject arising in numerous financial and economic planning problems. In this paper, Ensemble Neural Network system with Intelligent Piecewise Linear Representation for stock turning points detection is presented. The Intelligent piecewise linear representation method is able to generate numerous stocks turning signals from the historic data base, then Ensemble Neural Network system will be applied to train the pattern and retrieve similar stock price patterns from historic data for training. These turning signals represent short-term and long-term trading signals for selling or buying stocks from the market which are applied to forecast the future turning points from the set of test data. Experimental results demonstrate that the hybrid system can make a significant and constant amount of profit when compared with other approaches using stock data available in the market.

Air-Gapped Structures as Magnetic Elements for Use in Power Processing Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Ohri, A. K.

1977-01-01

Methodical approaches to the design of inductors for use in LC filters and dc-to-dc converters using air gapped magnetic structures are presented. Methods for the analysis and design of full wave rectifier LC filter circuits operating with the inductor current in both the continuous conduction and the discontinuous conduction modes are also described. In the continuous conduction mode, linear circuit analysis techniques are employed, while in the case of the discontinuous mode, the method of analysis requires computer solutions of the piecewise linear differential equations which describe the filter in the time domain. Procedures for designing filter inductors using air gapped cores are presented. The first procedure requires digital computation to yield a design which is optimized in the sense of minimum core volume and minimum number of turns. The second procedure does not yield an optimized design as defined above, but the design can be obtained by hand calculations or with a small calculator. The third procedure is based on the use of specially prepared magnetic core data and provides an easy way to quickly reach a workable design.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Identification of cascade water tanks using a PWARX model

NASA Astrophysics Data System (ADS)

Mattsson, Per; Zachariah, Dave; Stoica, Petre

2018-06-01

In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

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

Effect of smoothing on robust chaos.

PubMed

Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

2010-08-01

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

Geometric analysis and restitution of digital multispectral scanner data arrays

NASA Technical Reports Server (NTRS)

Baker, J. R.; Mikhail, E. M.

1975-01-01

An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.

On solving three-dimensional open-dimension rectangular packing problems

NASA Astrophysics Data System (ADS)

Junqueira, Leonardo; Morabito, Reinaldo

2017-05-01

In this article, a recently proposed three-dimensional open-dimension rectangular packing problem is considered, in which the objective is to find a minimal volume rectangular container that packs a set of rectangular boxes. The literature has tackled small-sized instances of this problem by means of optimization solvers, position-free mixed-integer programming (MIP) formulations and piecewise linearization approaches. In this study, the problem is alternatively addressed by means of grid-based position MIP formulations, whereas still considering optimization solvers and the same piecewise linearization techniques. A comparison of the computational performance of both models is then presented, when tested with benchmark problem instances and with new instances, and it is shown that the grid-based position MIP formulation can be competitive, depending on the characteristics of the instances. The grid-based position MIP formulation is also embedded with real-world practical constraints, such as cargo stability, and results are additionally presented.

[Biometric identification method for ECG based on the piecewise linear representation (PLR) and dynamic time warping (DTW)].

PubMed

Yang, Licai; Shen, Jun; Bao, Shudi; Wei, Shoushui

2013-10-01

To treat the problem of identification performance and the complexity of the algorithm, we proposed a piecewise linear representation and dynamic time warping (PLR-DTW) method for ECG biometric identification. Firstly we detected R peaks to get the heartbeats after denoising preprocessing. Then we used the PLR method to keep important information of an ECG signal segment while reducing the data dimension at the same time. The improved DTW method was used for similarity measurements between the test data and the templates. The performance evaluation was carried out on the two ECG databases: PTB and MIT-BIH. The analystic results showed that compared to the discrete wavelet transform method, the proposed PLR-DTW method achieved a higher accuracy rate which is nearly 8% of rising, and saved about 30% operation time, and this demonstrated that the proposed method could provide a better performance.

Shock Capturing with PDE-Based Artificial Viscosity for an Adaptive, Higher-Order Discontinuous Galerkin Finite Element Method

DTIC Science & Technology

2008-06-01

Geometry Interpolation The function space , VpH , consists of discontinuous, piecewise-polynomials. This work used a polynomial basis for VpH such...between a piecewise-constant and smooth variation of viscosity in both a one- dimensional and multi- dimensional setting. Before continuing with the ...inviscid, transonic flow past a NACA 0012 at zero angle of attack and freestream Mach number of M∞ = 0.95. The

Nonsmooth modal analysis of a N-degree-of-freedom system undergoing a purely elastic impact law

NASA Astrophysics Data System (ADS)

Legrand, Mathias; Junca, Stéphane; Heng, Sokly

2017-04-01

The dynamics of a N-degree-of-freedom autonomous oscillator undergoing an energy-preserving impact law on one of its masses is investigated in the light of nonlinear modal analysis. The impacted rigid foundation provides a natural Poincaré section of the investigated system from which is formulated a smooth First Return Map well-defined away from the grazing trajectory. In order to focus on the impact-induced nonlinearity, the oscillator is assumed linear. Continuous one-parameter families of T-periodic orbits featuring one impact per period and lying on two-dimensional invariant manifolds in the state-space are shown to exist. The geometry of these piecewise-smooth manifolds is such that a linear "flat" portion (on which contact is not activated) is continuously attached to a purely nonlinear portion (on which contact is activated once per period) exhibiting a velocity discontinuity through a grazing orbit. These features explain the newly introduced terminology "Nonsmooth modal analysis". The stability of the periodic orbits lying on the invariant manifolds is also explored by calculating the eigenvalues of the linearized First Return Map. Internal resonances and multiple impacts per period are not addressed in this work. However, the pre-stressed case is succinctly described and extensions to multiple oscillators as well as self-contact are discussed.

Global Patch Matching

NASA Astrophysics Data System (ADS)

Huang, X.; Hu, K.; Ling, X.; Zhang, Y.; Lu, Z.; Zhou, G.

2017-09-01

This paper introduces a novel global patch matching method that focuses on how to remove fronto-parallel bias and obtain continuous smooth surfaces with assuming that the scenes covered by stereos are piecewise continuous. Firstly, simple linear iterative cluster method (SLIC) is used to segment the base image into a series of patches. Then, a global energy function, which consists of a data term and a smoothness term, is built on the patches. The data term is the second-order Taylor expansion of correlation coefficients, and the smoothness term is built by combing connectivity constraints and the coplanarity constraints are combined to construct the smoothness term. Finally, the global energy function can be built by combining the data term and the smoothness term. We rewrite the global energy function in a quadratic matrix function, and use least square methods to obtain the optimal solution. Experiments on Adirondack stereo and Motorcycle stereo of Middlebury benchmark show that the proposed method can remove fronto-parallel bias effectively, and produce continuous smooth surfaces.

Development of a piecewise linear omnidirectional 3D image registration method

NASA Astrophysics Data System (ADS)

Bae, Hyunsoo; Kang, Wonjin; Lee, SukGyu; Kim, Youngwoo

2016-12-01

This paper proposes a new piecewise linear omnidirectional image registration method. The proposed method segments an image captured by multiple cameras into 2D segments defined by feature points of the image and then stitches each segment geometrically by considering the inclination of the segment in the 3D space. Depending on the intended use of image registration, the proposed method can be used to improve image registration accuracy or reduce the computation time in image registration because the trade-off between the computation time and image registration accuracy can be controlled for. In general, nonlinear image registration methods have been used in 3D omnidirectional image registration processes to reduce image distortion by camera lenses. The proposed method depends on a linear transformation process for omnidirectional image registration, and therefore it can enhance the effectiveness of the geometry recognition process, increase image registration accuracy by increasing the number of cameras or feature points of each image, increase the image registration speed by reducing the number of cameras or feature points of each image, and provide simultaneous information on shapes and colors of captured objects.

Control algorithms for dynamic attenuators.

PubMed

Hsieh, Scott S; Pelc, Norbert J

2014-06-01

The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods.

Stability and bifurcation analysis of oscillators with piecewise-linear characteristics - A general approach

NASA Technical Reports Server (NTRS)

Noah, S. T.; Kim, Y. B.

1991-01-01

A general approach is developed for determining the periodic solutions and their stability of nonlinear oscillators with piecewise-smooth characteristics. A modified harmonic balance/Fourier transform procedure is devised for the analysis. The procedure avoids certain numerical differentiation employed previously in determining the periodic solutions, therefore enhancing the reliability and efficiency of the method. Stability of the solutions is determined via perturbations of their state variables. The method is applied to a forced oscillator interacting with a stop of finite stiffness. Flip and fold bifurcations are found to occur. This led to the identification of parameter ranges in which chaotic response occurred.

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2013-01-01

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

A financial market model with two discontinuities: Bifurcation structures in the chaotic domain

NASA Astrophysics Data System (ADS)

Panchuk, Anastasiia; Sushko, Iryna; Westerhoff, Frank

2018-05-01

We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

NASA Astrophysics Data System (ADS)

Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu

2015-12-01

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.

Protein linear indices of the 'macromolecular pseudograph alpha-carbon atom adjacency matrix' in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in Arc repressor.

PubMed

Marrero-Ponce, Yovani; Medina-Marrero, Ricardo; Castillo-Garit, Juan A; Romero-Zaldivar, Vicente; Torrens, Francisco; Castro, Eduardo A

2005-04-15

A novel approach to bio-macromolecular design from a linear algebra point of view is introduced. A protein's total (whole protein) and local (one or more amino acid) linear indices are a new set of bio-macromolecular descriptors of relevance to protein QSAR/QSPR studies. These amino-acid level biochemical descriptors are based on the calculation of linear maps on Rn[f k(xmi):Rn-->Rn] in canonical basis. These bio-macromolecular indices are calculated from the kth power of the macromolecular pseudograph alpha-carbon atom adjacency matrix. Total linear indices are linear functional on Rn. That is, the kth total linear indices are linear maps from Rn to the scalar R[f k(xm):Rn-->R]. Thus, the kth total linear indices are calculated by summing the amino-acid linear indices of all amino acids in the protein molecule. A study of the protein stability effects for a complete set of alanine substitutions in the Arc repressor illustrates this approach. A quantitative model that discriminates near wild-type stability alanine mutants from the reduced-stability ones in a training series was obtained. This model permitted the correct classification of 97.56% (40/41) and 91.67% (11/12) of proteins in the training and test set, respectively. It shows a high Matthews correlation coefficient (MCC=0.952) for the training set and an MCC=0.837 for the external prediction set. Additionally, canonical regression analysis corroborated the statistical quality of the classification model (Rcanc=0.824). This analysis was also used to compute biological stability canonical scores for each Arc alanine mutant. On the other hand, the linear piecewise regression model compared favorably with respect to the linear regression one on predicting the melting temperature (tm) of the Arc alanine mutants. The linear model explains almost 81% of the variance of the experimental tm (R=0.90 and s=4.29) and the LOO press statistics evidenced its predictive ability (q2=0.72 and scv=4.79). Moreover, the TOMOCOMD-CAMPS method produced a linear piecewise regression (R=0.97) between protein backbone descriptors and tm values for alanine mutants of the Arc repressor. A break-point value of 51.87 degrees C characterized two mutant clusters and coincided perfectly with the experimental scale. For this reason, we can use the linear discriminant analysis and piecewise models in combination to classify and predict the stability of the mutant Arc homodimers. These models also permitted the interpretation of the driving forces of such folding process, indicating that topologic/topographic protein backbone interactions control the stability profile of wild-type Arc and its alanine mutants.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

NASA Technical Reports Server (NTRS)

Olson, Erik D.

2015-01-01

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies.

PubMed

Bardhan, Jaydeep P; Jungwirth, Pavel; Makowski, Lee

2012-09-28

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).

Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies

PubMed Central

Bardhan, Jaydeep P.; Jungwirth, Pavel; Makowski, Lee

2012-01-01

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular “linear response” model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution). PMID:23020318

Enhanced algorithms for stochastic programming

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

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Microwave moisture sensing through use of a piecewise density-independent function

USDA-ARS?s Scientific Manuscript database

Microwave moisture sensing provides a means to determine nondestructively the amount of water in materials. This is accomplished through the correlation of dielectric properties with moisture in the material. In this study, linear relationships between a density-independent function of the dielectri...

Building an Understanding of Functions: A Series of Activities for Pre-Calculus

ERIC Educational Resources Information Center

Carducci, Olivia M.

2008-01-01

Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

Coexistence and local μ-stability of multiple equilibrium points for memristive neural networks with nonmonotonic piecewise linear activation functions and unbounded time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2016-12-01

In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5 n equilibrium points located in ℜ n , and 3 n of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

Computation of the anharmonic orbits in two piecewise monotonic maps with a single discontinuity

NASA Astrophysics Data System (ADS)

Li, Yurong; Du, Zhengdong

2017-02-01

In this paper, the bifurcation values for two typical piecewise monotonic maps with a single discontinuity are computed. The variation of the parameter of those maps leads to a sequence of border-collision and period-doubling bifurcations, generating a sequence of anharmonic orbits on the boundary of chaos. The border-collision and period-doubling bifurcation values are computed by the word-lifting technique and the Maple fsolve function or the Newton-Raphson method, respectively. The scaling factors which measure the convergent rates of the bifurcation values and the width of the stable periodic windows, respectively, are investigated. We found that these scaling factors depend on the parameters of the maps, implying that they are not universal. Moreover, if one side of the maps is linear, our numerical results suggest that those quantities converge increasingly. In particular, for the linear-quadratic case, they converge to one of the Feigenbaum constants δ _F= 4.66920160\\cdots.

A Galerkin method for linear PDE systems in circular geometries with structural acoustic applications

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1994-01-01

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the two dimensional wave equations on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems.

Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays.

PubMed

Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde

2015-11-01

The problem of coexistence and dynamical behaviors of multiple equilibrium points is addressed for a class of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. By virtue of the fixed point theorem, nonsmooth analysis theory and other analytical tools, some sufficient conditions are established to guarantee that such n-dimensional memristive Cohen-Grossberg neural networks can have 5(n) equilibrium points, among which 3(n) equilibrium points are locally exponentially stable. It is shown that greater storage capacity can be achieved by neural networks with the non-monotonic activation functions introduced herein than the ones with Mexican-hat-type activation function. In addition, unlike most existing multistability results of neural networks with monotonic activation functions, those obtained 3(n) locally stable equilibrium points are located both in saturated regions and unsaturated regions. The theoretical findings are verified by an illustrative example with computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness

NASA Astrophysics Data System (ADS)

Shui, Xin; Wang, Shimin

2018-02-01

The design and characterization of a mechanical vibration absorber are addressed. A distinctive feature of the absorber is its tunable piecewise-linear stiffness, which is realized by means of a slider with two stop-blocks installed constraining the bilateral deflections of the elastic support. A new analytical approach named as the equivalent stiffness technique (EST) is introduced and then employed to obtain the analytical relations of the frequency, amplitude and phase with a view to exhibit a more comprehensive characterization of the absorber. Experiments are conducted to demonstrate the feasibility of the design. The experimental data show good agreement with the analytical results. The final results indicate that the tunable stiffness absorber (TSA) possesses a typical nonlinear characteristic at each given position of the slider, and its stiffness can be tuned in real time over a wide range by adjusting the slider position. Hence the TSA has a large optimum vibration-absorption range together with a wide suppression band around each optimal position, which contributes to its excellent capacity of vibration absorption.

Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system.

PubMed

Wang, Chunhua; Liu, Xiaoming; Xia, Hu

2017-03-01

In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.

Is long-term exposure to traffic pollution associated with mortality? A small-area study in London.

PubMed

Halonen, Jaana I; Blangiardo, Marta; Toledano, Mireille B; Fecht, Daniela; Gulliver, John; Ghosh, Rebecca; Anderson, H Ross; Beevers, Sean D; Dajnak, David; Kelly, Frank J; Wilkinson, Paul; Tonne, Cathryn

2016-01-01

Long-term exposure to primary traffic pollutants may be harmful for health but few studies have investigated effects on mortality. We examined associations for six primary traffic pollutants with all-cause and cause-specific mortality in 2003-2010 at small-area level using linear and piecewise linear Poisson regression models. In linear models most pollutants showed negative or null association with all-cause, cardiovascular or respiratory mortality. In the piecewise models we observed positive associations in the lowest exposure range (e.g. relative risk (RR) for all-cause mortality 1.07 (95% credible interval (CI) = 1.00-1.15) per 0.15 μg/m(3) increase in exhaust related primary particulate matter ≤2.5 μm (PM2.5)) whereas associations in the highest exposure range were negative (corresponding RR 0.93, 95% CI: 0.91-0.96). Overall, there was only weak evidence of positive associations with mortality. That we found the strongest positive associations in the lowest exposure group may reflect residual confounding by unmeasured confounders that varies by exposure group. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming

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

Sun Wei; Huang, Guo H., E-mail: huang@iseis.org; Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan, S4S 0A2

2012-06-15

Highlights: Black-Right-Pointing-Pointer Inexact piecewise-linearization-based fuzzy flexible programming is proposed. Black-Right-Pointing-Pointer It's the first application to waste management under multiple complexities. Black-Right-Pointing-Pointer It tackles nonlinear economies-of-scale effects in interval-parameter constraints. Black-Right-Pointing-Pointer It estimates costs more accurately than the linear-regression-based model. Black-Right-Pointing-Pointer Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerancemore » intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.« less

Mathematical Tools for Image Reconstruction

DTIC Science & Technology

1991-07-01

l.Diffuse tomography 2.Concentrating a signal in the physical and spectral domains. 3.New explicit solutions for the Kadomtsev - Petviashvili equation 4...the case of the Schroedinger equation it was possible to "beat Heisenberg" with piecewise linear potentials. Finally let me say that the paper Some

Control algorithms for dynamic attenuators

PubMed Central

Hsieh, Scott S.; Pelc, Norbert J.

2014-01-01

Purpose: The authors describe algorithms to control dynamic attenuators in CT and compare their performance using simulated scans. Dynamic attenuators are prepatient beam shaping filters that modulate the distribution of x-ray fluence incident on the patient on a view-by-view basis. These attenuators can reduce dose while improving key image quality metrics such as peak or mean variance. In each view, the attenuator presents several degrees of freedom which may be individually adjusted. The total number of degrees of freedom across all views is very large, making many optimization techniques impractical. The authors develop a theory for optimally controlling these attenuators. Special attention is paid to a theoretically perfect attenuator which controls the fluence for each ray individually, but the authors also investigate and compare three other, practical attenuator designs which have been previously proposed: the piecewise-linear attenuator, the translating attenuator, and the double wedge attenuator. Methods: The authors pose and solve the optimization problems of minimizing the mean and peak variance subject to a fixed dose limit. For a perfect attenuator and mean variance minimization, this problem can be solved in simple, closed form. For other attenuator designs, the problem can be decomposed into separate problems for each view to greatly reduce the computational complexity. Peak variance minimization can be approximately solved using iterated, weighted mean variance (WMV) minimization. Also, the authors develop heuristics for the perfect and piecewise-linear attenuators which do not require a priori knowledge of the patient anatomy. The authors compare these control algorithms on different types of dynamic attenuators using simulated raw data from forward projected DICOM files of a thorax and an abdomen. Results: The translating and double wedge attenuators reduce dose by an average of 30% relative to current techniques (bowtie filter with tube current modulation) without increasing peak variance. The 15-element piecewise-linear dynamic attenuator reduces dose by an average of 42%, and the perfect attenuator reduces dose by an average of 50%. Improvements in peak variance are several times larger than improvements in mean variance. Heuristic control eliminates the need for a prescan. For the piecewise-linear attenuator, the cost of heuristic control is an increase in dose of 9%. The proposed iterated WMV minimization produces results that are within a few percent of the true solution. Conclusions: Dynamic attenuators show potential for significant dose reduction. A wide class of dynamic attenuators can be accurately controlled using the described methods. PMID:24877818

Plate and butt-weld stresses beyond elastic limit, material and structural modeling

NASA Technical Reports Server (NTRS)

Verderaime, V.

1991-01-01

Ultimate safety factors of high performance structures depend on stress behavior beyond the elastic limit, a region not too well understood. An analytical modeling approach was developed to gain fundamental insights into inelastic responses of simple structural elements. Nonlinear material properties were expressed in engineering stresses and strains variables and combined with strength of material stress and strain equations similar to numerical piece-wise linear method. Integrations are continuous which allows for more detailed solutions. Included with interesting results are the classical combined axial tension and bending load model and the strain gauge conversion to stress beyond the elastic limit. Material discontinuity stress factors in butt-welds were derived. This is a working-type document with analytical methods and results applicable to all industries of high reliability structures.

Nonlinear Deformation of a Piecewise Homogeneous Cylinder Under the Action of Rotation

NASA Astrophysics Data System (ADS)

Akhundov, V. M.; Kostrova, M. M.

2018-05-01

Deformation of a piecewise cylinder under the action of rotation is investigated. The cylinder consists of an elastic matrix with circular fibers of square cross section made of a more rigid elastic material and arranged doubly periodically in the cylinder. Behavior of the cylinder under large displacements and deformations is examined using the equations of a nonlinear elasticity theory for cylinder constituents. The problem posed is solved by the finite-difference method using the method of continuation with respect to the rotational speed of the cylinder.

Bayesian hierarchical piecewise regression models: a tool to detect trajectory divergence between groups in long-term observational studies.

PubMed

Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J

2017-06-06

Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non-linear longitudinal outcomes, enabling the identification of the age at which risk factor trajectories diverge between groups of participants. The method is suitable for the analysis of unbalanced longitudinal data, with only a limited number of repeated measures per participants and where the time-related outcome is typically marked by transitional changes or by distinct phases of change over time.

A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fishes at river infrastructure.

PubMed

Boys, C A; Robinson, W; Miller, B; Pflugrath, B; Baumgartner, L J; Navarro, A; Brown, R; Deng, Z

2016-05-01

A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species, Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus, following simulated infrastructure passage in a barometric chamber. The probability of injuries such as swimbladder rupture, exophthalmia and haemorrhage, and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change, R(NE:A) ) reduced. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in R(NE:A) that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multispecies precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (R(NE:A) of 0·7) should protect downstream migrating juveniles of these two physoclistous species sufficiently. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones. © 2016 The Fisheries Society of the British Isles.

Dynamical properties of maps fitted to data in the noise-free limit

PubMed Central

Lindström, Torsten

2013-01-01

We argue that any attempt to classify dynamical properties from nonlinear finite time-series data requires a mechanistic model fitting the data better than piecewise linear models according to standard model selection criteria. Such a procedure seems necessary but still not sufficient. PMID:23768079

Sequential limiting in continuous and discontinuous Galerkin methods for the Euler equations

NASA Astrophysics Data System (ADS)

Dobrev, V.; Kolev, Tz.; Kuzmin, D.; Rieben, R.; Tomov, V.

2018-03-01

We present a new predictor-corrector approach to enforcing local maximum principles in piecewise-linear finite element schemes for the compressible Euler equations. The new element-based limiting strategy is suitable for continuous and discontinuous Galerkin methods alike. In contrast to synchronized limiting techniques for systems of conservation laws, we constrain the density, momentum, and total energy in a sequential manner which guarantees positivity preservation for the pressure and internal energy. After the density limiting step, the total energy and momentum gradients are adjusted to incorporate the irreversible effect of density changes. Antidiffusive corrections to bounds-compatible low-order approximations are limited to satisfy inequality constraints for the specific total and kinetic energy. An accuracy-preserving smoothness indicator is introduced to gradually adjust lower bounds for the element-based correction factors. The employed smoothness criterion is based on a Hessian determinant test for the density. A numerical study is performed for test problems with smooth and discontinuous solutions.

Refined Zigzag Theory for Laminated Composite and Sandwich Plates

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, Marco

2009-01-01

A refined zigzag theory is presented for laminated-composite and sandwich plates that includes the kinematics of first-order shear deformation theory as its baseline. The theory is variationally consistent and is derived from the virtual work principle. Novel piecewise-linear zigzag functions that provide a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories are used. The formulation does not enforce full continuity of the transverse shear stresses across the plate s thickness, yet is robust. Transverse-shear correction factors are not required to yield accurate results. The theory is devoid of the shortcomings inherent in the previous zigzag theories including shear-force inconsistency and difficulties in simulating clamped boundary conditions, which have greatly limited the accuracy of these theories. This new theory requires only C(sup 0)-continuous kinematic approximations and is perfectly suited for developing computationally efficient finite elements. The theory should be useful for obtaining relatively efficient, accurate estimates of structural response needed to design high-performance load-bearing aerospace structures.

Weak stability of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Catania, Davide; D'Abbicco, Marcello; Secchi, Paolo

2016-09-01

We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the Maxwell system for the electric and the magnetic fields. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. We study the linear stability of rectilinear plasma-vacuum interfaces by computing the Kreiss-Lopatinskiĭ determinant of an associated linearized boundary value problem. Apart from possible resonances, we obtain that the piecewise constant plasma-vacuum interfaces are always weakly linearly stable, independently of the size of tangential velocity, magnetic and electric fields on both sides of the characteristic discontinuity. We also prove that solutions to the linearized problem obey an energy estimate with a loss of regularity with respect to the source terms, both in the interior domain and on the boundary, due to the failure of the uniform Kreiss-Lopatinskiĭ condition, as the Kreiss-Lopatinskiĭ determinant associated with this linearized boundary value problem has roots on the boundary of the frequency space. In the proof of the a priori estimates, a crucial part is played by the construction of symmetrizers for a reduced differential system, which has poles at which the Kreiss-Lopatinskiĭ condition may fail simultaneously.

Longitudinal Models of Reading Achievement of Students with Learning Disabilities and without Disabilities

ERIC Educational Resources Information Center

Sullivan, Amanda L.; Kohli, Nidhi; Farnsworth, Elyse M.; Sadeh, Shanna; Jones, Leila

2017-01-01

Objective: Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. Method: We drew an analytic sample of 1,990 students from…

Computerized Method for the Generation of Molecular Transmittance Functions in the Infrared.

DTIC Science & Technology

1980-04-01

predict this behavior, we conclude that the first method using linear function of x is accurate enough to be used in the actual application. The...PIECEWISE- ANALITICAL TRANSMISSION FUNCTION.’//20X, * ’STANDARD DEVIATIONS BETWEEN THE ACTUAL TAU AND THE RECOMPUTED’, * ’ TAU VALUES ARE COMPUTED.’////) 77

The dynamical analysis of modified two-compartment neuron model and FPGA implementation

NASA Astrophysics Data System (ADS)

Lin, Qianjin; Wang, Jiang; Yang, Shuangming; Yi, Guosheng; Deng, Bin; Wei, Xile; Yu, Haitao

2017-10-01

The complexity of neural models is increasing with the investigation of larger biological neural network, more various ionic channels and more detailed morphologies, and the implementation of biological neural network is a task with huge computational complexity and power consumption. This paper presents an efficient digital design using piecewise linearization on field programmable gate array (FPGA), to succinctly implement the reduced two-compartment model which retains essential features of more complicated models. The design proposes an approximate neuron model which is composed of a set of piecewise linear equations, and it can reproduce different dynamical behaviors to depict the mechanisms of a single neuron model. The consistency of hardware implementation is verified in terms of dynamical behaviors and bifurcation analysis, and the simulation results including varied ion channel characteristics coincide with the biological neuron model with a high accuracy. Hardware synthesis on FPGA demonstrates that the proposed model has reliable performance and lower hardware resource compared with the original two-compartment model. These investigations are conducive to scalability of biological neural network in reconfigurable large-scale neuromorphic system.

Hierarchical structure in sharply divided phase space for the piecewise linear map

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ˜t-2 , the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Resonant activation in piecewise linear asymmetric potentials.

PubMed

Fiasconaro, Alessandro; Spagnolo, Bernardo

2011-04-01

This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time τ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of τ; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments. ©2011 American Physical Society

A study of different modeling choices for simulating platelets within the immersed boundary method

PubMed Central

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.

2012-01-01

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. PMID:23585704

A spatial domain decomposition approach to distributed H ∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

NASA Astrophysics Data System (ADS)

Wang, Jun-Wei; Liu, Ya-Qiang; Hu, Yan-Yan; Sun, Chang-Yin

2017-12-01

This paper discusses the design problem of distributed H∞ Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H∞ performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H∞ observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.

A new method for analysis of limit cycle behavior of the NASA/JPL 70-meter antenna axis servos

NASA Technical Reports Server (NTRS)

Hill, R. E.

1989-01-01

A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.

Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

NASA Astrophysics Data System (ADS)

Kaloerov, S. A.; Koshkin, A. A.

2017-11-01

An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

Stabilization for sampled-data neural-network-based control systems.

PubMed

Zhu, Xun-Lin; Wang, Youyi

2011-02-01

This paper studies the problem of stabilization for sampled-data neural-network-based control systems with an optimal guaranteed cost. Unlike previous works, the resulting closed-loop system with variable uncertain sampling cannot simply be regarded as an ordinary continuous-time system with a fast-varying delay in the state. By defining a novel piecewise Lyapunov functional and using a convex combination technique, the characteristic of sampled-data systems is captured. A new delay-dependent stabilization criterion is established in terms of linear matrix inequalities such that the maximal sampling interval and the minimal guaranteed cost control performance can be obtained. It is shown that the newly proposed approach can lead to less conservative and less complex results than the existing ones. Application examples are given to illustrate the effectiveness and the benefits of the proposed method.

The piecewise-linear dynamic attenuator reduces the impact of count rate loss with photon-counting detectors

NASA Astrophysics Data System (ADS)

Hsieh, Scott S.; Pelc, Norbert J.

2014-06-01

Photon counting x-ray detectors (PCXDs) offer several advantages compared to standard energy-integrating x-ray detectors, but also face significant challenges. One key challenge is the high count rates required in CT. At high count rates, PCXDs exhibit count rate loss and show reduced detective quantum efficiency in signal-rich (or high flux) measurements. In order to reduce count rate requirements, a dynamic beam-shaping filter can be used to redistribute flux incident on the patient. We study the piecewise-linear attenuator in conjunction with PCXDs without energy discrimination capabilities. We examined three detector models: the classic nonparalyzable and paralyzable detector models, and a ‘hybrid’ detector model which is a weighted average of the two which approximates an existing, real detector (Taguchi et al 2011 Med. Phys. 38 1089-102 ). We derive analytic expressions for the variance of the CT measurements for these detectors. These expressions are used with raw data estimated from DICOM image files of an abdomen and a thorax to estimate variance in reconstructed images for both the dynamic attenuator and a static beam-shaping (‘bowtie’) filter. By redistributing flux, the dynamic attenuator reduces dose by 40% without increasing peak variance for the ideal detector. For non-ideal PCXDs, the impact of count rate loss is also reduced. The nonparalyzable detector shows little impact from count rate loss, but with the paralyzable model, count rate loss leads to noise streaks that can be controlled with the dynamic attenuator. With the hybrid model, the characteristic count rates required before noise streaks dominate the reconstruction are reduced by a factor of 2 to 3. We conclude that the piecewise-linear attenuator can reduce the count rate requirements of the PCXD in addition to improving dose efficiency. The magnitude of this reduction depends on the detector, with paralyzable detectors showing much greater benefit than nonparalyzable detectors.

Linear stability analysis of collective neutrino oscillations without spurious modes

NASA Astrophysics Data System (ADS)

Morinaga, Taiki; Yamada, Shoichi

2018-01-01

Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.

Piecewise exponential survival times and analysis of case-cohort data.

PubMed

Li, Yan; Gail, Mitchell H; Preston, Dale L; Graubard, Barry I; Lubin, Jay H

2012-06-15

Case-cohort designs select a random sample of a cohort to be used as control with cases arising from the follow-up of the cohort. Analyses of case-cohort studies with time-varying exposures that use Cox partial likelihood methods can be computer intensive. We propose a piecewise-exponential approach where Poisson regression model parameters are estimated from a pseudolikelihood and the corresponding variances are derived by applying Taylor linearization methods that are used in survey research. The proposed approach is evaluated using Monte Carlo simulations. An illustration is provided using data from the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study of male smokers in Finland, where a case-cohort study of serum glucose level and pancreatic cancer was analyzed. Copyright © 2012 John Wiley & Sons, Ltd.

Equilibria of an epidemic game with piecewise linear social distancing cost.

PubMed

Reluga, Timothy C

2013-10-01

Around the world, infectious disease epidemics continue to threaten people's health. When epidemics strike, we often respond by changing our behaviors to reduce our risk of infection. This response is sometimes called "social distancing." Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on our behaviors. Differential population game theory provides a method for resolving this circular dependence. Here, I present the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, but bounded below by zero. Equilibrium solutions are constructed in closed-form for an open-ended epidemic. Constructions are also provided for epidemics that are stopped by the deployment of a vaccination that becomes available a fixed-time after the start of the epidemic. This can be used to anticipate a window of opportunity during which mass vaccination can significantly reduce the cost of an epidemic.

A piecewise regression approach for determining biologically relevant hydraulic thresholds for the protection of fish at river infrastructure

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

Boys, Craig A.; Robinson, Wayne; Miller, Brett

2016-05-13

Barotrauma injury can occur when fish are exposed to rapid decompression during downstream passage through river infrastructure. A piecewise regression approach was used to objectively quantify barotrauma injury thresholds in two physoclistous species (Murray cod Maccullochella peelii and silver perch Bidyanus bidyanus) following simulated infrastructure passage in barometric chambers. The probability of injuries such as swim bladder rupture; exophthalmia; and haemorrhage and emphysema in various organs increased as the ratio between the lowest exposure pressure and the acclimation pressure (ratio of pressure change RPCE/A) fell. The relationship was typically non-linear and piecewise regression was able to quantify thresholds in RPCE/Amore » that once exceeded resulted in a substantial increase in barotrauma injury. Thresholds differed among injury types and between species but by applying a multi-species precautionary principle, the maintenance of exposure pressures at river infrastructure above 70% of acclimation pressure (RPCE/A of 0.7) should sufficiently protect downstream migrating juveniles of these two physoclistous species. These findings have important implications for determining the risk posed by current infrastructures and informing the design and operation of new ones.« less

Existence of almost periodic solutions for forced perturbed systems with piecewise constant argument

NASA Astrophysics Data System (ADS)

Xia, Yonghui; Huang, Zhenkun; Han, Maoan

2007-09-01

Certain almost periodic forced perturbed systems with piecewise argument are considered in this paper. By using the contraction mapping principle and some new analysis technique, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution of these systems. Furthermore, we study the harmonic and subharmonic solutions of these systems. The obtained results generalize the previous known results such as [A.M. Fink, Almost Periodic Differential Equation, Lecture Notes in Math., volE 377, Springer-Verlag, Berlin, 1974; C.Y. He, Almost Periodic Differential Equations, Higher Education Press, Beijing, 1992 (in Chinese); Z.S. Lin, The existence of almost periodic solution of linear system, Acta Math. Sinica 22 (5) (1979) 515-528 (in Chinese); C.Y. He, Existence of almost periodic solutions of perturbation systems, Ann. Differential Equations 9 (2) (1992) 173-181; Y.H. Xia, M. Lin, J. Cao, The existence of almost periodic solutions of certain perturbation system, J. Math. Anal. Appl. 310 (1) (2005) 81-96]. Finally, a tangible example and its numeric simulations show the feasibility of our results, the comparison between non-perturbed system and perturbed system, the relation between systems with and without piecewise argument.

Tortuosity of lightning return stroke channels

NASA Technical Reports Server (NTRS)

Levine, D. M.; Gilson, B.

1984-01-01

Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data.

Holographic representation of space-variant systems: system theory.

PubMed

Marks Ii, R J; Krile, T F

1976-09-01

System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.

Piecewise Linear Approach for Timing Simulation of VLSI (Very-Large-Scale-Integrated) Circuits on Serial and Parallel Computers.

DTIC Science & Technology

1987-12-01

8217ftp.. *,*IS ~. ~bw ~ ft.. p ’ft ’ft ft.. ’ft *I~ P* ’ft ’p 0n-I ci via 1 ca j I .11’ ft~ ’ fttH vialca *- ’ft ft..I ft. ’ft ft.. --ft ..ft ’ft ftp

Bifurcation from an invariant to a non-invariant attractor

NASA Astrophysics Data System (ADS)

Mandal, D.

2016-12-01

Switching dynamical systems are very common in many areas of physics and engineering. We consider a piecewise linear map that periodically switches between more than one different functional forms. We show that in such systems it is possible to have a border collision bifurcation where the system transits from an invariant attractor to a non-invariant attractor.

On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1993-01-01

The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

Transformations based on continuous piecewise-affine velocity fields

DOE PAGES

Freifeld, Oren; Hauberg, Soren; Batmanghelich, Kayhan; ...

2017-01-11

Here, we propose novel finite-dimensional spaces of well-behaved Rn → Rn transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization overmore » monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available.« less

Transformations Based on Continuous Piecewise-Affine Velocity Fields

PubMed Central

Freifeld, Oren; Hauberg, Søren; Batmanghelich, Kayhan; Fisher, Jonn W.

2018-01-01

We propose novel finite-dimensional spaces of well-behaved ℝn → ℝn transformations. The latter are obtained by (fast and highly-accurate) integration of continuous piecewise-affine velocity fields. The proposed method is simple yet highly expressive, effortlessly handles optional constraints (e.g., volume preservation and/or boundary conditions), and supports convenient modeling choices such as smoothing priors and coarse-to-fine analysis. Importantly, the proposed approach, partly due to its rapid likelihood evaluations and partly due to its other properties, facilitates tractable inference over rich transformation spaces, including using Markov-Chain Monte-Carlo methods. Its applications include, but are not limited to: monotonic regression (more generally, optimization over monotonic functions); modeling cumulative distribution functions or histograms; time-warping; image warping; image registration; real-time diffeomorphic image editing; data augmentation for image classifiers. Our GPU-based code is publicly available. PMID:28092517

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

The Use of Orthogonal Polarizations in Microwave Imagery of Isolated Canine Kidney

NASA Astrophysics Data System (ADS)

Larsen, L. E.; Jacobi, J. H.

1980-06-01

A method of imaging biological targets using microwave radiation at a frequency of 4 GHz is presented. Linearly polarized radiation is transmitted through an isolated canine kidney and received with co-polarized and cross-polarized antennas. Images are displayed as the spatial variation of the magnitude of the transmission scattering parameter S21 for each mode of polarization. The relationship between the spatial variation of the magnitude of S21 and canine renal anatomy is discussed. It is shown that within the kidney the cross-polarized image tends to emphasize linear or piecewise linear structures, whereas the co-polarized image balances renal cortical lobulations.

Nonlinear analysis of a family of LC tuned inverters. [dc to square wave circuits for power conditioning

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1974-01-01

A family of four dc-to-square-wave LC tuned inverters are analyzed using singular point. Limit cycles and waveshape characteristics are given for three modes of oscillation: quasi-harmonic, relaxation, and discontinuous. An inverter in which the avalanche breakdown of the transistor emitter-to-base junction occurs is discussed and the starting characteristics of this family of inverters are presented. The LC tuned inverters are shown to belong to a family of inverters with a common equivalent circuit consisting of only three 'series' elements: a five-segment piecewise-linear current-controlled resistor, linear inductor, and linear capacitor.

A hierarchical preconditioner for the electric field integral equation on unstructured meshes based on primal and dual Haar bases

NASA Astrophysics Data System (ADS)

Adrian, S. B.; Andriulli, F. P.; Eibert, T. F.

2017-02-01

A new hierarchical basis preconditioner for the electric field integral equation (EFIE) operator is introduced. In contrast to existing hierarchical basis preconditioners, it works on arbitrary meshes and preconditions both the vector and the scalar potential within the EFIE operator. This is obtained by taking into account that the vector and the scalar potential discretized with loop-star basis functions are related to the hypersingular and the single layer operator (i.e., the well known integral operators from acoustics). For the single layer operator discretized with piecewise constant functions, a hierarchical preconditioner can easily be constructed. Thus the strategy we propose in this work for preconditioning the EFIE is the transformation of the scalar and the vector potential into operators equivalent to the single layer operator and to its inverse. More specifically, when the scalar potential is discretized with star functions as source and testing functions, the resulting matrix is a single layer operator discretized with piecewise constant functions and multiplied left and right with two additional graph Laplacian matrices. By inverting these graph Laplacian matrices, the discretized single layer operator is obtained, which can be preconditioned with the hierarchical basis. Dually, when the vector potential is discretized with loop functions, the resulting matrix can be interpreted as a hypersingular operator discretized with piecewise linear functions. By leveraging on a scalar Calderón identity, we can interpret this operator as spectrally equivalent to the inverse single layer operator. Then we use a linear-in-complexity, closed-form inverse of the dual hierarchical basis to precondition the hypersingular operator. The numerical results show the effectiveness of the proposed preconditioner and the practical impact of theoretical developments in real case scenarios.

A Parametric Computational Model of the Action Potential of Pacemaker Cells.

PubMed

Ai, Weiwei; Patel, Nitish D; Roop, Partha S; Malik, Avinash; Andalam, Sidharta; Yip, Eugene; Allen, Nathan; Trew, Mark L

2018-01-01

A flexible, efficient, and verifiable pacemaker cell model is essential to the design of real-time virtual hearts that can be used for closed-loop validation of cardiac devices. A new parametric model of pacemaker action potential is developed to address this need. The action potential phases are modeled using hybrid automaton with one piecewise-linear continuous variable. The model can capture rate-dependent dynamics, such as action potential duration restitution, conduction velocity restitution, and overdrive suppression by incorporating nonlinear update functions. Simulated dynamics of the model compared well with previous models and clinical data. The results show that the parametric model can reproduce the electrophysiological dynamics of a variety of pacemaker cells, such as sinoatrial node, atrioventricular node, and the His-Purkinje system, under varying cardiac conditions. This is an important contribution toward closed-loop validation of cardiac devices using real-time heart models.

Optimized Quasi-Interpolators for Image Reconstruction.

PubMed

Sacht, Leonardo; Nehab, Diego

2015-12-01

We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.

Shear waves in inhomogeneous, compressible fluids in a gravity field.

PubMed

Godin, Oleg A

2014-03-01

While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

Random center vortex lines in continuous 3D space-time

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

Höllwieser, Roman; Institute of Atomic and Subatomic Physics, Vienna University of Technology, Operngasse 9, 1040 Vienna; Altarawneh, Derar

2016-01-22

We present a model of center vortices, represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a cuboid with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configuration, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. Using the model, we study both vortex percolation andmore » the potential V(R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We have found three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature. The model reproduces the qualitative features of confinement physics seen in SU(2) Yang-Mills theory.« less

Monitoring with a modified Robel pole on meadows in the central Black Hills of South Dakaota

Treesearch

Daniel W. Uresk; Ted A. Benzon

2007-01-01

This study using a modified Robel pole was conducted in the central Black Hills, South Dakota. The objectives were to test the relationship between visual obstruction readings and standing herbage, develop guidelines for monitoring, and estimate sample size. The relationship between visual obstruction and standing herbage was linear with 2 segments in a piecewise model...

Minimum time acceleration of aircraft turbofan engines by using an algorithm based on nonlinear programming

NASA Technical Reports Server (NTRS)

Teren, F.

1977-01-01

Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.

A megahertz-frequency tunable piecewise-linear electromechanical resonator realized via nonlinear feedback

NASA Astrophysics Data System (ADS)

Bajaj, Nikhil; Chiu, George T.-C.; Rhoads, Jeffrey F.

2018-07-01

Vibration-based sensing modalities traditionally have relied upon monitoring small shifts in natural frequency in order to detect structural changes (such as those in mass or stiffness). In contrast, bifurcation-based sensing schemes rely on the detection of a qualitative change in the behavior of a system as a parameter is varied. This can produce easy-to-detect changes in response amplitude with high sensitivity to structural change, but requires resonant devices with specific dynamic behavior which is not always easily reproduced. Desirable behavior for such devices can be produced reliably via nonlinear feedback circuitry, but has in past efforts been largely limited to sub-MHz operation, partially due to the time delay limitations present in certain nonlinear feedback circuits, such as multipliers. This work demonstrates the design and implementation of a piecewise-linear resonator realized via diode- and integrated circuit-based feedback electronics and a quartz crystal resonator. The proposed system is fabricated and characterized, and the creation and selective placement of the bifurcation points of the overall electromechanical system is demonstrated by tuning the circuit gains. The demonstrated circuit operates at 16 MHz. Preliminary modeling and analysis is presented that qualitatively agrees with the experimentally-observed behavior.

Global and local curvature in density functional theory.

PubMed

Zhao, Qing; Ioannidis, Efthymios I; Kulik, Heather J

2016-08-07

Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.

DESCARTES' RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA.

PubMed

Bhaskar, Anand; Song, Yun S

2014-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.

DESCARTES’ RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA1

PubMed Central

Bhaskar, Anand; Song, Yun S.

2016-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the “folded” SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes’ rule of signs for polynomials to the Laplace transform of piecewise continuous functions. PMID:28018011

A Novel Multiobjective Evolutionary Algorithm Based on Regression Analysis

PubMed Central

Song, Zhiming; Wang, Maocai; Dai, Guangming; Vasile, Massimiliano

2015-01-01

As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m − 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m − 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper. PMID:25874246

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2015-01-01

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

Nonlinear filtering properties of detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken; Tsujimoto, Yutaka

2016-11-01

Detrended fluctuation analysis (DFA) has been widely used for quantifying long-range correlation and fractal scaling behavior. In DFA, to avoid spurious detection of scaling behavior caused by a nonstationary trend embedded in the analyzed time series, a detrending procedure using piecewise least-squares fitting has been applied. However, it has been pointed out that the nonlinear filtering properties involved with detrending may induce instabilities in the scaling exponent estimation. To understand this issue, we investigate the adverse effects of the DFA detrending procedure on the statistical estimation. We show that the detrending procedure using piecewise least-squares fitting results in the nonuniformly weighted estimation of the root-mean-square deviation and that this property could induce an increase in the estimation error. In addition, for comparison purposes, we investigate the performance of a centered detrending moving average analysis with a linear detrending filter and sliding window DFA and show that these methods have better performance than the standard DFA.

An approach for maximizing the smallest eigenfrequency of structure vibration based on piecewise constant level set method

NASA Astrophysics Data System (ADS)

Zhang, Zhengfang; Chen, Weifeng

2018-05-01

Maximization of the smallest eigenfrequency of the linearized elasticity system with area constraint is investigated. The elasticity system is extended into a large background domain, but the void is vacuum and not filled with ersatz material. The piecewise constant level set (PCLS) method is applied to present two regions, the original material region and the void region. A quadratic PCLS function is proposed to represent the characteristic function. Consequently, the functional derivative of the smallest eigenfrequency with respect to PCLS function takes nonzero value in the original material region and zero in the void region. A penalty gradient algorithm is proposed, which initializes the whole background domain with the original material and decreases the area of original material region till the area constraint is satisfied. 2D and 3D numerical examples are presented, illustrating the validity of the proposed algorithm.

Online Normalization Algorithm for Engine Turbofan Monitoring

DTIC Science & Technology

2014-10-02

Online Normalization Algorithm for Engine Turbofan Monitoring Jérôme Lacaille 1 , Anastasios Bellas 2 1 Snecma, 77550 Moissy-Cramayel, France...understand the behavior of a turbofan engine, one first needs to deal with the variety of data acquisition contexts. Each time a set of measurements is...it auto-adapts itself with piecewise linear models. 1. INTRODUCTION Turbofan engine abnormality diagnosis uses three steps: reduction of

Hamiltonian flows with random-walk behaviour originating from zero-sum games and fictitious play

NASA Astrophysics Data System (ADS)

van Strien, Sebastian

2011-06-01

In this paper we introduce Hamiltonian dynamics, inspired by zero-sum games (best response and fictitious play dynamics). The Hamiltonian functions we consider are continuous and piecewise affine (and of a very simple form). It follows that the corresponding Hamiltonian vector fields are discontinuous and multi-valued. Differential equations with discontinuities along a hyperplane are often called 'Filippov systems', and there is a large literature on such systems, see for example (di Bernardo et al 2008 Theory and applications Piecewise-Smooth Dynamical Systems (Applied Mathematical Sciences vol 163) (London: Springer); Kunze 2000 Non-Smooth Dynamical Systems (Lecture Notes in Mathematics vol 1744) (Berlin: Springer); Leine and Nijmeijer 2004 Dynamics and Bifurcations of Non-smooth Mechanical Systems (Lecture Notes in Applied and Computational Mechanics vol 18) (Berlin: Springer)). The special feature of the systems we consider here is that they have discontinuities along a large number of intersecting hyperplanes. Nevertheless, somewhat surprisingly, the flow corresponding to such a vector field exists, is unique and continuous. We believe that these vector fields deserve attention, because it turns out that the resulting dynamics are rather different from those found in more classically defined Hamiltonian dynamics. The vector field is extremely simple: outside codimension-one hyperplanes it is piecewise constant and so the flow phit piecewise a translation (without stationary points). Even so, the dynamics can be rather rich and complicated as a detailed study of specific examples show (see for example theorems 7.1 and 7.2 and also (Ostrovski and van Strien 2011 Regular Chaotic Dynf. 16 129-54)). In the last two sections of the paper we give some applications to game theory, and finish with posing a version of the Palis conjecture in the context of the class of non-smooth systems studied in this paper. To Jacob Palis on his 70th birthday.

Path Following in the Exact Penalty Method of Convex Programming.

PubMed

Zhou, Hua; Lange, Kenneth

2015-07-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

Path Following in the Exact Penalty Method of Convex Programming

PubMed Central

Zhou, Hua; Lange, Kenneth

2015-01-01

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value. PMID:26366044

Optimal control of parametric oscillations of compressed flexible bars

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

In this paper the problem of damping of the linear systems oscillations with piece-wise constant control is solved. The motion of bar construction is reduced to the form described by Hill's differential equation using the Bubnov-Galerkin method. To calculate switching moments of the one-side control the method of sequential linear programming is used. The elements of the fundamental matrix of the Hill's equation are approximated by trigonometric series. Examples of the optimal control of the systems for various initial conditions and different number of control stages have been calculated. The corresponding phase trajectories and transient processes are represented.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

The dynamics of two linearly coupled Goodwin oscillators

NASA Astrophysics Data System (ADS)

Antonova, A. O.; Reznik, S. N.; Todorov, M. D.

2017-10-01

In this paper the Puu model of the interaction of Goodwin's business cycles for two regions is reconsidered. We investigated the effect of the accelerator coefficients and the Hicksian 'ceiling' and 'floor' parameters on the time dynamics of incomes for different values of marginal propensity to import. The cases when the periods of isolated Goodwin's cycles are close, and when they differ approximately twice are considered. By perturbation theory we obtained the formulas for slowly varying amplitudes and phase difference of weakly nonlinear coupled Goodwin oscillations. The coupled oscillations of two Goodwin's cycles with piecewise linear accelerators with only 'floor' are considered.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

A prototype piecewise-linear dynamic attenuator

NASA Astrophysics Data System (ADS)

Hsieh, Scott S.; Peng, Mark V.; May, Christopher A.; Shunhavanich, Picha; Fleischmann, Dominik; Pelc, Norbert J.

2016-07-01

The piecewise-linear dynamic attenuator has been proposed as a mechanism in CT scanning for personalizing the x-ray illumination on a patient- and application-specific basis. Previous simulations have shown benefits in image quality, scatter, and dose objectives. We report on the first prototype implementation. This prototype is reduced in scale and speed and is integrated into a tabletop CT system with a smaller field of view (25 cm) and longer scan time (42 s) compared to a clinical system. Stainless steel wedges were machined and affixed to linear actuators, which were in turn held secure by a frame built using rapid prototyping technologies. The actuators were computer-controlled, with characteristic noise of about 100 microns. Simulations suggest that in a clinical setting, the impact of actuator noise could lead to artifacts of only 1 HU. Ring artifacts were minimized by careful design of the wedges. A water beam hardening correction was applied and the scan was collimated to reduce scatter. We scanned a 16 cm water cylinder phantom as well as an anthropomorphic pediatric phantom. The artifacts present in reconstructed images are comparable to artifacts normally seen with this tabletop system. Compared to a flat-field reference scan, increased detectability at reduced dose is shown and streaking is reduced. Artifacts are modest in our images and further refinement is possible. Issues of mechanical speed and stability in the challenging clinical CT environment will be addressed in a future design.

Growing Readers: A Hierarchical Linear Model of Children's Reading Growth During the First 2 Years of School

ERIC Educational Resources Information Center

McCoach, D. Betsy; O'Connell, Ann A.; Reis, Sally M.; Levitt, Heather A.

2006-01-01

Using the first 4 waves of data from the Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K), this piecewise 3-level (time-student-school) growth-curve model provides a portrait of students' reading growth over the first 2 years of school. On average, students make much greater reading gains in 1st grade than they do in kindergarten.…

COED Transactions, Vol. IX, No. 1, January 1977. Rapid Production of System Phase-Plane Portraits on the EAI 380 Hybrid/Analog Computer.

ERIC Educational Resources Information Center

Marcovitz, Alan B., Ed.

The method of phase-plane presentation as an educational tool in the study of the dynamic behavior of systems is discussed. In the treatment of nonlinear or piecewise-linear systems, the phase-plane portrait is used to exhibit the nature of singular points, regions of stability, and switching lines to aid comprehension. A technique is described by…

On Algorithms for Generating Computationally Simple Piecewise Linear Classifiers

DTIC Science & Technology

1989-05-01

suffers. - Waveform classification, e.g. speech recognition, seismic analysis (i.e. discrimination between earthquakes and nuclear explosions), target...assuming Gaussian distributions (B-G) d) Bayes classifier with probability densities estimated with the k-N-N method (B- kNN ) e) The -arest neighbour...range of classifiers are chosen including a fast, easy computable and often used classifier (B-G), reliable and complex classifiers (B- kNN and NNR

A Bayesian model averaging method for the derivation of reservoir operating rules

NASA Astrophysics Data System (ADS)

Zhang, Jingwen; Liu, Pan; Wang, Hao; Lei, Xiaohui; Zhou, Yanlai

2015-09-01

Because the intrinsic dynamics among optimal decision making, inflow processes and reservoir characteristics are complex, functional forms of reservoir operating rules are always determined subjectively. As a result, the uncertainty of selecting form and/or model involved in reservoir operating rules must be analyzed and evaluated. In this study, we analyze the uncertainty of reservoir operating rules using the Bayesian model averaging (BMA) model. Three popular operating rules, namely piecewise linear regression, surface fitting and a least-squares support vector machine, are established based on the optimal deterministic reservoir operation. These individual models provide three-member decisions for the BMA combination, enabling the 90% release interval to be estimated by the Markov Chain Monte Carlo simulation. A case study of China's the Baise reservoir shows that: (1) the optimal deterministic reservoir operation, superior to any reservoir operating rules, is used as the samples to derive the rules; (2) the least-squares support vector machine model is more effective than both piecewise linear regression and surface fitting; (3) BMA outperforms any individual model of operating rules based on the optimal trajectories. It is revealed that the proposed model can reduce the uncertainty of operating rules, which is of great potential benefit in evaluating the confidence interval of decisions.

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

PubMed Central

Zhao, Rui; Catalano, Paul; DeGruttola, Victor G.; Michor, Franziska

2017-01-01

The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data. PMID:28723910

Extraction of object skeletons in multispectral imagery by the orthogonal regression fitting

NASA Astrophysics Data System (ADS)

Palenichka, Roman M.; Zaremba, Marek B.

2003-03-01

Accurate and automatic extraction of skeletal shape of objects of interest from satellite images provides an efficient solution to such image analysis tasks as object detection, object identification, and shape description. The problem of skeletal shape extraction can be effectively solved in three basic steps: intensity clustering (i.e. segmentation) of objects, extraction of a structural graph of the object shape, and refinement of structural graph by the orthogonal regression fitting. The objects of interest are segmented from the background by a clustering transformation of primary features (spectral components) with respect to each pixel. The structural graph is composed of connected skeleton vertices and represents the topology of the skeleton. In the general case, it is a quite rough piecewise-linear representation of object skeletons. The positions of skeleton vertices on the image plane are adjusted by means of the orthogonal regression fitting. It consists of changing positions of existing vertices according to the minimum of the mean orthogonal distances and, eventually, adding new vertices in-between if a given accuracy if not yet satisfied. Vertices of initial piecewise-linear skeletons are extracted by using a multi-scale image relevance function. The relevance function is an image local operator that has local maximums at the centers of the objects of interest.

Comparison of linear, skewed-linear, and proportional hazard models for the analysis of lambing interval in Ripollesa ewes.

PubMed

Casellas, J; Bach, R

2012-06-01

Lambing interval is a relevant reproductive indicator for sheep populations under continuous mating systems, although there is a shortage of selection programs accounting for this trait in the sheep industry. Both the historical assumption of small genetic background and its unorthodox distribution pattern have limited its implementation as a breeding objective. In this manuscript, statistical performances of 3 alternative parametrizations [i.e., symmetric Gaussian mixed linear (GML) model, skew-Gaussian mixed linear (SGML) model, and piecewise Weibull proportional hazard (PWPH) model] have been compared to elucidate the preferred methodology to handle lambing interval data. More specifically, flock-by-flock analyses were performed on 31,986 lambing interval records (257.3 ± 0.2 d) from 6 purebred Ripollesa flocks. Model performances were compared in terms of deviance information criterion (DIC) and Bayes factor (BF). For all flocks, PWPH models were clearly preferred; they generated a reduction of 1,900 or more DIC units and provided BF estimates larger than 100 (i.e., PWPH models against linear models). These differences were reduced when comparing PWPH models with different number of change points for the baseline hazard function. In 4 flocks, only 2 change points were required to minimize the DIC, whereas 4 and 6 change points were needed for the 2 remaining flocks. These differences demonstrated a remarkable degree of heterogeneity across sheep flocks that must be properly accounted for in genetic evaluation models to avoid statistical biases and suboptimal genetic trends. Within this context, all 6 Ripollesa flocks revealed substantial genetic background for lambing interval with heritabilities ranging between 0.13 and 0.19. This study provides the first evidence of the suitability of PWPH models for lambing interval analysis, clearly discarding previous parametrizations focused on mixed linear models.

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers.

PubMed

Zhou, Haibo; Ying, Hao

2017-09-01

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

2018-04-01

We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

Charge tuning of nonresonant magnetoexciton phonon interactions in graphene.

PubMed

Rémi, Sebastian; Goldberg, Bennett B; Swan, Anna K

2014-02-07

Far from resonance, the coupling of the G-band phonon to magnetoexcitons in single layer graphene displays kinks and splittings versus filling factor that are well described by Pauli blocking and unblocking of inter- and intra-Landau level transitions. We explore the nonresonant electron-phonon coupling by high-magnetic field Raman scattering while electrostatic tuning of the carrier density controls the filling factor. We show qualitative and quantitative agreement between spectra and a linearized model of electron-phonon interactions in magnetic fields. The splitting is caused by dichroism of left- and right-handed circular polarized light due to lifting of the G-band phonon degeneracy, and the piecewise linear slopes are caused by the linear occupancy of sequential Landau levels versus ν.

Adaptive Multilinear Tensor Product Wavelets

DOE PAGES

Weiss, Kenneth; Lindstrom, Peter

2015-08-12

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how tomore » generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.« less

Effects of soil acidification and liming on the phytoavailability of cadmium in paddy soils of central subtropical China.

PubMed

Zhu, Hanhua; Chen, Cheng; Xu, Chao; Zhu, Qihong; Huang, Daoyou

2016-12-01

Intensive and paired soil and rice grain survey and multiple-field liming experiments were conducted to assess soil acidification in the past 30 years, quantify the relationships of Cd phytoavailability with soil acidity, and determine efficacies of liming on soil acidity and Cd phytoavailability in paddy soils of central subtropical China at a regional scale. Soil pH, total and extractable Cd (Cd tot and Cd ext ), rice grain Cd were determined, and all measured data were analyzed separately in groups of 0.1 pH units intervals. Paddy soil pH averagely declined at 0.031 unit yr -1 between 1980s and 2014 (P < 0.01). Piecewise means of log Cd transfer ratio kept around -0.062 between soil pH 4.0 and 5.5 and around -1.31 between pH 6.9 and 7.3, whereas linearly decreased by a factor of 0.76 with pH 5.5-6.9, and by a factor of 1.38 with pH 7.3-8.2 (P < 0.01), respectively. Similar responses to soil pH were observed for soil Cd ext to Cd tot ratio. However, the former exhibited a lag effect to soil acidification in the acidic soils and a leading effect in alkaline soils. Liming increased soil pH by 0.50 units, and decreased rice grain Cd by 35.3% and log Cd transfer ratio by a factor of 0.76 (P < 0.01). The piecewise relationship based on the survey precisely predicted the changes in Cd transfer ratio across the multiple-field liming experiments. In conclusion, soil acidification occurred and accelerated in the past 30 years, and piecewise-linearly increased Cd phytoavailability of paddy soils in central subtropical China. Mitigating soil acidification, i.e. liming, should be preferentially implemented to minimize Cd phytoavailability. Copyright © 2016 Elsevier Ltd. All rights reserved.

The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

PubMed

Pang, Haotian; Liu, Han; Vanderbei, Robert

2014-02-01

We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

Time-temperature effect in adhesively bonded joints

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

The viscoelastic analysis of an adhesively bonded lap joint was reconsidered. The adherends are approximated by essentially Reissner plates and the adhesive is linearly viscoelastic. The hereditary integrals are used to model the adhesive. A linear integral differential equations system for the shear and the tensile stress in the adhesive is applied. The equations have constant coefficients and are solved by using Laplace transforms. It is shown that if the temperature variation in time can be approximated by a piecewise constant function, then the method of Laplace transforms can be used to solve the problem. A numerical example is given for a single lap joint under various loading conditions.

The mechanical problems on additive manufacturing of viscoelastic solids with integral conditions on a surface increasing in the growth process

NASA Astrophysics Data System (ADS)

Parshin, D. A.; Manzhirov, A. V.

2018-04-01

Quasistatic mechanical problems on additive manufacturing aging viscoelastic solids are investigated. The processes of piecewise-continuous accretion of such solids are considered. The consideration is carried out in the framework of linear mechanics of growing solids. A theorem about commutativity of the integration over an arbitrary surface increasing in the solid growing process and the time-derived integral operator of viscoelasticity with a limit depending on the solid point is proved. This theorem provides an efficient way to construct on the basis of Saint-Venant principle solutions of nonclassical boundary-value problems for describing the mechanical behaviour of additively formed solids with integral satisfaction of boundary conditions on the surfaces expanding due to the additional material influx to the formed solid. The constructed solutions will retrace the evolution of the stress-strain state of the solids under consideration during and after the processes of their additive formation. An example of applying the proved theorem is given.

Linear functional minimization for inverse modeling

DOE PAGES

Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...

2015-06-01

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less

Refined Zigzag Theory for Homogeneous, Laminated Composite, and Sandwich Plates: A Homogeneous Limit Methodology for Zigzag Function Selection

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, marco

2010-01-01

The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is presented from a multi-scale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse kinematic field is that of first-order shear-deformation theory, whereas the fine kinematic field has a piecewise-linear zigzag distribution through the thickness. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct sets of zigzag functions. By examining elastostatic solutions for highly heterogeneous sandwich plates, the best-performing zigzag functions are identified. The RZT predictive capabilities to model homogeneous and highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy ; and a wide range of applicability. The present theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient CO-continuous finite elements, and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures.

Coupling of damped and growing modes in unstable shear flow

DOE PAGES

Fraser, A. E.; Terry, P. W.; Zweibel, E. G.; ...

2017-06-14

Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to smallmore » scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.« less

Coupling of damped and growing modes in unstable shear flow

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

Fraser, A. E.; Terry, P. W.; Zweibel, E. G.

Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to smallmore » scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.« less

Krill herd and piecewise-linear initialization algorithms for designing Takagi-Sugeno systems

NASA Astrophysics Data System (ADS)

Hodashinsky, I. A.; Filimonenko, I. V.; Sarin, K. S.

2017-07-01

A method for designing Takagi-Sugeno fuzzy systems is proposed which uses a piecewiselinear initialization algorithm for structure generation and a metaheuristic krill herd algorithm for parameter optimization. The obtained systems are tested against real data sets. The influence of some parameters of this algorithm on the approximation accuracy is analyzed. Estimates of the approximation accuracy and the number of fuzzy rules are compared with four known methods of design.

Collisionless tearing instability of a bi-Maxwellian neutral sheet - An integrodifferential treatment with exact particle orbits

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Chen, J.

1989-01-01

The integrodifferential equation describing the linear tearing instability in the bi-Maxwellian neutral sheet is solved without approximating the particle orbits or the eigenfunction psi. Results of this calculation are presented. Comparison between the exact solution and the three-region approximation motivates the piecewise-straight-line approximation, a simplification that allows faster solution of the integrodifferential equation, yet retains the important features of the exact solution.

Neighboring Extremal Guidance for Systems with Piecewise Linear Control Using Time As the Reference Variable

DTIC Science & Technology

1993-05-01

obtained to provide a nominal control history . The guidance law is found by minimizing the V second variation of the suboptimal trajectory...deviations from the suboptimal trajectory to required changes in the nominal control history . The deviations from the suboptimal trajectory, used together...with the precomputed gains, determines the change in the nominal control history required to meet the final constraints while minimizing the change in

Time-independent Anisotropic Plastic Behavior by Mechanical Subelement Models

NASA Technical Reports Server (NTRS)

Pian, T. H. H.

1983-01-01

The paper describes a procedure for modelling the anisotropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are considered as piecewise linear for simplicity. The model is incorporated in a finite element analysis program which is based on the assumed stress hybrid element and the iscoplasticity-theory.

Traveling waves in a spring-block chain sliding down a slope

NASA Astrophysics Data System (ADS)

Morales, J. E.; James, G.; Tonnelier, A.

2017-07-01

Traveling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anticontinuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.

Traveling waves in a spring-block chain sliding down a slope.

PubMed

Morales, J E; James, G; Tonnelier, A

2017-07-01

Traveling waves are studied in a spring slider-block model. We explicitly construct front waves (kinks) for a piecewise-linear spinodal friction force. Pulse waves are obtained as the matching of two traveling fronts with identical speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anticontinuum limit. The link with localized waves in a Burridge-Knopoff model of an earthquake fault is briefly discussed.

Chimeras with multiple coherent regions

NASA Astrophysics Data System (ADS)

Ujjwal, Sangeeta Rani; Ramaswamy, Ramakrishna

2013-09-01

We study chimeric states in a coupled phase oscillator system with piecewise linear nonlocal coupling. By modifying the details of the coupling, it is possible to obtain multiple chimeric states with a specified number of coherent regions and with specified phase relationships. The case of a two-component chimera is illustrated and the generalization to arbitrary chimeric configurations is discussed. The phase relations between the two clusters of phase oscillators is described in some detail.

Integrated Sensing and Processing (ISP) Phase 2: Demonstration and Evaluation for Distributed Sensor Networks and Missile Seeker Systems

DTIC Science & Technology

2007-05-29

International Conference Acoustics Speech and Signal Processing (ICASSP 2007) conference 15 − 20 April 2007 in Honolulu, Hawaii. 1. E. Near Term...from the sensor measured in feet. The detection performance of the footstep in the presence of interfering speech was characterized in previously...investigation, we developed a simple piecewise linear approximation to the probability of detection curve with no interfering speech . This approximation was

A method of power analysis based on piecewise discrete Fourier transform

NASA Astrophysics Data System (ADS)

Xin, Miaomiao; Zhang, Yanchi; Xie, Da

2018-04-01

The paper analyzes the existing feature extraction methods. The characteristics of discrete Fourier transform and piecewise aggregation approximation are analyzed. Combining with the advantages of the two methods, a new piecewise discrete Fourier transform is proposed. And the method is used to analyze the lighting power of a large customer in this paper. The time series feature maps of four different cases are compared with the original data, discrete Fourier transform, piecewise aggregation approximation and piecewise discrete Fourier transform. This new method can reflect both the overall trend of electricity change and its internal changes in electrical analysis.

Primal-mixed formulations for reaction-diffusion systems on deforming domains

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo

2015-10-01

We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.

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

Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com; Institut Matematik Kejuruteraan; Saaban, Azizan, E-mail: azizan.s@uum.edu.my

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputedmore » data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.« less

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

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

Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

2016-10-15

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

Geometric constrained variational calculus I: Piecewise smooth extremals

NASA Astrophysics Data System (ADS)

Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico

2015-05-01

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.

Longitudinal models of reading achievement of students with learning disabilities and without disabilities.

PubMed

Sullivan, Amanda L; Kohli, Nidhi; Farnsworth, Elyse M; Sadeh, Shanna; Jones, Leila

2017-09-01

Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. We drew an analytic sample of 1,990 students from the nationally representative Early Childhood Longitudinal Study-Kindergarten Cohort of 1998, using reading achievement scores from kindergarten through eighth grade to estimate three models of students' reading growth. The piecewise mixed-effects models provided the best functional form of the students' reading trajectories as indicated by model fit indices. Results showed slightly different trajectories between students with learning disabilities and without disabilities, with varying but divergent rates of growth throughout elementary grades, as well as an increasing gap over time. These results highlight the need for additional research on appropriate methods for modeling reading trajectories and the implications for students' response to instruction. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Instantaneous frequency based newborn EEG seizure characterisation

NASA Astrophysics Data System (ADS)

Mesbah, Mostefa; O'Toole, John M.; Colditz, Paul B.; Boashash, Boualem

2012-12-01

The electroencephalogram (EEG), used to noninvasively monitor brain activity, remains the most reliable tool in the diagnosis of neonatal seizures. Due to their nonstationary and multi-component nature, newborn EEG seizures are better represented in the joint time-frequency domain than in either the time domain or the frequency domain. Characterising newborn EEG seizure nonstationarities helps to better understand their time-varying nature and, therefore, allow developing efficient signal processing methods for both modelling and seizure detection and classification. In this article, we used the instantaneous frequency (IF) extracted from a time-frequency distribution to characterise newborn EEG seizures. We fitted four frequency modulated (FM) models to the extracted IFs, namely a linear FM, a piecewise-linear FM, a sinusoidal FM, and a hyperbolic FM. Using a database of 30-s EEG seizure epochs acquired from 35 newborns, we were able to show that, depending on EEG channel, the sinusoidal and piecewise-linear FM models best fitted 80-98% of seizure epochs. To further characterise the EEG seizures, we calculated the mean frequency and frequency span of the extracted IFs. We showed that in the majority of the cases (>95%), the mean frequency resides in the 0.6-3 Hz band with a frequency span of 0.2-1 Hz. In terms of the frequency of occurrence of the four seizure models, the statistical analysis showed that there is no significant difference( p = 0.332) between the two hemispheres. The results also indicate that there is no significant differences between the two hemispheres in terms of the mean frequency ( p = 0.186) and the frequency span ( p = 0.302).

Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming.

PubMed

Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen

2012-06-01

To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities. Copyright © 2012 Elsevier Ltd. All rights reserved.

Multiuser receiver for DS-CDMA signals in multipath channels: an enhanced multisurface method.

PubMed

Mahendra, Chetan; Puthusserypady, Sadasivan

2006-11-01

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

DETERMINING PARTICLE EMISSION SOURCE STRENGTHS FOR COMMON RESIDENTIAL INDOOR SOURCES USING REAL-TIME MEASUREMENTS AND PIECEWISE-CONTINUOUS SOLUTIONS TO THE MASS BALANCE EQUATION

EPA Science Inventory

A variety of common activities in the home, such as smoking and cooking, generate indoor particle concentrations. Mathematical indoor air quality models permit predictions of indoor pollutant concentrations in homes, provided that parameter values such as source strengths and ...

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.…

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; MacLaurin, James

2018-06-01

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ɛ-1 . That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-C a /ɛ ) .

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point

NASA Astrophysics Data System (ADS)

Liang, Feng; Wang, Dechang

In this paper, we suppose that a planar piecewise Hamiltonian system, with a straight line of separation, has a piecewise generalized homoclinic loop passing through a Saddle-Fold point, and assume that there exists a family of piecewise smooth periodic orbits near the loop. By studying the asymptotic expansion of the first order Melnikov function corresponding to the period annulus, we obtain the formulas of the first six coefficients in the expansion, based on which, we provide a lower bound for the maximal number of limit cycles bifurcated from the period annulus. As applications, two concrete systems are considered. Especially, the first one reveals that a quadratic piecewise Hamiltonian system can have five limit cycles near a generalized homoclinic loop under a quadratic piecewise smooth perturbation. Compared with the smooth case [Horozov & Iliev, 1994; Han et al., 1999], three more limit cycles are found.

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

NASA Astrophysics Data System (ADS)

Suresh, R.; Srinivasan, K.; Senthilkumar, D. V.; Raja Mohamed, I.; Murali, K.; Lakshmanan, M.; Kurths, J.

2013-07-01

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central unit (relay unit) and at least one of the outer units, ZLS occurs in the two outer units whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.

Higher direct bilirubin levels during mid-pregnancy are associated with lower risk of gestational diabetes mellitus.

PubMed

Liu, Chaoqun; Zhong, Chunrong; Zhou, Xuezhen; Chen, Renjuan; Wu, Jiangyue; Wang, Weiye; Li, Xiating; Ding, Huisi; Guo, Yanfang; Gao, Qin; Hu, Xingwen; Xiong, Guoping; Yang, Xuefeng; Hao, Liping; Xiao, Mei; Yang, Nianhong

2017-01-01

Bilirubin concentrations have been recently reported to be negatively associated with type 2 diabetes mellitus. We examined the association between bilirubin concentrations and gestational diabetes mellitus. In a prospective cohort study, 2969 pregnant women were recruited prior to 16 weeks of gestation and were followed up until delivery. The value of bilirubin was tested and oral glucose tolerance test was conducted to screen gestational diabetes mellitus. The relationship between serum bilirubin concentration and gestational weeks was studied by two-piecewise linear regression. A subsample of 1135 participants with serum bilirubin test during 16-18 weeks gestation was conducted to research the association between serum bilirubin levels and risk of gestational diabetes mellitus by logistic regression. Gestational diabetes mellitus developed in 8.5 % of the participants (223 of 2969). Two-piecewise linear regression analyses demonstrated that the levels of bilirubin decreased with gestational week up to the turning point 23 and after that point, levels of bilirubin were increased slightly. In multiple logistic regression analysis, the relative risk of developing gestational diabetes mellitus was lower in the highest tertile of direct bilirubin than that in the lowest tertile (RR 0.60; 95 % CI, 0.35-0.89). The results suggested that women with higher serum direct bilirubin levels during the second trimester of pregnancy have lower risk for development of gestational diabetes mellitus.

Optimized multiple linear mappings for single image super-resolution

NASA Astrophysics Data System (ADS)

Zhang, Kaibing; Li, Jie; Xiong, Zenggang; Liu, Xiuping; Gao, Xinbo

2017-12-01

Learning piecewise linear regression has been recognized as an effective way for example learning-based single image super-resolution (SR) in literature. In this paper, we employ an expectation-maximization (EM) algorithm to further improve the SR performance of our previous multiple linear mappings (MLM) based SR method. In the training stage, the proposed method starts with a set of linear regressors obtained by the MLM-based method, and then jointly optimizes the clustering results and the low- and high-resolution subdictionary pairs for regression functions by using the metric of the reconstruction errors. In the test stage, we select the optimal regressor for SR reconstruction by accumulating the reconstruction errors of m-nearest neighbors in the training set. Thorough experimental results carried on six publicly available datasets demonstrate that the proposed SR method can yield high-quality images with finer details and sharper edges in terms of both quantitative and perceptual image quality assessments.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems.

PubMed

Amaral, Gleison F V; Letellier, Christophe; Aguirre, Luis Antonio

2006-03-01

This paper proposes a procedure by which it is possible to synthesize Rossler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.

A variable-step-size robust delta modulator.

NASA Technical Reports Server (NTRS)

Song, C. L.; Garodnick, J.; Schilling, D. L.

1971-01-01

Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.

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

PubMed

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

2017-04-01

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

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

NASA Astrophysics Data System (ADS)

Hirata, Yoshito; di Bernardo, Mario; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-12-01

We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population.

Synthesis of stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Thornton, W. A.

1974-01-01

Computer programs for the synthesis of shells of various configurations were developed. The conditions considered are: (1) uniform shells (mainly cones) using a membrane buckling analysis, (2) completely uniform shells (cones, spheres, toroidal segments) using linear bending prebuckling analysis, and (3) revision of second design process to reduce the number of design variables to about 30 by considering piecewise uniform designs. A perturbation formula was derived and this allows exact derivatives of the general buckling load to be computed with little additional computer time.

Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

DTIC Science & Technology

2012-12-01

acoustics One begins with Eikonal equation for the acoustic phase function S(t,x) as derived from the geometric acoustics (high frequency) approximation to...zb(x) is smooth and reasonably approximated as piecewise linear. The time domain ray (characteristic) equations for the Eikonal equation are ẋ(t)= c...travel time is affected, which is more physically relevant than global error in φ since it provides the phase information for the Eikonal equation (2.1

Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part 1. Boundary Value Problems for Linear Ellilptic Equation of Second Order.

DTIC Science & Technology

1986-05-01

neighborhood of the Program PROBE of Noetic Technologies, St. Louis. corners of the domain, place where the type of the boundary condition changes, etc...is studied . , r ° -. o. - *- . ,. .- -*. ... - - . . . ’ , ..- , .- *- , . --s,." . ",-:, "j’ . ], k i-, j!3 ,, :,’ - .A L...Manual. Noetic Technologies Corp., St. Louis, Missouri (1985). 318] Szab’, B. A.: Implementation of a Finite Element Software System with h and p

Elimination of numerical diffusion in 1 - phase and 2 - phase flows

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

Rajamaeki, M.

1997-07-01

The new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) is capable of avoiding the excessive errors, numerical diffusion and also numerical dispersion. The hydraulics solver CFDPLIM uses PLIM and solves the time-dependent one-dimensional flow equations in network geometry. An example is given for 1-phase flow in the case when thermal-hydraulics and reactor kinetics are strongly coupled. Another example concerns oscillations in 2-phase flow. Both the example computations are not possible with conventional methods.

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata

PubMed Central

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-01-01

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research. PMID:28353664

Modeling and Density Estimation of an Urban Freeway Network Based on Dynamic Graph Hybrid Automata.

PubMed

Chen, Yangzhou; Guo, Yuqi; Wang, Ying

2017-03-29

In this paper, in order to describe complex network systems, we firstly propose a general modeling framework by combining a dynamic graph with hybrid automata and thus name it Dynamic Graph Hybrid Automata (DGHA). Then we apply this framework to model traffic flow over an urban freeway network by embedding the Cell Transmission Model (CTM) into the DGHA. With a modeling procedure, we adopt a dual digraph of road network structure to describe the road topology, use linear hybrid automata to describe multi-modes of dynamic densities in road segments and transform the nonlinear expressions of the transmitted traffic flow between two road segments into piecewise linear functions in terms of multi-mode switchings. This modeling procedure is modularized and rule-based, and thus is easily-extensible with the help of a combination algorithm for the dynamics of traffic flow. It can describe the dynamics of traffic flow over an urban freeway network with arbitrary topology structures and sizes. Next we analyze mode types and number in the model of the whole freeway network, and deduce a Piecewise Affine Linear System (PWALS) model. Furthermore, based on the PWALS model, a multi-mode switched state observer is designed to estimate the traffic densities of the freeway network, where a set of observer gain matrices are computed by using the Lyapunov function approach. As an example, we utilize the PWALS model and the corresponding switched state observer to traffic flow over Beijing third ring road. In order to clearly interpret the principle of the proposed method and avoid computational complexity, we adopt a simplified version of Beijing third ring road. Practical application for a large-scale road network will be implemented by decentralized modeling approach and distributed observer designing in the future research.

High resolution A/D conversion based on piecewise conversion at lower resolution

DOEpatents

Terwilliger, Steve [Albuquerque, NM

2012-06-05

Piecewise conversion of an analog input signal is performed utilizing a plurality of relatively lower bit resolution A/D conversions. The results of this piecewise conversion are interpreted to achieve a relatively higher bit resolution A/D conversion without sampling frequency penalty.

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects

DOE PAGES

Puso, M. A.; Kokko, E.; Settgast, R.; ...

2014-10-22

An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as non-proportional damping such that the time integration of the scheme is provably stable with a critical timemore » step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.« less

Affine connection form of Regge calculus

NASA Astrophysics Data System (ADS)

Khatsymovsky, V. M.

2016-12-01

Regge action is represented analogously to how the Palatini action for general relativity (GR) as some functional of the metric and a general connection as independent variables represents the Einstein-Hilbert action. The piecewise flat (or simplicial) spacetime of Regge calculus is equipped with some world coordinates and some piecewise affine metric which is completely defined by the set of edge lengths and the world coordinates of the vertices. The conjugate variables are the general nondegenerate matrices on the three-simplices which play the role of a general discrete connection. Our previous result on some representation of the Regge calculus action in terms of the local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as independent variables is somewhat modified for the considered case of the general linear group GL(4, R) of the connection matrices. As a result, we have some action invariant w.r.t. arbitrary change of coordinates of the vertices (and related GL(4, R) transformations in the four-simplices). Excluding GL(4, R) connection from this action via the equations of motion we have exactly the Regge action for the considered spacetime.

The application of the piecewise linear approximation to the spectral neighborhood of soil line for the analysis of the quality of normalization of remote sensing materials

NASA Astrophysics Data System (ADS)

Kulyanitsa, A. L.; Rukhovich, A. D.; Rukhovich, D. D.; Koroleva, P. V.; Rukhovich, D. I.; Simakova, M. S.

2017-04-01

The concept of soil line can be to describe the temporal distribution of spectral characteristics of the bare soil surface. In this case, the soil line can be referred to as the multi-temporal soil line, or simply temporal soil line (TSL). In order to create TSL for 8000 regular lattice points for the territory of three regions of Tula oblast, we used 34 Landsat images obtained in the period from 1985 to 2014 after their certain transformation. As Landsat images are the matrices of the values of spectral brightness, this transformation is the normalization of matrices. There are several methods of normalization that move, rotate, and scale the spectral plane. In our study, we applied the method of piecewise linear approximation to the spectral neighborhood of soil line in order to assess the quality of normalization mathematically. This approach allowed us to range normalization methods according to their quality as follows: classic normalization > successive application of the turn and shift > successive application of the atmospheric correction and shift > atmospheric correction > shift > turn > raw data. The normalized data allowed us to create the maps of the distribution of a and b coefficients of the TSL. The map of b coefficient is characterized by the high correlation with the ground-truth data obtained from 1899 soil pits described during the soil surveys performed by the local institute for land management (GIPROZEM).

Detection of kinetic change points in piece-wise linear single molecule motion

NASA Astrophysics Data System (ADS)

Hill, Flynn R.; van Oijen, Antoine M.; Duderstadt, Karl E.

2018-03-01

Single-molecule approaches present a powerful way to obtain detailed kinetic information at the molecular level. However, the identification of small rate changes is often hindered by the considerable noise present in such single-molecule kinetic data. We present a general method to detect such kinetic change points in trajectories of motion of processive single molecules having Gaussian noise, with a minimum number of parameters and without the need of an assumed kinetic model beyond piece-wise linearity of motion. Kinetic change points are detected using a likelihood ratio test in which the probability of no change is compared to the probability of a change occurring, given the experimental noise. A predetermined confidence interval minimizes the occurrence of false detections. Applying the method recursively to all sub-regions of a single molecule trajectory ensures that all kinetic change points are located. The algorithm presented allows rigorous and quantitative determination of kinetic change points in noisy single molecule observations without the need for filtering or binning, which reduce temporal resolution and obscure dynamics. The statistical framework for the approach and implementation details are discussed. The detection power of the algorithm is assessed using simulations with both single kinetic changes and multiple kinetic changes that typically arise in observations of single-molecule DNA-replication reactions. Implementations of the algorithm are provided in ImageJ plugin format written in Java and in the Julia language for numeric computing, with accompanying Jupyter Notebooks to allow reproduction of the analysis presented here.

Spatial distribution of loggerhead turtle (Caretta caretta) emergences along a highly dynamic beach in the northern Gulf of Mexico

USGS Publications Warehouse

Lamont, Margaret M.; Houser, Chris

2014-01-01

As coastlines change due to sea level rise and an increasing human presence, understanding how species, such as marine turtles, respond to alterations in habitat is necessary for proper management and conservation. Survey data from a major nesting beach in the northern Gulf of Mexico, where a revetment was installed, was used to assess spatial distribution of loggerhead emergences. Through use of Quadrat analysis and piecewise linear regression with breakpoint, we present evidence to suggest that nest site selection in loggerheads is determined in the nearshore environment, and by characteristics such as wave height, alongshore currents, depth and patterns of erosion and accretion. Areas of relatively dense nesting were found in areas with relatively strong alongshore currents, relatively small waves, a steep offshore slope and the largest historical rates of erosion. Areas of relatively dense nesting also corresponded to areas of low nesting success. Both nesting and non-nesting emergences were clustered immediately adjacent to the revetment and at other eroding sites along the beach. These results suggest that alterations to the nearshore environment from activities such as construction of a jetty, dredging or installation of pilings, may impact sea turtle nest distribution alongshore. We also show that piecewise linear regression with breakpoint is a technique that can be used with geomorphological and oceanographic data to predict locations of nest clumping and may be useful for managers at other nesting beaches.

Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

NASA Astrophysics Data System (ADS)

Everett, R. A.; Packer, A. M.; Kuang, Y.

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

NASA Astrophysics Data System (ADS)

Everett, R. A.; Packer, A. M.; Kuang, Y.

2014-04-01

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

An algorithm for the numerical solution of linear differential games

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

Polovinkin, E S; Ivanov, G E; Balashov, M V

2001-10-31

A numerical algorithm for the construction of stable Krasovskii bridges, Pontryagin alternating sets, and also of piecewise program strategies solving two-person linear differential (pursuit or evasion) games on a fixed time interval is developed on the basis of a general theory. The aim of the first player (the pursuer) is to hit a prescribed target (terminal) set by the phase vector of the control system at the prescribed time. The aim of the second player (the evader) is the opposite. A description of numerical algorithms used in the solution of differential games of the type under consideration is presented andmore » estimates of the errors resulting from the approximation of the game sets by polyhedra are presented.« less

Atmospheric gradients from very long baseline interferometry observations

NASA Technical Reports Server (NTRS)

Macmillan, D. S.

1995-01-01

Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Daily average gradient effects can be as large as 50 mm of delay at a 7 deg elevation. To model gradients, the constrained estimation of gradient paramters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990-1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990-1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties.

Influence of surface error on electromagnetic performance of reflectors based on Zernike polynomials

NASA Astrophysics Data System (ADS)

Li, Tuanjie; Shi, Jiachen; Tang, Yaqiong

2018-04-01

This paper investigates the influence of surface error distribution on the electromagnetic performance of antennas. The normalized Zernike polynomials are used to describe a smooth and continuous deformation surface. Based on the geometrical optics and piecewise linear fitting method, the electrical performance of reflector described by the Zernike polynomials is derived to reveal the relationship between surface error distribution and electromagnetic performance. Then the relation database between surface figure and electric performance is built for ideal and deformed surfaces to realize rapidly calculation of far-field electric performances. The simulation analysis of the influence of Zernike polynomials on the electrical properties for the axis-symmetrical reflector with the axial mode helical antenna as feed is further conducted to verify the correctness of the proposed method. Finally, the influence rules of surface error distribution on electromagnetic performance are summarized. The simulation results show that some terms of Zernike polynomials may decrease the amplitude of main lobe of antenna pattern, and some may reduce the pointing accuracy. This work extracts a new concept for reflector's shape adjustment in manufacturing process.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Cohen, D.

1985-01-01

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Refinement of Timoshenko Beam Theory for Composite and Sandwich Beams Using Zigzag Kinematics

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, Marco

2007-01-01

A new refined theory for laminated-composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining accurate estimates of structural response of laminated composites.

Estimation of High-Dimensional Graphical Models Using Regularized Score Matching

PubMed Central

Lin, Lina; Drton, Mathias; Shojaie, Ali

2017-01-01

Graphical models are widely used to model stochastic dependences among large collections of variables. We introduce a new method of estimating undirected conditional independence graphs based on the score matching loss, introduced by Hyvärinen (2005), and subsequently extended in Hyvärinen (2007). The regularized score matching method we propose applies to settings with continuous observations and allows for computationally efficient treatment of possibly non-Gaussian exponential family models. In the well-explored Gaussian setting, regularized score matching avoids issues of asymmetry that arise when applying the technique of neighborhood selection, and compared to existing methods that directly yield symmetric estimates, the score matching approach has the advantage that the considered loss is quadratic and gives piecewise linear solution paths under ℓ1 regularization. Under suitable irrepresentability conditions, we show that ℓ1-regularized score matching is consistent for graph estimation in sparse high-dimensional settings. Through numerical experiments and an application to RNAseq data, we confirm that regularized score matching achieves state-of-the-art performance in the Gaussian case and provides a valuable tool for computationally efficient estimation in non-Gaussian graphical models. PMID:28638498

Evolution of conditional cooperation under multilevel selection.

PubMed

Zhang, Huanren; Perc, Matjaž

2016-03-11

We study the emergence of conditional cooperation in the presence of both intra-group and inter-group selection. Individuals play public goods games within their groups using conditional strategies, which are represented as piecewise linear response functions. Accordingly, groups engage in conflicts with a certain probability. In contrast to previous studies, we consider continuous contribution levels and a rich set of conditional strategies, allowing for a wide range of possible interactions between strategies. We find that the existence of conditional strategies enables the stabilization of cooperation even under strong intra-group selection. The strategy that eventually dominates in the population has two key properties: (i) It is unexploitable with strong intra-group selection; (ii) It can achieve full contribution to outperform other strategies in the inter-group selection. The success of this strategy is robust to initial conditions as well as changes to important parameters. We also investigate the influence of different factors on cooperation levels, including group conflicts, group size, and migration rate. Their effect on cooperation can be attributed to and explained by their influence on the relative strength of intra-group and inter-group selection.

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain.

PubMed

Pang, Jiahao; Cheung, Gene

2017-04-01

Inverse imaging problems are inherently underdetermined, and hence, it is important to employ appropriate image priors for regularization. One recent popular prior-the graph Laplacian regularizer-assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper, we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the continuous domain, providing insights into several fundamental aspects of graph Laplacian regularization for image denoising. Specifically, we first show the convergence of the graph Laplacian regularizer to a continuous-domain functional, integrating a norm measured in a locally adaptive metric space. Focusing on image denoising, we derive an optimal metric space assuming non-local self-similarity of pixel patches, leading to an optimal graph Laplacian regularizer for denoising in the discrete domain. We then interpret graph Laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations, e.g., its tendency to promote piecewise smooth signals under certain settings. To verify our analysis, an iterative image denoising algorithm is developed. Experimental results show that our algorithm performs competitively with state-of-the-art denoising methods, such as BM3D for natural images, and outperforms them significantly for piecewise smooth images.

Stability of barotropic vortex strip on a rotating sphere

PubMed Central

Sohn, Sung-Ik; Kim, Sun-Chul

2018-01-01

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined. PMID:29507524

Stability of barotropic vortex strip on a rotating sphere.

PubMed

Sohn, Sung-Ik; Sakajo, Takashi; Kim, Sun-Chul

2018-02-01

We study the stability of a barotropic vortex strip on a rotating sphere, as a simple model of jet streams. The flow is approximated by a piecewise-continuous vorticity distribution by zonal bands of uniform vorticity. The linear stability analysis shows that the vortex strip becomes stable as the strip widens or the rotation speed increases. When the vorticity constants in the upper and the lower regions of the vortex strip have the same positive value, the inner flow region of the vortex strip becomes the most unstable. However, when the upper and the lower vorticity constants in the polar regions have different signs, a complex pattern of instability is found, depending on the wavenumber of perturbations, and interestingly, a boundary far away from the vortex strip can be unstable. We also compute the nonlinear evolution of the vortex strip on the rotating sphere and compare with the linear stability analysis. When the width of the vortex strip is small, we observe a good agreement in the growth rate of perturbation at an early time, and the eigenvector corresponding to the unstable eigenvalue coincides with the most unstable part of the flow. We demonstrate that a large structure of rolling-up vortex cores appears in the vortex strip after a long-time evolution. Furthermore, the geophysical relevance of the model to jet streams of Jupiter, Saturn and Earth is examined.

Piecewise-Planar StereoScan: Sequential Structure and Motion using Plane Primitives.

PubMed

Raposo, Carolina; Antunes, Michel; P Barreto, Joao

2017-08-09

The article describes a pipeline that receives as input a sequence of stereo images, and outputs the camera motion and a Piecewise-Planar Reconstruction (PPR) of the scene. The pipeline, named Piecewise-Planar StereoScan (PPSS), works as follows: the planes in the scene are detected for each stereo view using semi-dense depth estimation; the relative pose is computed by a new closed-form minimal algorithm that only uses point correspondences whenever plane detections do not fully constrain the motion; the camera motion and the PPR are jointly refined by alternating between discrete optimization and continuous bundle adjustment; and, finally, the detected 3D planes are segmented in images using a new framework that handles low texture and visibility issues. PPSS is extensively validated in indoor and outdoor datasets, and benchmarked against two popular point-based SfM pipelines. The experiments confirm that plane-based visual odometry is resilient to situations of small image overlap, poor texture, specularity, and perceptual aliasing where the fast LIBVISO2 pipeline fails. The comparison against VisualSfM+CMVS/PMVS shows that, for a similar computational complexity, PPSS is more accurate and provides much more compelling and visually pleasant 3D models. These results strongly suggest that plane primitives are an advantageous alternative to point correspondences for applications of SfM and 3D reconstruction in man-made environments.

Solutions of some problems in applied mathematics using MACSYMA

NASA Technical Reports Server (NTRS)

Punjabi, Alkesh; Lam, Maria

1987-01-01

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Cytogenetic effect of low dose gamma-radiation in Hordeum vulgare seedlings: non-linear dose-effect relationship.

PubMed

Geras'kin, Stanislav A; Oudalova, Alla A; Kim, Jin Kyu; Dikarev, Vladimir G; Dikareva, Nina S

2007-03-01

The induction of chromosome aberrations in Hordeum vulgare germinated seeds was studied after ionizing irradiation with doses in the range of 10-1,000 mGy. The relationship between the frequency of aberrant cells and the absorbed dose was found to be nonlinear. A dose-independent plateau in the dose range from about 50 to 500 mGy was observed, where the level of cytogenetic damage was significantly different from the spontaneous level. The comparison of the goodness of the experimental data fitting with mathematical models of different complexity, using the most common quantitative criteria, demonstrated the advantage of a piecewise linear model over linear and polynomial models in approximating the frequency of cytogenetical disturbances. The results of the study support the hypothesis of indirect mechanisms of mutagenesis induced by low doses. Fundamental and applied implications of these findings are discussed.

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program. [subroutines and flow charts

NASA Technical Reports Server (NTRS)

Utku, S.

1969-01-01

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

A green vehicle routing problem with customer satisfaction criteria

NASA Astrophysics Data System (ADS)

Afshar-Bakeshloo, M.; Mehrabi, A.; Safari, H.; Maleki, M.; Jolai, F.

2016-12-01

This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers' satisfaction have been taken into account. Meanwhile, the introduced model prepares an effective dashboard for decision-makers that determines appropriate routes, the best mixed fleet, speed and idle time of vehicles. Additionally, some new factors evaluate the greening of each decision based on three criteria. This model applies piecewise linear functions (PLFs) to linearize a nonlinear fuzzy interval for incorporating customers' satisfaction into other linear objectives. We have presented a mixed integer linear programming formulation for the S-GVRP. This model enriches managerial insights by providing trade-offs between customers' satisfaction, total costs and emission levels. Finally, we have provided a numerical study for showing the applicability of the model.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The non-linear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

2018-04-01

In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

Age-related changes in spatiotemporal characteristics of gait accompany ongoing lower limb linear growth in late childhood and early adolescence.

PubMed

Froehle, Andrew W; Nahhas, Ramzi W; Sherwood, Richard J; Duren, Dana L

2013-05-01

Walking gait is generally held to reach maturity, including walking at adult-like velocities, by 7-8 years of age. Lower limb length, however, is a major determinant of gait, and continues to increase until 13-15 years of age. This study used a sample from the Fels Longitudinal Study (ages 8-30 years) to test the hypothesis that walking with adult-like velocity on immature lower limbs results in the retention of immature gait characteristics during late childhood and early adolescence. There was no relationship between walking velocity and age in this sample, whereas the lower limb continued to grow, reaching maturity at 13.2 years in females and 15.6 years in males. Piecewise linear mixed models regression analysis revealed significant age-related trends in normalized cadence, initial double support time, single support time, base of support, and normalized step length in both sexes. Each trend reached its own, variable-specific age at maturity, after which the gait variables' relationships with age reached plateaus and did not differ significantly from zero. Offsets in ages at maturity occurred among the gait variables, and between the gait variables and lower limb length. The sexes also differed in their patterns of maturation. Generally, however, immature walkers of both sexes took more frequent and relatively longer steps than did mature walkers. These results support the hypothesis that maturational changes in gait accompany ongoing lower limb growth, with implications for diagnosing, preventing, and treating movement-related disorders and injuries during late childhood and early adolescence. Copyright © 2012 Elsevier B.V. All rights reserved.

Continued Rapid Uplift at Laguna del Maule Volcanic Field (Chile) from 2007 through 2014

NASA Astrophysics Data System (ADS)

Le Mével, H.; Feigl, K. L.; Cordova, L.; DeMets, C.; Lundgren, P.

2014-12-01

The current rate of uplift at Laguna del Maule (LdM) volcanic field in Chile is among the highest ever observed geodetically for a volcano that is not actively erupting. Using data from interferometric synthetic aperture radar (InSAR) and the Global Positioning System (GPS) recorded at five continuously operating stations, we measure the deformation field with dense sampling in time (1/day) and space (1/hectare). These data track the temporal evolution of the current unrest episode from its inception (sometime between 2004 and 2007) to vertical velocities faster than 200 mm/yr that continue through (at least) July 2014. Building on our previous work, we evaluate the temporal evolution by analyzing data from InSAR (ALOS, TerraSAR-X, TanDEM-X) and GPS [http://dx.doi.org/ 10.1093/gji/ggt438]. In addition, we consider InSAR data from (ERS, ENVISAT, COSMO-Skymed, and UAVSAR), as well as constraints from magneto-telluric (MT), seismic, and gravity surveys. The goal is to test the hypothesis that a recent magma intrusion is feeding a large, existing magma reservoir. What will happen next? To address this question, we analyze the temporal evolution of deformation at other large silicic systems such as Yellowstone, Long Valley, and Three Sisters, during well-studied episodes of unrest. We consider several parameterizations, including piecewise linear, parabolic, and Gaussian functions of time. By choosing the best-fitting model, we expect to constrain the time scales of such episodes and elucidate the processes driving them.

A tutorial on the piecewise regression approach applied to bedload transport data

Treesearch

Sandra E. Ryan; Laurie S. Porth

2007-01-01

This tutorial demonstrates the application of piecewise regression to bedload data to define a shift in phase of transport so that the reader may perform similar analyses on available data. The use of piecewise regression analysis implicitly recognizes different functions fit to bedload data over varying ranges of flow. The transition from primarily low rates of sand...

Application of NASTRAN in nonlinear analysis of a cartridge case neck separation malfunction

NASA Technical Reports Server (NTRS)

Yang, J. C. S.; Frederick, D. L.

1975-01-01

The problem of case neck separation malfunction in the field of ammunition structural analysis is investigated. The axi-symmetric solid of revolution RING element was utilized in the manual piecewise linear analysis to obtain the expansion of the wall of the cartridge case and barrel chamber by the pressure of propellant gases and the stresses in the structure. The analysis included the varying material properties along the wall of the case and the chamber. Additional instructions were provided to change the element material ID's without recomputing the entire stiffness matrix.

Local Bifurcations and Optimal Theory in a Delayed Predator-Prey Model with Threshold Prey Harvesting

NASA Astrophysics Data System (ADS)

Tankam, Israel; Tchinda Mouofo, Plaire; Mendy, Abdoulaye; Lam, Mountaga; Tewa, Jean Jules; Bowong, Samuel

2015-06-01

We investigate the effects of time delay and piecewise-linear threshold policy harvesting for a delayed predator-prey model. It is the first time that Holling response function of type III and the present threshold policy harvesting are associated with time delay. The trajectories of our delayed system are bounded; the stability of each equilibrium is analyzed with and without delay; there are local bifurcations as saddle-node bifurcation and Hopf bifurcation; optimal harvesting is also investigated. Numerical simulations are provided in order to illustrate each result.

FAST TRACK COMMUNICATION: Weyl law for fat fractals

NASA Astrophysics Data System (ADS)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Threshold detection in an on-off binary communications channel with atmospheric scintillation

NASA Technical Reports Server (NTRS)

Webb, W. E.; Marino, J. T., Jr.

1974-01-01

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-emperical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. Bit error probabilities for non-optimum threshold detection system were also investigated.

On Compressible Vortex Sheets

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2005-05-01

We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.

Threshold detection in an on-off binary communications channel with atmospheric scintillation

NASA Technical Reports Server (NTRS)

Webb, W. E.

1975-01-01

The optimum detection threshold in an on-off binary optical communications system operating in the presence of atmospheric turbulence was investigated assuming a poisson detection process and log normal scintillation. The dependence of the probability of bit error on log amplitude variance and received signal strength was analyzed and semi-empirical relationships to predict the optimum detection threshold derived. On the basis of this analysis a piecewise linear model for an adaptive threshold detection system is presented. The bit error probabilities for nonoptimum threshold detection systems were also investigated.

Interaction function of oscillating coupled neurons

PubMed Central

Dodla, Ramana; Wilson, Charles J.

2013-01-01

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses, and parameterizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms. PMID:24229210

Endogenous Business Cycle Dynamics within Metzlers Inventory Model: Adding an Inventory Floor.

PubMed

Sushko, Irina; Wegener, Michael; Westerhoff, Frank; Zaklan, Georg

2009-04-01

Metzlers inventory model may produce dampened fluctuations in economic activity, thus contributing to our understanding of business cycle dynamics. For some parameter combinations, however, the model generates oscillations with increasing amplitude, implying that the inventory stock of firms eventually turns negative. Taking this observation into account, we reformulate Metzlers model by simply putting a floor to the inventory level. Within the new piecewise linear model, endogenous business cycle dynamics may now be triggered via a center bifurcation, i.e. for certain parameter combinations production changes are (quasi-)periodic.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

A FORTRAN program for multivariate survival analysis on the personal computer.

PubMed

Mulder, P G

1988-01-01

In this paper a FORTRAN program is presented for multivariate survival or life table regression analysis in a competing risks' situation. The relevant failure rate (for example, a particular disease or mortality rate) is modelled as a log-linear function of a vector of (possibly time-dependent) explanatory variables. The explanatory variables may also include the variable time itself, which is useful for parameterizing piecewise exponential time-to-failure distributions in a Gompertz-like or Weibull-like way as a more efficient alternative to Cox's proportional hazards model. Maximum likelihood estimates of the coefficients of the log-linear relationship are obtained from the iterative Newton-Raphson method. The program runs on a personal computer under DOS; running time is quite acceptable, even for large samples.

Least Squares Approximation By G1 Piecewise Parametric Cubes

DTIC Science & Technology

1993-12-01

ADDRESS(ES) 10.SPONSORING/MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not...CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) Parametric piecewise cubic polynomials are used throughout...piecewise parametric cubic polynomial to a sequence of ordered points in the plane. Cubic Bdzier curves are used as a basis. The parameterization, the

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

A new framework for modeling decisions about changing information: The Piecewise Linear Ballistic Accumulator model

PubMed Central

Heathcote, Andrew

2016-01-01

In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We use a random-dot motion paradigm along with cognitive modeling to investigate how the decision process is updated when a stimulus changes. Participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. To further investigate the underlying changes in the decision process, we developed a Piecewise Linear Ballistic Accumulator model (PLBA). The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modeling framework using a non-parametric approximate Bayesian algorithm. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Thus, the perceptual decision process was slow to react to, and underestimated, new contrary motion information. PMID:26760448

Model of random center vortex lines in continuous 2 +1 -dimensional spacetime

NASA Astrophysics Data System (ADS)

Altarawneh, Derar; Engelhardt, Michael; Höllwieser, Roman

2016-12-01

A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2 +1 -dimensional space-time. These random lines are modeled as being piecewise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing, and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. We study both vortex percolation and the potential V (R ) between the quark and antiquark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions, and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.

Some Properties of Generalized Connections in Quantum Gravity

NASA Astrophysics Data System (ADS)

Velhinho, J. M.

2002-12-01

Theories of connections play an important role in fundamental interactions, including Yang-Mills theories and gravity in the Ashtekar formulation. Typically in such cases, the classical configuration space {A}/ {G} of connections modulo gauge transformations is an infinite dimensional non-linear space of great complexity. Having in mind a rigorous quantization procedure, methods of functional calculus in an extension of {A}/ {G} have been developed. For a compact gauge group G, the compact space /line { {A}{ {/}} {G}} ( ⊃ {A}/ {G}) introduced by Ashtekar and Isham using C*-algebraic methods is a natural candidate to replace {A}/ {G} in the quantum context, 1 allowing the construction of diffeomorphism invariant measures. 2,3,4 Equally important is the space of generalized connections bar {A} introduced in a similar way by Baez. 5 bar {A} is particularly useful for the definition of vector fields in /line { {A}{ {/}} {G}} , fundamental in the construction of quantum observables. 6 These works crucially depend on the use of (generalized) Wilson variables associated to certain types of curves. We will consider the case of piecewise analytic curves, 1,2,5 althought most of the arguments apply equally to the piecewise smooth case. 7,8...

Mitigation of epidemics in contact networks through optimal contact adaptation *

PubMed Central

Youssef, Mina; Scoglio, Caterina

2013-01-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights. PMID:23906209

Mitigation of epidemics in contact networks through optimal contact adaptation.

PubMed

Youssef, Mina; Scoglio, Caterina

2013-08-01

This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.

The non-linear association between low-level lead exposure and maternal stress among pregnant women.

PubMed

Li, Shufang; Xu, Jian; Liu, Zhiwei; Yan, Chong-Huai

2017-03-01

Neuro-developmental impairments in the developing fetus due to exposure to low-level lead have been well documented. However, few studies have investigated the relation between maternal stress levels and low-level lead exposure among pregnant women. To investigate the relation between maternal blood lead and stress levels during index pregnancy. 1931 pregnant women (gestational week 28-36) were investigated using stratified-cluster-sampling in Shanghai in 2010. Maternal life event stress and emotional stress were assessed using "Life-Event-Stress-Scale-for-Pregnant-Women" (LESPW) and "Symptom-Checklist-90-Revised" (SCL-90-R), respectively. Maternal whole blood lead levels were determined, and other data on covariates were obtained from maternal interviews and medical records. Two piecewise linear regression models were applied to assess the relations between blood lead and stress levels using a data-driven approach according to spline smoothing fitting of the data. Maternal blood lead levels ranged from 0.80 to 14.84μg/dL, and the geometric mean was 3.97μg/dL. The P-values for the two piecewise linear models against the single linear regression models were 0.010, 0.003 and 0.017 for models predicting GSI, depression and anxiety symptom scores, respectively. When blood lead levels were below 2.57μg/dL, each unit increase in log10 transformed blood lead levels (μg/dL) was associated with about 18% increase in maternal GSI, depression and anxiety symptom scores (P GSI =0.013, P depression =0.002, P anxiety =0.019, respectively). However, no significant relation was found when blood lead levels were above 2.57μg/dL (all P-values>0.05). Our findings suggested a nonlinear relationship between blood lead and emotional stress levels among pregnant women. Emotional stress increased along with blood lead levels, and appeared to be plateaued when blood lead levels reached 2.57μg/dL. Copyright © 2016 Elsevier B.V. All rights reserved.

Variational models for discontinuity detection

NASA Astrophysics Data System (ADS)

Vitti, Alfonso; Battista Benciolini, G.

2010-05-01

The Mumford-Shah variational model produces a smooth approximation of the data and detects data discontinuities by solving a minimum problem involving an energy functional. The Blake-Zisserman model permits also the detection of discontinuities in the first derivative of the approximation. This model can result in a quasi piece-wise linear approximation, whereas the Mumford-Shah can result in a quasi piece-wise constant approximation. The two models are well known in the mathematical literature and are widely adopted in computer vision for image segmentation. In Geodesy the Blake-Zisserman model has been applied successfully to the detection of cycle-slips in linear combinations of GPS measurements. Few attempts to apply the model to time series of coordinates have been done so far. The problem of detecting discontinuities in time series of GNSS coordinates is well know and its relevance increases as the quality of geodetic measurements, analysis techniques, models and products improves. The application of the Blake-Zisserman model appears reasonable and promising due to the model characteristic to detect both position and velocity discontinuities in the same time series. The detection of position and velocity changes is of great interest in geophysics where the discontinuity itself can be the very relevant object. In the work for the realization of reference frames, detecting position and velocity discontinuities may help to define models that can handle non-linear motions. In this work the Mumford-Shah and the Blake-Zisserman models are briefly presented, the treatment is carried out from a practical viewpoint rather than from a theoretical one. A set of time series of GNSS coordinates has been processed and the results are presented in order to highlight the capabilities and the weakness of the variational approach. A first attempt to derive some indication for the automatic set up of the model parameters has been done. The underlying relation that could links the parameter values to the statistical properties of the data has been investigated.

An application of analyzing the trajectories of two disorders: A parallel piecewise growth model of substance use and attention-deficit/hyperactivity disorder.

PubMed

Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G Leonard; Parks, Craig; Roll, John

2015-12-01

Researchers often want to examine 2 comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of 2 disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than 2 growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention-deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive-behavioral therapy treatment for a substance use disorder and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these 2 disorders concurrently allowed us to determine whether elevated levels of 1 disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and substance use separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or substance use disorder) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

NASA Astrophysics Data System (ADS)

Zheng, Youqi; Choi, Sooyoung; Lee, Deokjung

2017-12-01

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Optimal perturbations of a finite-width mixing layer near the trailing edge

NASA Astrophysics Data System (ADS)

Gumbart, James C.; Rabchuk, James

2002-03-01

The trailing edge of a surface separating two fluid flows can act as an efficient receptor for acoustic or other disturbances. The incident wave energy is converted by a linear mechanism into incipient flow instabilities which lead further downstream to the transition to turbulence. Understanding this process is essential for analyzing feedback loops and other resonances which can cause unwanted structural vibrations in the surface material or directed acoustic emissions from the mixing region. Previously, the modes of instability in a finite-width mixing layer near the trailing edge were studied as a function of frequency by assuming that vorticity was continually being introduced into the flow at the trailing edge by the forcing field. It was found that the initial amplitude of the growing instability mode was a sharply decreasing function of forcing frequency, and that the initial amplitude was a minimum for the frequency at which the rate of instability growth was a maximum^1. This result has led to a study of the adjoint equation for the perturbation stream function, whose eigensolutions are known to be associated with the optimal perturbation field for the frequency of forcing leading to the greatest instability growth downstream. We have obtained these solutions for a piecewise linear velocity profile near the trailing edge using group-theoretic techniques and have shown that they are indeed optimal. We have also analyzed the nature of the physical forcing field that might produce these optimal perturbations. ^1 Rabchuk, J.A., July 2000, Physics of Fluids.

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Slow relaxation in weakly open rational polygons.

PubMed

Kokshenev, Valery B; Vicentini, Eduardo

2003-07-01

The interplay between the regular (piecewise-linear) and irregular (vertex-angle) boundary effects in nonintegrable rational polygonal billiards (of m equal sides) is discussed. Decay dynamics in polygons (of perimeter P(m) and small opening Delta) is analyzed through the late-time survival probability S(m) approximately equal t(-delta). Two distinct slow relaxation channels are established. The primary universal channel exhibits relaxation of regular sliding orbits, with delta=1. The secondary channel is given by delta>1 and becomes open when m>P(m)/Delta. It originates from vertex order-disorder dual effects and is due to relaxation of chaoticlike excitations.

Advanced control concepts. [for shuttle ascent vehicles

NASA Technical Reports Server (NTRS)

Sharp, J. B.; Coppey, J. M.

1973-01-01

The problems of excess control devices and insufficient trim control capability on shuttle ascent vehicles were investigated. The trim problem is solved at all time points of interest using Lagrangian multipliers and a Simplex based iterative algorithm developed as a result of the study. This algorithm has the capability to solve any bounded linear problem with physically realizable constraints, and to minimize any piecewise differentiable cost function. Both solution methods also automatically distribute the command torques to the control devices. It is shown that trim requirements are unrealizable if only the orbiter engines and the aerodynamic surfaces are used.

Effects of static tensile load on the thermal expansion of Gr/PI composite material

NASA Technical Reports Server (NTRS)

Farley, G. L.

1981-01-01

The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.

On estimating the effects of clock instability with flicker noise characteristics

NASA Technical Reports Server (NTRS)

Wu, S. C.

1981-01-01

A scheme for flicker noise generation is given. The second approach is that of successive segmentation: A clock fluctuation is represented by 2N piecewise linear segments and then converted into a summation of N+1 triangular pulse train functions. The statistics of the clock instability are then formulated in terms of two sample variances at N+1 specified averaging times. The summation converges very rapidly that a value of N 6 is seldom necessary. An application to radio interferometric geodesy shows excellent agreement between the two approaches. Limitations to and the relative merits of the two approaches are discussed.

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Monte Carlo Simulation of Nonlinear Radiation Induced Plasmas. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wang, B. S.

1972-01-01

A Monte Carlo simulation model for radiation induced plasmas with nonlinear properties due to recombination was, employing a piecewise linearized predict-correct iterative technique. Several important variance reduction techniques were developed and incorporated into the model, including an antithetic variates technique. This approach is especially efficient for plasma systems with inhomogeneous media, multidimensions, and irregular boundaries. The Monte Carlo code developed has been applied to the determination of the electron energy distribution function and related parameters for a noble gas plasma created by alpha-particle irradiation. The characteristics of the radiation induced plasma involved are given.

Memristor emulator causes dissimilarity on a coupled memristive systems

NASA Astrophysics Data System (ADS)

Sabarathinam, S.; Prasad, Awadhesh

2018-04-01

The memristor is known as abasic fourth passive solid state circuit element. Itgaining increasing attention to create the next generation electronic devices commonly used as fundamental chaotic circuit although often arbitrary (typically piecewise linear or cubic) fluxcharge characteristics. In thispresent work, the causes of the memristor emulator studied in a coupled memristive chaoticoscillator for the first time. We confirm that the emulator that allows synchronization between theoscillators and cause the dissimilarity between the systems when increasing the couplingstrength, and co-efficient of the memristor emulator. The detailed statistical analysis was performed to confirm such phenomenon.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

NASA Astrophysics Data System (ADS)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are equal for both numerical methods, then PLMDE uniformly produces lower errors than WENO for the fixed computation cost on the test problems considered here.

Model-Based Engine Control Architecture with an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and implementation of an extended Kalman filter (EKF) for model-based engine control (MBEC). Previously proposed MBEC architectures feature an optimal tuner Kalman Filter (OTKF) to produce estimates of both unmeasured engine parameters and estimates for the health of the engine. The success of this approach relies on the accuracy of the linear model and the ability of the optimal tuner to update its tuner estimates based on only a few sensors. Advances in computer processing are making it possible to replace the piece-wise linear model, developed off-line, with an on-board nonlinear model running in real-time. This will reduce the estimation errors associated with the linearization process, and is typically referred to as an extended Kalman filter. The nonlinear extended Kalman filter approach is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (C-MAPSS40k) and compared to the previously proposed MBEC architecture. The results show that the EKF reduces the estimation error, especially during transient operation.

Hypothalamic stimulation and baroceptor reflex interaction on renal nerve activity.

NASA Technical Reports Server (NTRS)

Wilson, M. F.; Ninomiya, I.; Franz, G. N.; Judy, W. V.

1971-01-01

The basal level of mean renal nerve activity (MRNA-0) measured in anesthetized cats was found to be modified by the additive interaction of hypothalamic and baroceptor reflex influences. Data were collected with the four major baroceptor nerves either intact or cut, and with mean aortic pressure (MAP) either clamped with a reservoir or raised with l-epinephrine. With intact baroceptor nerves, MRNA stayed essentially constant at level MRNA-0 for MAP below an initial pressure P1, and fell approximately linearly to zero as MAP was raised to P2. Cutting the baroceptor nerves kept MRNA at MRNA-0 (assumed to represent basal central neural output) independent of MAP. The addition of hypothalamic stimulation produced nearly constant increments in MRNA for all pressure levels up to P2, with complete inhibition at some level above P2. The increments in MRNA depended on frequency and location of the stimulus. A piecewise linear model describes MRNA as a linear combination of hypothalamic, basal central neural, and baroceptor reflex activity.

Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data

PubMed Central

Swihart, Bruce J.; Caffo, Brian S.; Crainiceanu, Ciprian; Punjabi, Naresh M.

2013-01-01

Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of subjects and repeated measures within those subjects, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. Supplementary material includes the analyzed data set as well as the code for a reproducible analysis. PMID:22241689

Stability analysis of confined V-shaped flames in high-velocity streams.

PubMed

El-Rabii, Hazem; Joulin, Guy; Kazakov, Kirill A

2010-06-01

The problem of linear stability of confined V-shaped flames with arbitrary gas expansion is addressed. Using the on-shell description of flame dynamics, a general equation governing propagation of disturbances of an anchored flame is obtained. This equation is solved analytically for V-flames anchored in high-velocity channel streams. It is demonstrated that dynamics of the flame disturbances in this case is controlled by the memory effects associated with vorticity generated by the perturbed flame. The perturbation growth rate spectrum is determined, and explicit analytical expressions for the eigenfunctions are given. It is found that the piecewise linear V structure is unstable for all values of the gas expansion coefficient. Despite the linearity of the basic pattern, however, evolutions of the V-flame disturbances are completely different from those found for freely propagating planar flames or open anchored flames. The obtained results reveal strong influence of the basic flow and the channel walls on the stability properties of confined V-flames.

Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines.

PubMed

Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William

2016-01-01

Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001) when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001) and slopes (p < 0.001) of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001), which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather than the coefficients. Moreover, use of cubic regression splines provides biological meaningful growth velocity and acceleration curves despite increased complexity in coefficient interpretation. Through this stepwise approach, we provide a set of tools to model longitudinal childhood data for non-statisticians using linear mixed-effect models.

Analysis Balance Parameter of Optimal Ramp metering

NASA Astrophysics Data System (ADS)

Li, Y.; Duan, N.; Yang, X.

2018-05-01

Ramp metering is a motorway control method to avoid onset congestion through limiting the access of ramp inflows into the main road of the motorway. The optimization model of ramp metering is developed based upon cell transmission model (CTM). With the piecewise linear structure of CTM, the corresponding motorway traffic optimization problem can be formulated as a linear programming (LP) problem. It is known that LP problem can be solved by established solution algorithms such as SIMPLEX or interior-point methods for the global optimal solution. The commercial software (CPLEX) is adopted in this study to solve the LP problem within reasonable computational time. The concept is illustrated through a case study of the United Kingdom M25 Motorway. The optimal solution provides useful insights and guidances on how to manage motorway traffic in order to maximize the corresponding efficiency.

Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Kent, James

2015-01-01

The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

Pattern formations and optimal packing.

PubMed

Mityushev, Vladimir

2016-04-01

Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary value problems. We demonstrate an intimate connection between pattern formations and optimal random packing on the plane. The main study is based on the following two points. First, the diffusive flux in reaction-diffusion systems is approximated by piecewise linear functions in the framework of structural approximations. This leads to a discrete network approximation of the considered continuous problem. Second, the discrete energy minimization yields optimal random packing of the domains (disks) in the representative cell. Therefore, the general problem of pattern formations based on the reaction-diffusion equations is reduced to the geometric problem of random packing. It is demonstrated that all random packings can be divided onto classes associated with classes of isomorphic graphs obtained from the Delaunay triangulation. The unique optimal solution is constructed in each class of the random packings. If the number of disks per representative cell is finite, the number of classes of isomorphic graphs, hence, the number of optimal packings is also finite. Copyright © 2016 Elsevier Inc. All rights reserved.

Solution Path for Pin-SVM Classifiers With Positive and Negative $\\tau $ Values.

PubMed

Huang, Xiaolin; Shi, Lei; Suykens, Johan A K

2017-07-01

Applying the pinball loss in a support vector machine (SVM) classifier results in pin-SVM. The pinball loss is characterized by a parameter τ . Its value is related to the quantile level and different τ values are suitable for different problems. In this paper, we establish an algorithm to find the entire solution path for pin-SVM with different τ values. This algorithm is based on the fact that the optimal solution to pin-SVM is continuous and piecewise linear with respect to τ . We also show that the nonnegativity constraint on τ is not necessary, i.e., τ can be extended to negative values. First, in some applications, a negative τ leads to better accuracy. Second, τ = -1 corresponds to a simple solution that links SVM and the classical kernel rule. The solution for τ = -1 can be obtained directly and then be used as a starting point of the solution path. The proposed method efficiently traverses τ values through the solution path, and then achieves good performance by a suitable τ . In particular, τ = 0 corresponds to C-SVM, meaning that the traversal algorithm can output a result at least as good as C-SVM with respect to validation error.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Cooper, D. E.; Cohen, D.

1986-01-01

This study investigates the effects of a uniform temperature change on the stresses and deformations of composite tubes and determines the accuracy of an approximate solution based on the principle of complementary virtual work. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory, which predicts that the expansion will be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depend on stacking sequence. For tubes with a specific number of axial and circumferential layers, thermally induced interlaminar stresses can be controlled by altering stacking arrangement.

Unsupervised parameter optimization for automated retention time alignment of severely shifted gas chromatographic data using the piecework alignment algorithm.

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

Pierce, Karisa M.; Wright, Bob W.; Synovec, Robert E.

2007-02-02

First, simulated chromatographic separations with declining retention time precision were used to study the performance of the piecewise retention time alignment algorithm and to demonstrate an unsupervised parameter optimization method. The average correlation coefficient between the first chromatogram and every other chromatogram in the data set was used to optimize the alignment parameters. This correlation method does not require a training set, so it is unsupervised and automated. This frees the user from needing to provide class information and makes the alignment algorithm more generally applicable to classifying completely unknown data sets. For a data set of simulated chromatograms wheremore » the average chromatographic peak was shifted past two neighboring peaks between runs, the average correlation coefficient of the raw data was 0.46 ± 0.25. After automated, optimized piecewise alignment, the average correlation coefficient was 0.93 ± 0.02. Additionally, a relative shift metric and principal component analysis (PCA) were used to independently quantify and categorize the alignment performance, respectively. The relative shift metric was defined as four times the standard deviation of a given peak’s retention time in all of the chromatograms, divided by the peak-width-at-base. The raw simulated data sets that were studied contained peaks with average relative shifts ranging between 0.3 and 3.0. Second, a “real” data set of gasoline separations was gathered using three different GC methods to induce severe retention time shifting. In these gasoline separations, retention time precision improved ~8 fold following alignment. Finally, piecewise alignment and the unsupervised correlation optimization method were applied to severely shifted GC separations of reformate distillation fractions. The effect of piecewise alignment on peak heights and peak areas is also reported. Piecewise alignment either did not change the peak height, or caused it to slightly decrease. The average relative difference in peak height after piecewise alignment was –0.20%. Piecewise alignment caused the peak areas to either stay the same, slightly increase, or slightly decrease. The average absolute relative difference in area after piecewise alignment was 0.15%.« less

The question of nonlinearity in the dose-response relation between particulate matter air pollution and mortality: can Akaike's Information Criterion be trusted to take the right turn?

PubMed

Roberts, Steven; Martin, Michael A

2006-12-15

The shape of the dose-response relation between particulate matter air pollution and mortality is crucial for public health assessment, and departures of this relation from linearity could have important regulatory consequences. A number of investigators have studied the shape of the particulate matter-mortality dose-response relation and concluded that the relation could be adequately described by a linear model. Some of these researchers examined the hypothesis of linearity by comparing Akaike's Information Criterion (AIC) values obtained under linear, piecewise linear, and spline alternative models. However, at the current time, the efficacy of the AIC in this context has not been assessed. The authors investigated AIC as a means of comparing competing dose-response models, using data from Cook County, Illinois, for the period 1987-2000. They found that if nonlinearities exist, the AIC is not always successful in detecting them. In a number of the scenarios considered, AIC was equivocal, picking the correct simulated dose-response model about half of the time. These findings suggest that further research into the shape of the dose-response relation using alternative model selection criteria may be warranted.

Glomerular structural-functional relationship models of diabetic nephropathy are robust in type 1 diabetic patients.

PubMed

Mauer, Michael; Caramori, Maria Luiza; Fioretto, Paola; Najafian, Behzad

2015-06-01

Studies of structural-functional relationships have improved understanding of the natural history of diabetic nephropathy (DN). However, in order to consider structural end points for clinical trials, the robustness of the resultant models needs to be verified. This study examined whether structural-functional relationship models derived from a large cohort of type 1 diabetic (T1D) patients with a wide range of renal function are robust. The predictability of models derived from multiple regression analysis and piecewise linear regression analysis was also compared. T1D patients (n = 161) with research renal biopsies were divided into two equal groups matched for albumin excretion rate (AER). Models to explain AER and glomerular filtration rate (GFR) by classical DN lesions in one group (T1D-model, or T1D-M) were applied to the other group (T1D-test, or T1D-T) and regression analyses were performed. T1D-M-derived models explained 70 and 63% of AER variance and 32 and 21% of GFR variance in T1D-M and T1D-T, respectively, supporting the substantial robustness of the models. Piecewise linear regression analyses substantially improved predictability of the models with 83% of AER variance and 66% of GFR variance explained by classical DN glomerular lesions alone. These studies demonstrate that DN structural-functional relationship models are robust, and if appropriate models are used, glomerular lesions alone explain a major proportion of AER and GFR variance in T1D patients. © The Author 2014. Published by Oxford University Press on behalf of ERA-EDTA. All rights reserved.

Algorithms for the explicit computation of Penrose diagrams

NASA Astrophysics Data System (ADS)

Schindler, J. C.; Aguirre, A.

2018-05-01

An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form . The resulting diagram coordinates are shown to extend the metric continuously and nondegenerately across an arbitrary number of horizons. The method is extended to include piecewise approximations to dynamically evolving spacetimes using a standard hypersurface junction procedure. Examples generated by an implementation of the algorithm are shown for standard and new cases. In the appendix, this algorithm is compared to existing methods.

A fast and accurate online sequential learning algorithm for feedforward networks.

PubMed

Liang, Nan-Ying; Huang, Guang-Bin; Saratchandran, P; Sundararajan, N

2006-11-01

In this paper, we develop an online sequential learning algorithm for single hidden layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes in a unified framework. The algorithm is referred to as online sequential extreme learning machine (OS-ELM) and can learn data one-by-one or chunk-by-chunk (a block of data) with fixed or varying chunk size. The activation functions for additive nodes in OS-ELM can be any bounded nonconstant piecewise continuous functions and the activation functions for RBF nodes can be any integrable piecewise continuous functions. In OS-ELM, the parameters of hidden nodes (the input weights and biases of additive nodes or the centers and impact factors of RBF nodes) are randomly selected and the output weights are analytically determined based on the sequentially arriving data. The algorithm uses the ideas of ELM of Huang et al. developed for batch learning which has been shown to be extremely fast with generalization performance better than other batch training methods. Apart from selecting the number of hidden nodes, no other control parameters have to be manually chosen. Detailed performance comparison of OS-ELM is done with other popular sequential learning algorithms on benchmark problems drawn from the regression, classification and time series prediction areas. The results show that the OS-ELM is faster than the other sequential algorithms and produces better generalization performance.

Gradient-based controllers for timed continuous Petri nets

NASA Astrophysics Data System (ADS)

Lefebvre, Dimitri; Leclercq, Edouard; Druaux, Fabrice; Thomas, Philippe

2015-07-01

This paper is about control design for timed continuous Petri nets that are described as piecewise affine systems. In this context, the marking vector is considered as the state space vector, weighted marking of place subsets are defined as the model outputs and the model inputs correspond to multiplicative control actions that slow down the firing rate of some controllable transitions. Structural and functional sensitivity of the outputs with respect to the inputs are discussed in terms of Petri nets. Then, gradient-based controllers (GBC) are developed in order to adapt the control actions of the controllable transitions according to desired trajectories of the outputs.

Effects of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, C.; Altamimi, Z.; Chin, T. M.; Collilieux, X.; Dach, R.; Heflin, M. B.; Gross, R. S.; König, R.; Lemoine, F. G.; MacMillan, D. S.; Parker, J. W.; van Dam, T. M.; Wu, X.

2013-12-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS global networks used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, the effect of non-tidal atmospheric loading (NTAL) corrections on the TRF is assessed adopting a Remove/Restore approach: (i) Focusing on the a-posteriori approach, the NTAL model derived from the National Center for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations. (ii) Adopting a Kalman-filter based approach, a linear TRF is estimated combining the 4 SG solutions free from NTAL displacements. (iii) Linear fits to the NTAL displacements removed at step (i) are restored to the linear reference frame estimated at (ii). The velocity fields of the (standard) linear reference frame in which the NTAL model has not been removed and the one in which the model has been removed/restored are compared and discussed.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Analysis and modeling of a family of two-transistor parallel inverters

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1973-01-01

A family of five static dc-to-square-wave inverters, each employing a square-loop magnetic core in conjunction with two switching transistors, is analyzed using piecewise-linear models for the nonlinear characteristics of the transistors, diodes, and saturable-core devices. Four of the inverters are analyzed in detail for the first time. These analyses show that, by proper choice of a frame of reference, each of the five quite differently appearing inverter circuits can be described by a common equivalent circuit. This equivalent circuit consists of a five-segment nonlinear resistor, a nonlinear saturable reactor, and a linear capacitor. Thus, by proper interpretation and identification of the parameters in the different circuits, the results of a detailed solution for one of the inverter circuits provide similar information and insight into the local and global behavior of each inverter in the family.

Aircraft MSS data registration and vegetation classification of wetland change detection

USGS Publications Warehouse

Christensen, E.J.; Jensen, J.R.; Ramsey, Elijah W.; Mackey, H.E.

1988-01-01

Portions of the Savannah River floodplain swamp were evaluated for vegetation change using high resolution (5a??6 m) aircraft multispectral scanner (MSS) data. Image distortion from aircraft movement prevented precise image-to-image registration in some areas. However, when small scenes were used (200-250 ha), a first-order linear transformation provided registration accuracies of less than or equal to one pixel. A larger area was registered using a piecewise linear method. Five major wetland classes were identified and evaluated for change. Phenological differences and the variable distribution of vegetation limited wetland type discrimination. Using unsupervised methods and ground-collected vegetation data, overall classification accuracies ranged from 84 per cent to 87 per cent for each scene. Results suggest that high-resolution aircraft MSS data can be precisely registered, if small areas are used, and that wetland vegetation change can be accurately detected and monitored.

LETTER TO THE EDITOR: Fractal diffusion coefficient from dynamical zeta functions

NASA Astrophysics Data System (ADS)

Cristadoro, Giampaolo

2006-03-01

Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

Generation and tooth contact analysis of spiral bevel gears with predesigned parabolic functions of transmission errors

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Lee, Hong-Tao

1989-01-01

A new approach for determination of machine-tool settings for spiral bevel gears is proposed. The proposed settings provide a predesigned parabolic function of transmission errors and the desired location and orientation of the bearing contact. The predesigned parabolic function of transmission errors is able to absorb piece-wise linear functions of transmission errors that are caused by the gear misalignment and reduce gear noise. The gears are face-milled by head cutters with conical surfaces or surfaces of revolution. A computer program for simulation of meshing, bearing contact and determination of transmission errors for misaligned gear has been developed.

Development of models of the magnetorheological fluid damper

NASA Astrophysics Data System (ADS)

Kazakov, Yu. B.; Morozov, N. A.; Nesterov, S. A.

2017-06-01

The algorithm for analytical calculation of a power characteristic of magnetorheological (MR) dampers taking into account the rheological properties of MR fluid is considered. The nonlinear magnetorheological characteristics are represented by piecewise linear approximation to MR fluid areas with different viscosities. The extended calculated power characteristics of a MR damper are received and they coincide with actual results. The finite element model of a MR damper is developed; it allows carrying out the analysis of a MR damper taking into account the mutual influence of electromagnetic, hydrodynamic and thermal fields. The results of finite element simulation coincide with analytical solutions that allows using them for design development of a MR damper.

Design of multi-body Lambert type orbits with specified departure and arrival positions

NASA Astrophysics Data System (ADS)

Ishii, Nobuaki; Kawaguchi, Jun'ichiro; Matsuo, Hiroki

1991-10-01

A new procedure for designing a multi-body Lambert type orbit comprising a multiple swingby process is developed, aiming at relieving a numerical difficulty inherent to a highly nonlinear swingby mechanism. The proposed algorithm, Recursive Multi-Step Linearization, first divides a whole orbit into several trajectory segments. Then, with a maximum use of piecewised transition matrices, a segmentized orbit is repeatedly upgraded until an approximated orbit initially based on a patched conics method eventually converges. In application to the four body earth-moon system with sun's gravitation, one of the double lunar swingby orbits including 12 lunar swingbys is successfully designed without any velocity mismatch.

Hiding message into DNA sequence through DNA coding and chaotic maps.

PubMed

Liu, Guoyan; Liu, Hongjun; Kadir, Abdurahman

2014-09-01

The paper proposes an improved reversible substitution method to hide data into deoxyribonucleic acid (DNA) sequence, and four measures have been taken to enhance the robustness and enlarge the hiding capacity, such as encode the secret message by DNA coding, encrypt it by pseudo-random sequence, generate the relative hiding locations by piecewise linear chaotic map, and embed the encoded and encrypted message into a randomly selected DNA sequence using the complementary rule. The key space and the hiding capacity are analyzed. Experimental results indicate that the proposed method has a better performance compared with the competing methods with respect to robustness and capacity.

A boundary-value problem for a first-order hyperbolic system in a two-dimensional domain

NASA Astrophysics Data System (ADS)

Zhura, N. A.; Soldatov, A. P.

2017-06-01

We consider a strictly hyperbolic first-order system of three equations with constant coefficients in a bounded piecewise-smooth domain. The boundary of the domain is assumed to consist of six smooth non-characteristic arcs. A boundary-value problem in this domain is posed by alternately prescribing one or two linear combinations of the components of the solution on these arcs. We show that this problem has a unique solution under certain additional conditions on the coefficients of these combinations, the boundary of the domain and the behaviour of the solution near the characteristics passing through the corner points of the domain.

Experimental verification of rank 1 chaos in switch-controlled Chua circuit.

PubMed

Oksasoglu, Ali; Ozoguz, Serdar; Demirkol, Ahmet S; Akgul, Tayfun; Wang, Qiudong

2009-03-01

In this paper, we provide the first experimental proof for the existence of rank 1 chaos in the switch-controlled Chua circuit by following a step-by-step procedure given by the theory of rank 1 maps. At the center of this procedure is a periodically kicked limit cycle obtained from the unforced system. Then, this limit cycle is subjected to periodic kicks by adding externally controlled switches to the original circuit. Both the smooth nonlinearity and the piecewise linear cases are considered in this experimental investigation. Experimental results are found to be in concordance with the conclusions of the theory.

Self-sustained peristaltic waves: Explicit asymptotic solutions

NASA Astrophysics Data System (ADS)

Dudchenko, O. A.; Guria, G. Th.

2012-02-01

A simple nonlinear model for the coupled problem of fluid flow and contractile wall deformation is proposed to describe peristalsis. In the context of the model the ability of a transporting system to perform autonomous peristaltic pumping is interpreted as the ability to propagate sustained waves of wall deformation. Piecewise-linear approximations of nonlinear functions are used to analytically demonstrate the existence of traveling-wave solutions. Explicit formulas are derived which relate the speed of self-sustained peristaltic waves to the rheological properties of the transporting vessel and the transported fluid. The results may contribute to the development of diagnostic and therapeutic procedures for cases of peristaltic motility disorders.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.

PubMed

Tsyganov, M A; Ivanitsky, G R; Zemskov, E P

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Wave reflection in a reaction-diffusion system: Breathing patterns and attenuation of the echo

NASA Astrophysics Data System (ADS)

Tsyganov, M. A.; Ivanitsky, G. R.; Zemskov, E. P.

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Vision-based guidance for an automated roving vehicle

NASA Technical Reports Server (NTRS)

Griffin, M. D.; Cunningham, R. T.; Eskenazi, R.

1978-01-01

A controller designed to guide an automated vehicle to a specified target without external intervention is described. The intended application is to the requirements of planetary exploration, where substantial autonomy is required because of the prohibitive time lags associated with closed-loop ground control. The guidance algorithm consists of a set of piecewise-linear control laws for velocity and steering commands, and is executable in real time with fixed-point arithmetic. The use of a previously-reported object tracking algorithm for the vision system to provide position feedback data is described. Test results of the control system on a breadboard rover at the Jet Propulsion Laboratory are included.

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

Aleshin, S. S., E-mail: aless2001@mail.ru; Lobanov, A. E., E-mail: lobanov@phys.msu.ru; Kharlanov, O. G., E-mail: okharl@mail.ru

The effect of flavor day-night asymmetry is considered for solar neutrinos of energy about 1 MeV under the assumption that the electron-density distribution within the Earth is approximately piecewise continuous on the scale of the neutrino-oscillation length. In this approximation, the resulting asymmetry factor for beryllium neutrinos does not depend on the structure of the inner Earth's layers or on the properties of the detector used. Its numerical estimate is on the order of -4 Multiplication-Sign 10{sup -4}, which is far beyond the reach of present-day experiments.

Piecewise adiabatic following in non-Hermitian cycling

NASA Astrophysics Data System (ADS)

Gong, Jiangbin; Wang, Qing-hai

2018-05-01

The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.

Brittle failure of rock: A review and general linear criterion

NASA Astrophysics Data System (ADS)

Labuz, Joseph F.; Zeng, Feitao; Makhnenko, Roman; Li, Yuan

2018-07-01

A failure criterion typically is phenomenological since few models exist to theoretically derive the mathematical function. Indeed, a successful failure criterion is a generalization of experimental data obtained from strength tests on specimens subjected to known stress states. For isotropic rock that exhibits a pressure dependence on strength, a popular failure criterion is a linear equation in major and minor principal stresses, independent of the intermediate principal stress. A general linear failure criterion called Paul-Mohr-Coulomb (PMC) contains all three principal stresses with three material constants: friction angles for axisymmetric compression ϕc and extension ϕe and isotropic tensile strength V0. PMC provides a framework to describe a nonlinear failure surface by a set of planes "hugging" the curved surface. Brittle failure of rock is reviewed and multiaxial test methods are summarized. Equations are presented to implement PMC for fitting strength data and determining the three material parameters. A piecewise linear approximation to a nonlinear failure surface is illustrated by fitting two planes with six material parameters to form either a 6- to 12-sided pyramid or a 6- to 12- to 6-sided pyramid. The particular nature of the failure surface is dictated by the experimental data.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Trajectories of age-related cognitive decline and potential associated factors of cognitive function in senior citizens of Beijing.

PubMed

Li, He; Lv, Chenlong; Zhang, Ting; Chen, Kewei; Chen, Chuansheng; Gai, Guozhong; Hu, Liangping; Wang, Yongyan; Zhang, Zhanjun

2014-01-01

With a longer life expectancy and an increased prevalence of neurodegenerative diseases, investigations on trajectories of cognitive aging have become exciting and promising. This study aimed to estimate the patterns of age-related cognitive decline and the potential associated factors of cognitive function in community-dwelling residents of Beijing, China. In this study, 1248 older adults aged 52-88 years [including 175 mild cognitive impairment (MCI) subjects] completed a battery of neuropsychological scales. The personal information, including demographic information, medical history, eating habits, lifestyle regularity and leisure activities, was also collected. All cognitive function exhibited an agerelated decline in normal volunteers. Piece-wise linear fitting results suggested that performance on the Auditory Verbal Learning Test remained stable until 58 years of age and continued to decline thereafter. The decline in processing speed and executive function began during the early 50's. Scores on visual-spatial and language tests declined after 66 years of age. The decline stage of the general mental status ranged from 63 to 70 years of age. However, the MCI group did not exhibit an obvious age-related decline in most cognitive tests. Multivariate linear regression analyses indicated that education, gender, leisure activities, diabetes and eating habits were associated with cognitive abilities. These results indicated various trajectories of age-related decline across multiple cognitive domains. We also found different patterns of agerelated cognitive decline between MCI and normal elderly. These findings could help improve the guidance of cognitive intervention program and have implications for public policy issues.

Boolean Operations with Prism Algebraic Patches

PubMed Central

Bajaj, Chandrajit; Paoluzzi, Alberto; Portuesi, Simone; Lei, Na; Zhao, Wenqi

2009-01-01

In this paper we discuss a symbolic-numeric algorithm for Boolean operations, closed in the algebra of curved polyhedra whose boundary is triangulated with algebraic patches (A-patches). This approach uses a linear polyhedron as a first approximation of both the arguments and the result. On each triangle of a boundary representation of such linear approximation, a piecewise cubic algebraic interpolant is built, using a C1-continuous prism algebraic patch (prism A-patch) that interpolates the three triangle vertices, with given normal vectors. The boundary representation only stores the vertices of the initial triangulation and their external vertex normals. In order to represent also flat and/or sharp local features, the corresponding normal-per-face and/or normal-per-edge may be also given, respectively. The topology is described by storing, for each curved triangle, the two triples of pointers to incident vertices and to adjacent triangles. For each triangle, a scaffolding prism is built, produced by its extreme vertices and normals, which provides a containment volume for the curved interpolating A-patch. When looking for the result of a regularized Boolean operation, the 0-set of a tri-variate polynomial within each such prism is generated, and intersected with the analogous 0-sets of the other curved polyhedron, when two prisms have non-empty intersection. The intersection curves of the boundaries are traced and used to decompose each boundary into the 3 standard classes of subpatches, denoted in, out and on. While tracing the intersection curves, the locally refined triangulation of intersecting patches is produced, and added to the boundary representation. PMID:21516262

A method to characterize average cervical spine ligament response based on raw data sets for implementation into injury biomechanics models.

PubMed

Mattucci, Stephen F E; Cronin, Duane S

2015-01-01

Experimental testing on cervical spine ligaments provides important data for advanced numerical modeling and injury prediction; however, accurate characterization of individual ligament response and determination of average mechanical properties for specific ligaments has not been adequately addressed in the literature. Existing methods are limited by a number of arbitrary choices made during the curve fits that often misrepresent the characteristic shape response of the ligaments, which is important for incorporation into numerical models to produce a biofidelic response. A method was developed to represent the mechanical properties of individual ligaments using a piece-wise curve fit with first derivative continuity between adjacent regions. The method was applied to published data for cervical spine ligaments and preserved the shape response (toe, linear, and traumatic regions) up to failure, for strain rates of 0.5s(-1), 20s(-1), and 150-250s(-1), to determine the average force-displacement curves. Individual ligament coefficients of determination were 0.989 to 1.000 demonstrating excellent fit. This study produced a novel method in which a set of experimental ligament material property data exhibiting scatter was fit using a characteristic curve approach with a toe, linear, and traumatic region, as often observed in ligaments and tendons, and could be applied to other biological material data with a similar characteristic shape. The resultant average cervical spine ligament curves provide an accurate representation of the raw test data and the expected material property effects corresponding to varying deformation rates. Copyright © 2014 Elsevier Ltd. All rights reserved.

On the Existence of Step-To-Step Breakpoint Transitions in Accelerated Sprinting

PubMed Central

McGhie, David; Danielsen, Jørgen; Sandbakk, Øyvind; Haugen, Thomas

2016-01-01

Accelerated running is characterised by a continuous change of kinematics from one step to the next. It has been argued that breakpoints in the step-to-step transitions may occur, and that these breakpoints are an essential characteristic of dynamics during accelerated running. We examined this notion by comparing a continuous exponential curve fit (indicating continuity, i.e., smooth transitions) with linear piecewise fitting (indicating breakpoint). We recorded the kinematics of 24 well trained sprinters during a 25 m sprint run with start from competition starting blocks. Kinematic data were collected for 24 anatomical landmarks in 3D, and the location of centre of mass (CoM) was calculated from this data set. The step-to-step development of seven variables (four related to CoM position, and ground contact time, aerial time and step length) were analysed by curve fitting. In most individual sprints (in total, 41 sprints were successfully recorded) no breakpoints were identified for the variables investigated. However, for the mean results (i.e., the mean curve for all athletes) breakpoints were identified for the development of vertical CoM position, angle of acceleration and distance between support surface and CoM. It must be noted that for these variables the exponential fit showed high correlations (r2>0.99). No relationship was found between the occurrences of breakpoints for different variables as investigated using odds ratios (Mantel-Haenszel Chi-square statistic). It is concluded that although breakpoints regularly appear during accelerated running, these are not the rule and thereby unlikely a fundamental characteristic, but more likely an expression of imperfection of performance. PMID:27467387

Using within-day hive weight changes to measure environmental effects on honey bee colonies

PubMed Central

Holst, Niels; Weiss, Milagra; Carroll, Mark J.; McFrederick, Quinn S.; Barron, Andrew B.

2018-01-01

Patterns in within-day hive weight data from two independent datasets in Arizona and California were modeled using piecewise regression, and analyzed with respect to honey bee colony behavior and landscape effects. The regression analysis yielded information on the start and finish of a colony’s daily activity cycle, hive weight change at night, hive weight loss due to departing foragers and weight gain due to returning foragers. Assumptions about the meaning of the timing and size of the morning weight changes were tested in a third study by delaying the forager departure times from one to three hours using screen entrance gates. A regression of planned vs. observed departure delays showed that the initial hive weight loss around dawn was largely due to foragers. In a similar experiment in Australia, hive weight loss due to departing foragers in the morning was correlated with net bee traffic (difference between the number of departing bees and the number of arriving bees) and from those data the payload of the arriving bees was estimated to be 0.02 g. The piecewise regression approach was then used to analyze a fifth study involving hives with and without access to natural forage. The analysis showed that, during a commercial pollination event, hives with previous access to forage had a significantly higher rate of weight gain as the foragers returned in the afternoon, and, in the weeks after the pollination event, a significantly higher rate of weight loss in the morning, as foragers departed. This combination of continuous weight data and piecewise regression proved effective in detecting treatment differences in foraging activity that other methods failed to detect. PMID:29791462

Using within-day hive weight changes to measure environmental effects on honey bee colonies.

PubMed

Meikle, William G; Holst, Niels; Colin, Théotime; Weiss, Milagra; Carroll, Mark J; McFrederick, Quinn S; Barron, Andrew B

2018-01-01

Patterns in within-day hive weight data from two independent datasets in Arizona and California were modeled using piecewise regression, and analyzed with respect to honey bee colony behavior and landscape effects. The regression analysis yielded information on the start and finish of a colony's daily activity cycle, hive weight change at night, hive weight loss due to departing foragers and weight gain due to returning foragers. Assumptions about the meaning of the timing and size of the morning weight changes were tested in a third study by delaying the forager departure times from one to three hours using screen entrance gates. A regression of planned vs. observed departure delays showed that the initial hive weight loss around dawn was largely due to foragers. In a similar experiment in Australia, hive weight loss due to departing foragers in the morning was correlated with net bee traffic (difference between the number of departing bees and the number of arriving bees) and from those data the payload of the arriving bees was estimated to be 0.02 g. The piecewise regression approach was then used to analyze a fifth study involving hives with and without access to natural forage. The analysis showed that, during a commercial pollination event, hives with previous access to forage had a significantly higher rate of weight gain as the foragers returned in the afternoon, and, in the weeks after the pollination event, a significantly higher rate of weight loss in the morning, as foragers departed. This combination of continuous weight data and piecewise regression proved effective in detecting treatment differences in foraging activity that other methods failed to detect.

Weak-noise limit of a piecewise-smooth stochastic differential equation.

PubMed

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

Modeling the effects of AADT on predicting multiple-vehicle crashes at urban and suburban signalized intersections.

PubMed

Chen, Chen; Xie, Yuanchang

2016-06-01

Annual Average Daily Traffic (AADT) is often considered as a main covariate for predicting crash frequencies at urban and suburban intersections. A linear functional form is typically assumed for the Safety Performance Function (SPF) to describe the relationship between the natural logarithm of expected crash frequency and covariates derived from AADTs. Such a linearity assumption has been questioned by many researchers. This study applies Generalized Additive Models (GAMs) and Piecewise Linear Negative Binomial (PLNB) regression models to fit intersection crash data. Various covariates derived from minor-and major-approach AADTs are considered. Three different dependent variables are modeled, which are total multiple-vehicle crashes, rear-end crashes, and angle crashes. The modeling results suggest that a nonlinear functional form may be more appropriate. Also, the results show that it is important to take into consideration the joint safety effects of multiple covariates. Additionally, it is found that the ratio of minor to major-approach AADT has a varying impact on intersection safety and deserves further investigations. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stereo matching and view interpolation based on image domain triangulation.

PubMed

Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce

2013-09-01

This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.

Linearized motion estimation for articulated planes.

PubMed

Datta, Ankur; Sheikh, Yaser; Kanade, Takeo

2011-04-01

In this paper, we describe the explicit application of articulation constraints for estimating the motion of a system of articulated planes. We relate articulations to the relative homography between planes and show that these articulations translate into linearized equality constraints on a linear least-squares system, which can be solved efficiently using a Karush-Kuhn-Tucker system. The articulation constraints can be applied for both gradient-based and feature-based motion estimation algorithms and to illustrate this, we describe a gradient-based motion estimation algorithm for an affine camera and a feature-based motion estimation algorithm for a projective camera that explicitly enforces articulation constraints. We show that explicit application of articulation constraints leads to numerically stable estimates of motion. The simultaneous computation of motion estimates for all of the articulated planes in a scene allows us to handle scene areas where there is limited texture information and areas that leave the field of view. Our results demonstrate the wide applicability of the algorithm in a variety of challenging real-world cases such as human body tracking, motion estimation of rigid, piecewise planar scenes, and motion estimation of triangulated meshes.

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

An unsteady lifting surface method for single rotation propellers

NASA Technical Reports Server (NTRS)

Williams, Marc H.

1990-01-01

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Variable Camber Continuous Aerodynamic Control Surfaces and Methods for Active Wing Shaping Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T. (Inventor)

2016-01-01

An aerodynamic control apparatus for an air vehicle improves various aerodynamic performance metrics by employing multiple spanwise flap segments that jointly form a continuous or a piecewise continuous trailing edge to minimize drag induced by lift or vortices. At least one of the multiple spanwise flap segments includes a variable camber flap subsystem having multiple chordwise flap segments that may be independently actuated. Some embodiments also employ a continuous leading edge slat system that includes multiple spanwise slat segments, each of which has one or more chordwise slat segment. A method and an apparatus for implementing active control of a wing shape are also described and include the determination of desired lift distribution to determine the improved aerodynamic deflection of the wings. Flap deflections are determined and control signals are generated to actively control the wing shape to approximate the desired deflection.

Selection of optimal oligonucleotide probes for microarrays usingmultiple criteria, global alignment and parameter estimation.

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

Li, Xingyuan; He, Zhili; Zhou, Jizhong

2005-10-30

The oligonucleotide specificity for microarray hybridizationcan be predicted by its sequence identity to non-targets, continuousstretch to non-targets, and/or binding free energy to non-targets. Mostcurrently available programs only use one or two of these criteria, whichmay choose 'false' specific oligonucleotides or miss 'true' optimalprobes in a considerable proportion. We have developed a software tool,called CommOligo using new algorithms and all three criteria forselection of optimal oligonucleotide probes. A series of filters,including sequence identity, free energy, continuous stretch, GC content,self-annealing, distance to the 3'-untranslated region (3'-UTR) andmelting temperature (Tm), are used to check each possibleoligonucleotide. A sequence identity is calculated based onmore » gapped globalalignments. A traversal algorithm is used to generate alignments for freeenergy calculation. The optimal Tm interval is determined based on probecandidates that have passed all other filters. Final probes are pickedusing a combination of user-configurable piece-wise linear functions andan iterative process. The thresholds for identity, stretch and freeenergy filters are automatically determined from experimental data by anaccessory software tool, CommOligo_PE (CommOligo Parameter Estimator).The program was used to design probes for both whole-genome and highlyhomologous sequence data. CommOligo and CommOligo_PE are freely availableto academic users upon request.« less

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

PubMed

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

Analysis of cardiovascular regulation.

PubMed

Wilhelm, F H; Grossman, P; Roth, W T

1999-01-01

Adequate characterization of hemodynamic and autonomic responses to physical and mental stress can elucidate underlying mechanisms of cardiovascular disease or anxiety disorders. We developed a physiological signal processing system for analysis of continuously recorded ECG, arterial blood pressure (BP), and respiratory signals using the programming language Matlab. Data collection devices are a 16-channel digital, physiological recorder (Vitaport), a finger arterial pressure transducer (Finapres), and a respiratory inductance plethysmograph (Respitrace). Besides the conventional analysis of the physiological channels, power spectral density and transfer functions of respiration, heart rate, and blood pressure variability are used to characterize respiratory sinus arrhythmia (RSA), 0.10-Hz BP oscillatory activity (Mayer-waves), and baroreflex sensitivity. The arterial pressure transducer waveforms permit noninvasive estimation of stroke volume, cardiac output, and systemic vascular resistance. Time trends in spectral composition of indices are assessed using complex demodulation. Transient dynamic changes of cardiovascular parameters at the onset of stress and recovery periods are quantified using a regression breakpoint model that optimizes piecewise linear curve fitting. Approximate entropy (ApEn) is computed to quantify the degree of chaos in heartbeat dynamics. Using our signal processing system we found distinct response patterns in subgroups of patients with coronary artery disease or anxiety disorders, which were related to specific pharmacological and behavioral factors.

Modeling of driver's collision avoidance maneuver based on controller switching model.

PubMed

Kim, Jong-Hae; Hayakawa, Soichiro; Suzuki, Tatsuya; Hayashi, Koji; Okuma, Shigeru; Tsuchida, Nuio; Shimizu, Masayuki; Kido, Shigeyuki

2005-12-01

This paper presents a modeling strategy of human driving behavior based on the controller switching model focusing on the driver's collision avoidance maneuver. The driving data are collected by using the three-dimensional (3-D) driving simulator based on the CAVE Automatic Virtual Environment (CAVE), which provides stereoscopic immersive virtual environment. In our modeling, the control scenario of the human driver, that is, the mapping from the driver's sensory information to the operation of the driver such as acceleration, braking, and steering, is expressed by Piecewise Polynomial (PWP) model. Since the PWP model includes both continuous behaviors given by polynomials and discrete logical conditions, it can be regarded as a class of Hybrid Dynamical System (HDS). The identification problem for the PWP model is formulated as the Mixed Integer Linear Programming (MILP) by transforming the switching conditions into binary variables. From the obtained results, it is found that the driver appropriately switches the "control law" according to the sensory information. In addition, the driving characteristics of the beginner driver and the expert driver are compared and discussed. These results enable us to capture not only the physical meaning of the driving skill but the decision-making aspect (switching conditions) in the driver's collision avoidance maneuver as well.

Class Identification Efficacy in Piecewise GMM with Unknown Turning Points

ERIC Educational Resources Information Center

Ning, Ling; Luo, Wen

2018-01-01

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

Uniformly high-order accurate non-oscillatory schemes, 1

NASA Technical Reports Server (NTRS)

Harten, A.; Osher, S.

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

A refined analysis of composite laminates. [theory of statics and dynamics

NASA Technical Reports Server (NTRS)

Srinivas, S.

1973-01-01

The purpose of this paper is to develop a sufficiently accurate analysis, which is much simpler than exact three-dimensional analysis, for statics and dynamics of composite laminates. The governing differential equations and boundary conditions are derived by following a variational approach. The displacements are assumed piecewise linear across the thickness and the effects of transverse shear deformations and rotary inertia are included. A procedure for obtaining the general solution of the above governing differential equations in the form of hyperbolic-trigonometric series is given. The accuracy of the present theory is assessed by obtaining results for free vibrations and flexure of simply supported rectangular laminates and comparing them with results from exact three-dimensional analysis.

Numerical solution of the unsteady Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Osher, Stanley J.; Engquist, Bjoern

1985-01-01

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

Evolution of complex dynamics

NASA Astrophysics Data System (ADS)

Wilds, Roy; Kauffman, Stuart A.; Glass, Leon

2008-09-01

We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1982-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series. [and] An Inversion Method for Laplace Transforms, Fourier Transforms, and Fourier Series. Integral Transforms and Series Expansions. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 324 and 325.

ERIC Educational Resources Information Center

Grimm, C. A.

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

Examining the Earnings Trajectories of Community College Students Using a Piecewise Growth Curve Modeling Approach

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2016-01-01

Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this article we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from two popular econometric approaches:…

Harmonics analysis of the ITER poloidal field converter based on a piecewise method

NASA Astrophysics Data System (ADS)

Xudong, WANG; Liuwei, XU; Peng, FU; Ji, LI; Yanan, WU

2017-12-01

Poloidal field (PF) converters provide controlled DC voltage and current to PF coils. The many harmonics generated by the PF converter flow into the power grid and seriously affect power systems and electric equipment. Due to the complexity of the system, the traditional integral operation in Fourier analysis is complicated and inaccurate. This paper presents a piecewise method to calculate the harmonics of the ITER PF converter. The relationship between the grid input current and the DC output current of the ITER PF converter is deduced. The grid current is decomposed into the sum of some simple functions. By calculating simple function harmonics based on the piecewise method, the harmonics of the PF converter under different operation modes are obtained. In order to examine the validity of the method, a simulation model is established based on Matlab/Simulink and a relevant experiment is implemented in the ITER PF integration test platform. Comparative results are given. The calculated results are found to be consistent with simulation and experiment. The piecewise method is proved correct and valid for calculating the system harmonics.

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. First, that the network is piecewise convex as a function of the input data. Second, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Third, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize the objective on certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space. Copyright © 2017 Elsevier Ltd. All rights reserved.

Galerkin projection for geometrically-exact multilayer beams allowing for ply drop-off

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

Vu-Quoc, L.; Deng, H.

1995-12-31

Focusing on the static case in the present work, we develop a Galerkin projection of the resulting nonlinear governing equations of equilibrium for geometrically exact sandwich beams and 1-D plates developed. In the proposed theory, each layer in the beam can have different thickness and length. As such one can use the present formulation to model an important class of multilayer structures having ply drop-off. No restriction is imposed on the magnitude of the displacement field, whose continuity across the layer interfaces is exactly enforced. The layer cross section in the deformed beam is assumed to remain straight, but notmore » orthogonal to the layer centroidal line, thus shear deformation in each layer is accounted for. Also no restriction is imposed on the rotation of a layer cross section. It follows that the overall cross section in the deformed beam is continuous piecewise linear, and can be best thought of as a chain of rigid links, connected by hinges. The overall deformation of a multilayer beam can be described by the deformation of a reference layer. The unknown kinematic quantities are therefore the two displacement components of the deformed centroidal line of a reference layer, and the finite rotations of the layers. The present theory can be used to analyze large deformation in sandwich beams. Numerical examples, such as roll-up maneuver and sandwich beam with ply drop-off, which underline the salient features of the formulation are presented. Saint-Venant principle is demonstrated for very short sandwich beams. The readers are referred to the paper for detail.« less

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

A state space approach for piecewise-linear recurrent neural networks for identifying computational dynamics from neural measurements.

PubMed

Durstewitz, Daniel

2017-06-01

The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects of the nonlinear dynamics underlying observed neuronal time series, and directly link these to computational properties.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints.

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

Hybrid Kalman Filter: A New Approach for Aircraft Engine In-Flight Diagnostics

NASA Technical Reports Server (NTRS)

Kobayashi, Takahisa; Simon, Donald L.

2006-01-01

In this paper, a uniquely structured Kalman filter is developed for its application to in-flight diagnostics of aircraft gas turbine engines. The Kalman filter is a hybrid of a nonlinear on-board engine model (OBEM) and piecewise linear models. The utilization of the nonlinear OBEM allows the reference health baseline of the in-flight diagnostic system to be updated to the degraded health condition of the engines through a relatively simple process. Through this health baseline update, the effectiveness of the in-flight diagnostic algorithm can be maintained as the health of the engine degrades over time. Another significant aspect of the hybrid Kalman filter methodology is its capability to take advantage of conventional linear and nonlinear Kalman filter approaches. Based on the hybrid Kalman filter, an in-flight fault detection system is developed, and its diagnostic capability is evaluated in a simulation environment. Through the evaluation, the suitability of the hybrid Kalman filter technique for aircraft engine in-flight diagnostics is demonstrated.

[Shock shape representation of sinus heart rate based on cloud model].

PubMed

Yin, Wenfeng; Zhao, Jie; Chen, Tiantian; Zhang, Junjian; Zhang, Chunyou; Li, Dapeng; An, Baijing

2014-04-01

The present paper is to analyze the trend of sinus heart rate RR interphase sequence after a single ventricular premature beat and to compare it with the two parameters, turbulence onset (TO) and turbulence slope (TS). Based on the acquisition of sinus rhythm concussion sample, we in this paper use a piecewise linearization method to extract its linear characteristics, following which we describe shock form with natural language through cloud model. In the process of acquisition, we use the exponential smoothing method to forecast the position where QRS wave may appear to assist QRS wave detection, and use template to judge whether current cardiac is sinus rhythm. And we choose some signals from MIT-BIH Arrhythmia Database to detect whether the algorithm is effective in Matlab. The results show that our method can correctly detect the changing trend of sinus heart rate. The proposed method can achieve real-time detection of sinus rhythm shocks, which is simple and easily implemented, so that it is effective as a supplementary method.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

The role of density discontinuity in the inviscid instability of two-phase parallel flows

NASA Astrophysics Data System (ADS)

Behzad, M.; Ashgriz, N.

2014-02-01

We re-examine the inviscid instability of two-phase parallel flows with piecewise linear velocity profiles. Although such configuration has been theoretically investigated, we employ the concept of waves resonance to physically interpret the instability mechanism as well as the essential role of density discontinuity in the flow. Upon performing linear stability analysis, we demonstrate the existence of neutrally stable "density" and "density-vorticity" waves which are emerged due to the density jump in the flow, in addition to the well-known vorticity waves. Such waves are capable of resonating with each other to form unstable modes in the flow. Although unstable modes in this study are classified as the "shear instability" type, we demonstrate that they are not necessarily of the Rayleigh type. The results also show that the density can have both stabilizing and destabilizing effects on the flow stability. We verify that the difference in the resonating pair of neutral waves leads to such distinct behavior of the density variation.

Stress estimation in reservoirs using an integrated inverse method

NASA Astrophysics Data System (ADS)

Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre

2018-05-01

Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

Global dynamics for switching systems and their extensions by linear differential equations

NASA Astrophysics Data System (ADS)

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-01

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

PubMed

Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

2018-01-01

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

NASA Technical Reports Server (NTRS)

Kuhlman, J. M.; Shu, J. Y.

1981-01-01

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).

Instabilities in a staircase stratified shear flow

NASA Astrophysics Data System (ADS)

Ponetti, G.; Balmforth, N. J.; Eaves, T. S.

2018-01-01

We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.

Global dynamics for switching systems and their extensions by linear differential equations.

PubMed

Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin

2018-03-15

Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.

What Can Tobit-Piecewise Regression Tell Us about the Determinants of Household Educational Debt?

ERIC Educational Resources Information Center

Thipbharos, Titirut

2014-01-01

Educational debt as part of household debt remains a problem for Thailand. The significant factors of household characteristics with regard to educational debt are shown by constructing a Tobit-piecewise regression for three different clusters, namely poor, middle and affluent households in Thailand. It was found that household debt is likely to…

Examining the Earnings Trajectories of Community College Students Using a Piecewise Growth Curve Modeling Approach. A CAPSEE Working Paper

ERIC Educational Resources Information Center

Jaggars, Shanna Smith; Xu, Di

2015-01-01

Policymakers have become increasingly concerned with measuring--and holding colleges accountable for--students' labor market outcomes. In this paper we introduce a piecewise growth curve approach to analyzing community college students' labor market outcomes, and we discuss how this approach differs from Mincerian and fixed-effects approaches. Our…

Conventional and Piecewise Growth Modeling Techniques: Applications and Implications for Investigating Head Start Children's Early Literacy Learning

ERIC Educational Resources Information Center

Hindman, Annemarie H.; Cromley, Jennifer G.; Skibbe, Lori E.; Miller, Alison L.

2011-01-01

This article reviews the mechanics of conventional and piecewise growth models to demonstrate the unique affordances of each technique for examining the nature and predictors of children's early literacy learning during the transition from preschool through first grade. Using the nationally representative Family and Child Experiences Survey…

Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop

NASA Astrophysics Data System (ADS)

Xiong, Yanqin

2016-06-01

This paper is concerned with the bifurcation problem of limit cycles by perturbing a piecewise Hamiltonian system with a double homoclinic loop. First, the derivative of the first Melnikov function is provided. Then, we use it, together with the analytic method, to derive the asymptotic expansion of the first Melnikov function near the loop. Meanwhile, we present the first coefficients in the expansion, which can be applied to study the limit cycle bifurcation near the loop. We give sufficient conditions for this system to have 14 limit cycles in the neighborhood of the loop. As an application, a piecewise polynomial Liénard system is investigated, finding six limit cycles with the help of the obtained method.

Quasi-conformal mapping with genetic algorithms applied to coordinate transformations

NASA Astrophysics Data System (ADS)

González-Matesanz, F. J.; Malpica, J. A.

2006-11-01

In this paper, piecewise conformal mapping for the transformation of geodetic coordinates is studied. An algorithm, which is an improved version of a previous algorithm published by Lippus [2004a. On some properties of piecewise conformal mappings. Eesti NSV Teaduste Akademmia Toimetised Füüsika-Matemaakika 53, 92-98; 2004b. Transformation of coordinates using piecewise conformal mapping. Journal of Geodesy 78 (1-2), 40] is presented; the improvement comes from using a genetic algorithm to partition the complex plane into convex polygons, whereas the original one did so manually. As a case study, the method is applied to the transformation of the Spanish datum ED50 and ETRS89, and both its advantages and disadvantages are discussed herein.

An analytical mechanical model to describe the response of NiTi rotary endodontic files in a curved root canal.

PubMed

Leroy, Agnès Marie Françoise; Bahia, Maria Guiomar de Azevedo; Ehrlacher, Alain; Buono, Vicente Tadeu Lopes

2012-08-01

To build a mathematical model describing the mechanical behavior of NiTi rotary files while they are rotating in a root canal. The file was seen as a beam undergoing large transformations. The instrument was assumed to be rotating steadily in the root canal, and the geometry of the canal was considered as a known parameter of the problem. The formulae of large transformations mechanics then allowed the calculation of the Green-Lagrange strain field in the file. The non-linear mechanical behavior of NiTi was modeled as a continuous piecewise linear function, assuming that the material did not reach plastic deformation. Criteria locating the changes of behavior of NiTi were established and the tension field in the file, and the external efforts applied on it were calculated. The unknown variable of torsion was deduced from the equilibrium equation system using a Coulomb contact law which solved the problem on a cycle of rotation. In order to verify that the model described well reality, three-point bending experiments were managed on superelastic NiTi wires, whose results were compared to the theoretical ones. It appeared that the model gave a good mentoring of the empirical results in the range of bending angles that interested us. Knowing the geometry of the root canal, one is now able to write the equations of the strain and stress fields in the endodontic instrument, and to quantify the impact of each macroscopic parameter of the problem on its response. This should be useful to predict failure of the files under rotating bending fatigue, and to optimize the geometry of the files. Copyright © 2012 Elsevier B.V. All rights reserved.

Exposure–response relationships for select cancer and non-cancer health outcomes in a cohort of US firefighters from San Francisco, Chicago and Philadelphia (1950–2009)

PubMed Central

Daniels, Robert D.; Bertke, Stephen; Dahm, Matthew M.; Yiin, James H.; Kubale, Travis L.; Hales, Thomas R.; Baris, Dalsu; Zahm, Shelia H.; Beaumont, James J.; Waters, Kathleen M.; Pinkerton, Lynne E.

2015-01-01

Objectives To examine exposure–response relationships between surrogates of firefighting exposure and select outcomes among previously studied US career firefighters. Methods Eight cancer and four non-cancer outcomes were examined using conditional logistic regression. Incidence density sampling was used to match each case to 200 controls on attained age. Days accrued in firefighting assignments (exposed-days), run totals (fire-runs) and run times (fire-hours) were used as exposure surrogates. HRs comparing 75th and 25th centiles of lagged cumulative exposures were calculated using loglinear, linear, log-quadratic, power and restricted cubic spline general relative risk models. Piecewise constant models were used to examine risk differences by time since exposure, age at exposure and calendar period. Results Among 19 309 male firefighters eligible for the study, there were 1333 cancer deaths and 2609 cancer incidence cases. Significant positive associations between fire-hours and lung cancer mortality and incidence were evident. A similar relation between leukaemia mortality and fire-runs was also found. The lung cancer associations were nearly linear in cumulative exposure, while the association with leukaemia mortality was attenuated at higher exposure levels and greater for recent exposures. Significant negative associations were evident for the exposure surrogates and colorectal and prostate cancers, suggesting a healthy worker survivor effect possibly enhanced by medical screening. Conclusions Lung cancer and leukaemia mortality risks were modestly increasing with firefighter exposures. These findings add to evidence of a causal association between firefighting and cancer. Nevertheless, small effects merit cautious interpretation. We plan to continue to follow the occurrence of disease and injury in this cohort. PMID:25673342

Linearization of Positional Response Curve of a Fiber-optic Displacement Sensor

NASA Astrophysics Data System (ADS)

Babaev, O. G.; Matyunin, S. A.; Paranin, V. D.

2018-01-01

Currently, the creation of optical measuring instruments and sensors for measuring linear displacement is one of the most relevant problems in the area of instrumentation. Fiber-optic contactless sensors based on the magneto-optical effect are of special interest. They are essentially contactless, non-electrical and have a closed optical channel not subject to contamination. The main problem of this type of sensors is the non-linearity of their positional response curve due to the hyperbolic nature of the magnetic field intensity variation induced by moving the magnetic source mounted on the controlled object relative to the sensing element. This paper discusses an algorithmic method of linearizing the positional response curve of fiber-optic displacement sensors in any selected range of the displacements to be measured. The method is divided into two stages: 1 - definition of the calibration function, 2 - measurement and linearization of the positional response curve (including its temperature stabilization). The algorithm under consideration significantly reduces the number of points of the calibration function, which is essential for the calibration of temperature dependence, due to the use of the points that randomly deviate from the grid points with uniform spacing. Subsequent interpolation of the deviating points and piecewise linear-plane approximation of the calibration function reduces the microcontroller storage capacity for storing the calibration function and the time required to process the measurement results. The paper also presents experimental results of testing real samples of fiber-optic displacement sensors.

Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

PubMed

Zana, F; Klein, J C

2001-01-01

This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

Reprint of Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-04-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method

NASA Astrophysics Data System (ADS)

D'Ambra, Pasqua; Tartaglione, Gaetano

2015-03-01

Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions.

PubMed

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-03-02

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn)featuresfromfixedslidingwindowsonreal-timesteeringwheelanglestimeseries. Afterthat, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: "wake" and "drowsy". The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the "awake" state, and 15.15% false detections of the "drowsy" state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue.

Online Detection of Driver Fatigue Using Steering Wheel Angles for Real Driving Conditions

PubMed Central

Li, Zuojin; Li, Shengbo Eben; Li, Renjie; Cheng, Bo; Shi, Jinliang

2017-01-01

This paper presents a drowsiness on-line detection system for monitoring driver fatigue level under real driving conditions, based on the data of steering wheel angles (SWA) collected from sensors mounted on the steering lever. The proposed system firstly extracts approximate entropy (ApEn) features from fixed sliding windows on real-time steering wheel angles time series. After that, this system linearizes the ApEn features series through an adaptive piecewise linear fitting using a given deviation. Then, the detection system calculates the warping distance between the linear features series of the sample data. Finally, this system uses the warping distance to determine the drowsiness state of the driver according to a designed binary decision classifier. The experimental data were collected from 14.68 h driving under real road conditions, including two fatigue levels: “wake” and “drowsy”. The results show that the proposed system is capable of working online with an average 78.01% accuracy, 29.35% false detections of the “awake” state, and 15.15% false detections of the “drowsy” state. The results also confirm that the proposed method based on SWA signal is valuable for applications in preventing traffic accidents caused by driver fatigue. PMID:28257094

Unified halo-independent formalism from convex hulls for direct dark matter searches

NASA Astrophysics Data System (ADS)

Gelmini, Graciela B.; Huh, Ji-Haeng; Witte, Samuel J.

2017-12-01

Using the Fenchel-Eggleston theorem for convex hulls (an extension of the Caratheodory theorem), we prove that any likelihood can be maximized by either a dark matter 1- speed distribution F(v) in Earth's frame or 2- Galactic velocity distribution fgal(vec u), consisting of a sum of delta functions. The former case applies only to time-averaged rate measurements and the maximum number of delta functions is (Script N‑1), where Script N is the total number of data entries. The second case applies to any harmonic expansion coefficient of the time-dependent rate and the maximum number of terms is Script N. Using time-averaged rates, the aforementioned form of F(v) results in a piecewise constant unmodulated halo function tilde eta0BF(vmin) (which is an integral of the speed distribution) with at most (Script N-1) downward steps. The authors had previously proven this result for likelihoods comprised of at least one extended likelihood, and found the best-fit halo function to be unique. This uniqueness, however, cannot be guaranteed in the more general analysis applied to arbitrary likelihoods. Thus we introduce a method for determining whether there exists a unique best-fit halo function, and provide a procedure for constructing either a pointwise confidence band, if the best-fit halo function is unique, or a degeneracy band, if it is not. Using measurements of modulation amplitudes, the aforementioned form of fgal(vec u), which is a sum of Galactic streams, yields a periodic time-dependent halo function tilde etaBF(vmin, t) which at any fixed time is a piecewise constant function of vmin with at most Script N downward steps. In this case, we explain how to construct pointwise confidence and degeneracy bands from the time-averaged halo function. Finally, we show that requiring an isotropic Galactic velocity distribution leads to a Galactic speed distribution F(u) that is once again a sum of delta functions, and produces a time-dependent tilde etaBF(vmin, t) function (and a time-averaged tilde eta0BF(vmin)) that is piecewise linear, differing significantly from best-fit halo functions obtained without the assumption of isotropy.

Difference equation state approximations for nonlinear hereditary control problems

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589

PROGRAM VSAERO: A computer program for calculating the non-linear aerodynamic characteristics of arbitrary configurations: User's manual

NASA Technical Reports Server (NTRS)

Maskew, B.

1982-01-01

VSAERO is a computer program used to predict the nonlinear aerodynamic characteristics of arbitrary three-dimensional configurations in subsonic flow. Nonlinear effects of vortex separation and vortex surface interaction are treated in an iterative wake-shape calculation procedure, while the effects of viscosity are treated in an iterative loop coupling potential-flow and integral boundary-layer calculations. The program employs a surface singularity panel method using quadrilateral panels on which doublet and source singularities are distributed in a piecewise constant form. This user's manual provides a brief overview of the mathematical model, instructions for configuration modeling and a description of the input and output data. A listing of a sample case is included.

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

Enhancements of Bayesian Blocks; Application to Large Light Curve Databases

NASA Technical Reports Server (NTRS)

Scargle, Jeff

2015-01-01

Bayesian Blocks are optimal piecewise linear representations (step function fits) of light-curves. The simple algorithm implementing this idea, using dynamic programming, has been extended to include more data modes and fitness metrics, multivariate analysis, and data on the circle (Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations, Scargle, Norris, Jackson and Chiang 2013, ApJ, 764, 167), as well as new results on background subtraction and refinement of the procedure for precise timing of transient events in sparse data. Example demonstrations will include exploratory analysis of the Kepler light curve archive in a search for "star-tickling" signals from extraterrestrial civilizations. (The Cepheid Galactic Internet, Learned, Kudritzki, Pakvasa1, and Zee, 2008, arXiv: 0809.0339; Walkowicz et al., in progress).

Efficient Digital Implementation of The Sigmoidal Function For Artificial Neural Network

NASA Astrophysics Data System (ADS)

Pratap, Rana; Subadra, M.

2011-10-01

An efficient piecewise linear approximation of a nonlinear function (PLAN) is proposed. This uses simulink environment design to perform a direct transformation from X to Y, where X is the input and Y is the approximated sigmoidal output. This PLAN is then used within the outputs of an artificial neural network to perform the nonlinear approximation. In This paper, is proposed a method to implement in FPGA (Field Programmable Gate Array) circuits different approximation of the sigmoid function.. The major benefit of the proposed method resides in the possibility to design neural networks by means of predefined block systems created in System Generator environment and the possibility to create a higher level design tools used to implement neural networks in logical circuits.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

NASA Astrophysics Data System (ADS)

de Niem, D.; Kührt, E.; Motschmann, U.

2007-02-01

A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.

Fatigue life prediction of rotor blade composites: Validation of constant amplitude formulations with variable amplitude experiments

NASA Astrophysics Data System (ADS)

Westphal, T.; Nijssen, R. P. L.

2014-12-01

The effect of Constant Life Diagram (CLD) formulation on the fatigue life prediction under variable amplitude (VA) loading was investigated based on variable amplitude tests using three different load spectra representative for wind turbine loading. Next to the Wisper and WisperX spectra, the recently developed NewWisper2 spectrum was used. Based on these variable amplitude fatigue results the prediction accuracy of 4 CLD formulations is investigated. In the study a piecewise linear CLD based on the S-N curves for 9 load ratios compares favourably in terms of prediction accuracy and conservativeness. For the specific laminate used in this study Boerstra's Multislope model provides a good alternative at reduced test effort.

Modeling and analysis of several classes of self-oscillating inverters. I - State-plane representations. II - Model extension, classification, and duality relationships

NASA Technical Reports Server (NTRS)

Lee, F. C. Y.; Wilson, T. G.

1982-01-01

The present investigation is concerned with an important class of power conditioning networks, taking into account self-oscillating dc-to-square-wave transistor inverters. The considered circuits are widely used both as the principal power converting and processing means in many systems and as low-power analog-to-discrete-time converters for controlling the switching of the output-stage semiconductors in a variety of power conditioning systems. Aspects of piecewise-linear modeling are discussed, taking into consideration component models, and an equivalent-circuit model. Questions of singular point analysis and state plane representation are also investigated, giving attention to limit cycles, starting circuits, the region of attraction, a hard oscillator, and a soft oscillator.

Maximum safe speed estimation using planar quintic Bezier curve with C2 continuity

NASA Astrophysics Data System (ADS)

Ibrahim, Mohamad Fakharuddin; Misro, Md Yushalify; Ramli, Ahmad; Ali, Jamaludin Md

2017-08-01

This paper describes an alternative way in estimating design speed or the maximum speed allowed for a vehicle to drive safely on a road using curvature information from Bezier curve fitting on a map. We had tested on some route in Tun Sardon Road, Balik Pulau, Penang, Malaysia. We had proposed to use piecewise planar quintic Bezier curve while satisfying the curvature continuity between joined curves in the process of mapping the road. By finding the derivatives of quintic Bezier curve, the value of curvature was calculated and design speed was derived. In this paper, a higher order of Bezier Curve had been used. A higher degree of curve will give more freedom for users to control the shape of the curve compared to curve in lower degree.

Simulating transient dynamics of the time-dependent time fractional Fokker-Planck systems

NASA Astrophysics Data System (ADS)

Kang, Yan-Mei

2016-09-01

For a physically realistic type of time-dependent time fractional Fokker-Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker-Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed.

Trajectory Calculator for Finite-Radius Cutter on a Lathe

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Strekalov, Dmitry; Yu, Nan

2009-01-01

A computer program calculates the two-dimensional trajectory (radial vs. axial position) of a finite-radius-of-curvature cutting tool on a lathe so as to cut a workpiece to a piecewise-continuous, analytically defined surface of revolution. (In the original intended application, the tool is a diamond cutter, and the workpiece is made of a crystalline material and is to be formed into an optical resonator disk.) The program also calculates an optimum cutting speed as F/L, where F is a material-dependent empirical factor and L is the effective instantaneous length of the cutting edge.

The Use of Piecewise Growth Models to Estimate Learning Trajectories and RtI Instructional Effects in a Comparative Interrupted Time-Series Design

ERIC Educational Resources Information Center

Zvoch, Keith

2016-01-01

Piecewise growth models (PGMs) were used to estimate and model changes in the preliteracy skill development of kindergartners in a moderately sized school district in the Pacific Northwest. PGMs were applied to interrupted time-series (ITS) data that arose within the context of a response-to-intervention (RtI) instructional framework. During the…

RATE OF APPROXIMATION OF PIECEWISE-ANALYTIC FUNCTIONS BY RATIONAL FRACTIONS IN THE L_p-METRICS, 0 < p\\leq\\infty

NASA Astrophysics Data System (ADS)

Vjačeslavov, N. S.

1980-02-01

In this paper estimates are found for L_pR_n(f) - the least deviation in the L_p-metric, 0 < p\\leq\\infty, of a piecewise analytic function f from the rational functions of degree at most n. It is shown that these estimates are sharp in a well-defined sense.Bibliography: 12 titles.

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Gherlone, Marco; Versino, Daniele; DiSciuva, Marco

2012-01-01

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C(sup 0)-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite element approximations thus provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

Pituitary iron and volume imaging in healthy controls.

PubMed

Noetzli, L J; Panigrahy, A; Hyderi, A; Dongelyan, A; Coates, T D; Wood, J C

2012-02-01

Patients with transfusional iron overload develop iron deposits in the pituitary gland, which are associated with volume loss and HH. The purpose of this study was to characterize R2 and volumetric data in a healthy population for diagnostic use in patients with transfusional iron overload. One hundred healthy controls without iron overload between the ages of 2 and 48 were recruited to have MR imaging of the brain to assess their pituitary R2 and volume. Pituitary R2 was assessed with a 8-echo spin-echo sequence, and pituitary volumes, by a 3D spoiled gradient-echo sequence with 1-mm(3) resolution. A 2-component continuous piecewise linear approximation was used for creating volumetric and R2 nomograms. Equations were generated from regression relationships for convenient z-score calculation. Pituitary R2 rose weakly with age (r(2) = 0.19, P < .0001). Anterior and total pituitary volumes increased steadily up to 18 years of age, after which volume slightly decreased. Females had larger pituitary glands, most likely representing their larger lactotroph population. From these data, a clinician can calculate the z scores for R2 and pituitary volume in patients with iron overload. Normal ranges are well-differentiated from values previously associated with endocrine disease in transfusional siderosis; this finding suggests that preclinical iron overload can be recognized and appropriately treated.

Analytic and Computational Perspectives of Multi-Scale Theory for Homogeneous, Laminated Composite, and Sandwich Beams and Plates

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Gherlone, Marco; Versino, Daniele; Di Sciuva, Marco

2012-01-01

This paper reviews the theoretical foundation and computational mechanics aspects of the recently developed shear-deformation theory, called the Refined Zigzag Theory (RZT). The theory is based on a multi-scale formalism in which an equivalent single-layer plate theory is refined with a robust set of zigzag local layer displacements that are free of the usual deficiencies found in common plate theories with zigzag kinematics. In the RZT, first-order shear-deformation plate theory is used as the equivalent single-layer plate theory, which represents the overall response characteristics. Local piecewise-linear zigzag displacements are used to provide corrections to these overall response characteristics that are associated with the plate heterogeneity and the relative stiffnesses of the layers. The theory does not rely on shear correction factors and is equally accurate for homogeneous, laminated composite, and sandwich beams and plates. Regardless of the number of material layers, the theory maintains only seven kinematic unknowns that describe the membrane, bending, and transverse shear plate-deformation modes. Derived from the virtual work principle, RZT is well-suited for developing computationally efficient, C0-continuous finite elements; formulations of several RZT-based elements are highlighted. The theory and its finite elements provide a unified and reliable computational platform for the analysis and design of high-performance load-bearing aerospace structures.

On piecewise interpolation techniques for estimating solar radiation missing values in Kedah

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

Saaban, Azizan; Zainudin, Lutfi; Bakar, Mohd Nazari Abu

2014-12-04

This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Errormore » (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.« less

Limit cycles via higher order perturbations for some piecewise differential systems

NASA Astrophysics Data System (ADS)

Buzzi, Claudio A.; Lima, Maurício Firmino Silva; Torregrosa, Joan

2018-05-01

A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x‧ ,y‧) =(- y + εf(x , y , ε) , x + εg(x , y , ε)) . In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n , no more than Nn - 1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Liénard differential systems providing better upper bounds for higher order perturbation in ε, showing also when they are reached. The Poincaré-Pontryagin-Melnikov theory is the main technique used to prove all the results.

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

Automatic variance reduction for Monte Carlo simulations via the local importance function transform

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

Turner, S.A.

1996-02-01

The author derives a transformed transport problem that can be solved theoretically by analog Monte Carlo with zero variance. However, the Monte Carlo simulation of this transformed problem cannot be implemented in practice, so he develops a method for approximating it. The approximation to the zero variance method consists of replacing the continuous adjoint transport solution in the transformed transport problem by a piecewise continuous approximation containing local biasing parameters obtained from a deterministic calculation. He uses the transport and collision processes of the transformed problem to bias distance-to-collision and selection of post-collision energy groups and trajectories in a traditionalmore » Monte Carlo simulation of ``real`` particles. He refers to the resulting variance reduction method as the Local Importance Function Transform (LIFI) method. He demonstrates the efficiency of the LIFT method for several 3-D, linearly anisotropic scattering, one-group, and multigroup problems. In these problems the LIFT method is shown to be more efficient than the AVATAR scheme, which is one of the best variance reduction techniques currently available in a state-of-the-art Monte Carlo code. For most of the problems considered, the LIFT method produces higher figures of merit than AVATAR, even when the LIFT method is used as a ``black box``. There are some problems that cause trouble for most variance reduction techniques, and the LIFT method is no exception. For example, the author demonstrates that problems with voids, or low density regions, can cause a reduction in the efficiency of the LIFT method. However, the LIFT method still performs better than survival biasing and AVATAR in these difficult cases.« less

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals

PubMed Central

Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G.

2016-01-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors’ previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp–p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat. PMID:27382478

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

PubMed

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.

Recent work on material interface reconstruction

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

Mosso, S.J.; Swartz, B.K.

1997-12-31

For the last 15 years, many Eulerian codes have relied on a series of piecewise linear interface reconstruction algorithms developed by David Youngs. In a typical Youngs` method, the material interfaces were reconstructed based upon nearly cell values of volume fractions of each material. The interfaces were locally represented by linear segments in two dimensions and by pieces of planes in three dimensions. The first step in such reconstruction was to locally approximate an interface normal. In Youngs` 3D method, a local gradient of a cell-volume-fraction function was estimated and taken to be the local interface normal. A linear interfacemore » was moved perpendicular to the now known normal until the mass behind it matched the material volume fraction for the cell in question. But for distorted or nonorthogonal meshes, the gradient normal estimate didn`t accurately match that of linear material interfaces. Moreover, curved material interfaces were also poorly represented. The authors will present some recent work in the computation of more accurate interface normals, without necessarily increasing stencil size. Their estimate of the normal is made using an iterative process that, given mass fractions for nearby cells of known but arbitrary variable density, converges in 3 or 4 passes in practice (and quadratically--like Newton`s method--in principle). The method reproduces a linear interface in both orthogonal and nonorthogonal meshes. The local linear approximation is generally 2nd-order accurate, with a 1st-order accurate normal for curved interfaces in both two and three dimensional polyhedral meshes. Recent work demonstrating the interface reconstruction for curved surfaces will /be discussed.« less

Evolutionary technology adoption in an oligopoly market with forward-looking firms

NASA Astrophysics Data System (ADS)

Lamantia, F.; Radi, D.

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

Neighboring Optimal Aircraft Guidance in a General Wind Environment

NASA Technical Reports Server (NTRS)

Jardin, Matthew R. (Inventor)

2003-01-01

Method and system for determining an optimal route for an aircraft moving between first and second waypoints in a general wind environment. A selected first wind environment is analyzed for which a nominal solution can be determined. A second wind environment is then incorporated; and a neighboring optimal control (NOC) analysis is performed to estimate an optimal route for the second wind environment. In particular examples with flight distances of 2500 and 6000 nautical miles in the presence of constant or piecewise linearly varying winds, the difference in flight time between a nominal solution and an optimal solution is 3.4 to 5 percent. Constant or variable winds and aircraft speeds can be used. Updated second wind environment information can be provided and used to obtain an updated optimal route.

Acousto-optic replication of ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Yushkov, Konstantin B.; Molchanov, Vladimir Ya.; Ovchinnikov, Andrey V.; Chefonov, Oleg V.

2017-10-01

Precisely controlled sequences of ultrashort laser pulses are required in various scientific and engineering applications. We developed a phase-only acousto-optic pulse shaping method for replication of ultrashort laser pulses in a TW laser system. A sequence of several Fourier-transform-limited pulses is generated from a single femtosecond laser pulse by means of applying a piecewise linear phase modulation over the whole emission spectrum. Analysis demonstrates that the main factor which limits maximum delay between the pulse replicas is spectral resolution of the acousto-optic dispersive delay line used for pulse shaping. In experiments with a Cr:forsterite laser system, we obtained delays from 0.3 to 3.5 ps between two replicas of 190 fs transform-limited pulses at the central wavelength of laser emission, 1230 nm.

Evolutionary technology adoption in an oligopoly market with forward-looking firms.

PubMed

Lamantia, F; Radi, D

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

Image encryption algorithm based on multiple mixed hash functions and cyclic shift

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Zhu, Xiaoqiang; Wu, Xiangjun; Zhang, Yingqian

2018-08-01

This paper proposes a new one-time pad scheme for chaotic image encryption that is based on the multiple mixed hash functions and the cyclic-shift function. The initial value is generated using both information of the plaintext image and the chaotic sequences, which are calculated from the SHA1 and MD5 hash algorithms. The scrambling sequences are generated by the nonlinear equations and logistic map. This paper aims to improve the deficiencies of traditional Baptista algorithms and its improved algorithms. We employ the cyclic-shift function and piece-wise linear chaotic maps (PWLCM), which give each shift number the characteristics of chaos, to diffuse the image. Experimental results and security analysis show that the new scheme has better security and can resist common attacks.

Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation

PubMed Central

Gao, Zhanheng; Yu, Zeyun; Holst, Michael

2012-01-01

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522

Colorimetric characterization models based on colorimetric characteristics evaluation for active matrix organic light emitting diode panels.

PubMed

Gong, Rui; Xu, Haisong; Tong, Qingfen

2012-10-20

The colorimetric characterization of active matrix organic light emitting diode (AMOLED) panels suffers from their poor channel independence. Based on the colorimetric characteristics evaluation of channel independence and chromaticity constancy, an accurate colorimetric characterization method, namely, the polynomial compensation model (PC model) considering channel interactions was proposed for AMOLED panels. In this model, polynomial expressions are employed to calculate the relationship between the prediction errors of XYZ tristimulus values and the digital inputs to compensate the XYZ prediction errors of the conventional piecewise linear interpolation assuming the variable chromaticity coordinates (PLVC) model. The experimental results indicated that the proposed PC model outperformed other typical characterization models for the two tested AMOLED smart-phone displays and for the professional liquid crystal display monitor as well.

Low-complexity piecewise-affine virtual sensors: theory and design

NASA Astrophysics Data System (ADS)

Rubagotti, Matteo; Poggi, Tomaso; Oliveri, Alberto; Pascucci, Carlo Alberto; Bemporad, Alberto; Storace, Marco

2014-03-01

This paper is focused on the theoretical development and the hardware implementation of low-complexity piecewise-affine direct virtual sensors for the estimation of unmeasured variables of interest of nonlinear systems. The direct virtual sensor is designed directly from measured inputs and outputs of the system and does not require a dynamical model. The proposed approach allows one to design estimators which mitigate the effect of the so-called 'curse of dimensionality' of simplicial piecewise-affine functions, and can be therefore applied to relatively high-order systems, enjoying convergence and optimality properties. An automatic toolchain is also presented to generate the VHDL code describing the digital circuit implementing the virtual sensor, starting from the set of measured input and output data. The proposed methodology is applied to generate an FPGA implementation of the virtual sensor for the estimation of vehicle lateral velocity, using a hardware-in-the-loop setting.

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.

Unsteady flows in rotor-stator cascades

NASA Astrophysics Data System (ADS)

Lee, Yu-Tai; Bein, Thomas W.; Feng, Jin Z.; Merkle, Charles L.

1991-03-01

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

Variable neighborhood search to solve the vehicle routing problem for hazardous materials transportation.

PubMed

Bula, Gustavo Alfredo; Prodhon, Caroline; Gonzalez, Fabio Augusto; Afsar, H Murat; Velasco, Nubia

2017-02-15

This work focuses on the Heterogeneous Fleet Vehicle Routing problem (HFVRP) in the context of hazardous materials (HazMat) transportation. The objective is to determine a set of routes that minimizes the total expected routing risk. This is a nonlinear function, and it depends on the vehicle load and the population exposed when an incident occurs. Thus, a piecewise linear approximation is used to estimate it. For solving the problem, a variant of the Variable Neighborhood Search (VNS) algorithm is employed. To improve its performance, a post-optimization procedure is implemented via a Set Partitioning (SP) problem. The SP is solved on a pool of routes obtained from executions of the local search procedure embedded on the VNS. The algorithm is tested on two sets of HFVRP instances based on literature with up to 100 nodes, these instances are modified to include vehicle and arc risk parameters. The results are competitive in terms of computational efficiency and quality attested by a comparison with Mixed Integer Linear Programming (MILP) previously proposed. Copyright © 2016 Elsevier B.V. All rights reserved.

Nonlinear modeling of wave-topography interactions, shear instabilities and shear induced wave breaking using vortex method

NASA Astrophysics Data System (ADS)

Guha, Anirban

2017-11-01

Theoretical studies on linear shear instabilities as well as different kinds of wave interactions often use simple velocity and/or density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Moreover, such simple profiles provide a minimal model to obtain a mechanistic understanding of shear instabilities. Here we have extended this minimal paradigm into nonlinear domain using vortex method. Making use of unsteady Bernoulli's equation in presence of linear shear, and extending Birkhoff-Rott equation to multiple interfaces, we have numerically simulated the interaction between multiple fully nonlinear waves. This methodology is quite general, and has allowed us to simulate diverse problems that can be essentially reduced to the minimal system with interacting waves, e.g. spilling and plunging breakers, stratified shear instabilities (Holmboe, Taylor-Caulfield, stratified Rayleigh), jet flows, and even wave-topography interaction problem like Bragg resonance. We found that the minimal models capture key nonlinear features (e.g. wave breaking features like cusp formation and roll-ups) which are observed in experiments and/or extensive simulations with smooth, realistic profiles.

A modelling approach to assessing the timescale uncertainties in proxy series with chronological errors

NASA Astrophysics Data System (ADS)

Divine, D. V.; Godtliebsen, F.; Rue, H.

2012-01-01

The paper proposes an approach to assessment of timescale errors in proxy-based series with chronological uncertainties. The method relies on approximation of the physical process(es) forming a proxy archive by a random Gamma process. Parameters of the process are partly data-driven and partly determined from prior assumptions. For a particular case of a linear accumulation model and absolutely dated tie points an analytical solution is found suggesting the Beta-distributed probability density on age estimates along the length of a proxy archive. In a general situation of uncertainties in the ages of the tie points the proposed method employs MCMC simulations of age-depth profiles yielding empirical confidence intervals on the constructed piecewise linear best guess timescale. It is suggested that the approach can be further extended to a more general case of a time-varying expected accumulation between the tie points. The approach is illustrated by using two ice and two lake/marine sediment cores representing the typical examples of paleoproxy archives with age models based on tie points of mixed origin.

EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN.

PubMed

Nguyen, Dang-Manh; Peters, Jörg

2017-01-01

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters NP 0 that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NP 0 filters outperform the more complex known boundary filters. NP 0 filters typically reduce the L ∞ error in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NP 0 filtering can be implemented as forming linear combinations of the data with short rational weights. Exact derivatives of the convolved output are easy to compute.

EXPLICIT LEAST-DEGREE BOUNDARY FILTERS FOR DISCONTINUOUS GALERKIN*

PubMed Central

Nguyen, Dang-Manh; Peters, Jörg

2017-01-01

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided for non-periodic boundary conditions. Recently, position-dependent smoothness-increasing accuracy-preserving (PSIAC) filters were shown to be a superset of the well-known one-sided RLKV and SRV filters. Since PSIAC filters can be formulated symbolically, PSIAC filtering amounts to forming linear products with local DG output and so offers a more stable and efficient implementation. The paper introduces a new class of PSIAC filters NP0 that have small support and are piecewise constant. Extensive numerical experiments for the canonical hyperbolic test equation show NP0 filters outperform the more complex known boundary filters. NP0 filters typically reduce the L∞ error in the boundary region below that of the interior where optimally superconvergent symmetric filters of the same support are applied. NP0 filtering can be implemented as forming linear combinations of the data with short rational weights. Exact derivatives of the convolved output are easy to compute. PMID:29081643

Optimal Operation System of the Integrated District Heating System with Multiple Regional Branches

NASA Astrophysics Data System (ADS)

Kim, Ui Sik; Park, Tae Chang; Kim, Lae-Hyun; Yeo, Yeong Koo

This paper presents an optimal production and distribution management for structural and operational optimization of the integrated district heating system (DHS) with multiple regional branches. A DHS consists of energy suppliers and consumers, district heating pipelines network and heat storage facilities in the covered region. In the optimal management system, production of heat and electric power, regional heat demand, electric power bidding and sales, transport and storage of heat at each regional DHS are taken into account. The optimal management system is formulated as a mixed integer linear programming (MILP) where the objectives is to minimize the overall cost of the integrated DHS while satisfying the operation constraints of heat units and networks as well as fulfilling heating demands from consumers. Piecewise linear formulation of the production cost function and stairwise formulation of the start-up cost function are used to compute nonlinear cost function approximately. Evaluation of the total overall cost is based on weekly operations at each district heat branches. Numerical simulations show the increase of energy efficiency due to the introduction of the present optimal management system.

Sensitivity of control-augmented structure obtained by a system decomposition method

NASA Technical Reports Server (NTRS)

Sobieszczanskisobieski, Jaroslaw; Bloebaum, Christina L.; Hajela, Prabhat

1988-01-01

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Robust sensor fault detection and isolation of gas turbine engines subjected to time-varying parameter uncertainties

NASA Astrophysics Data System (ADS)

Pourbabaee, Bahareh; Meskin, Nader; Khorasani, Khashayar

2016-08-01

In this paper, a novel robust sensor fault detection and isolation (FDI) strategy using the multiple model-based (MM) approach is proposed that remains robust with respect to both time-varying parameter uncertainties and process and measurement noise in all the channels. The scheme is composed of robust Kalman filters (RKF) that are constructed for multiple piecewise linear (PWL) models that are constructed at various operating points of an uncertain nonlinear system. The parameter uncertainty is modeled by using a time-varying norm bounded admissible structure that affects all the PWL state space matrices. The robust Kalman filter gain matrices are designed by solving two algebraic Riccati equations (AREs) that are expressed as two linear matrix inequality (LMI) feasibility conditions. The proposed multiple RKF-based FDI scheme is simulated for a single spool gas turbine engine to diagnose various sensor faults despite the presence of parameter uncertainties, process and measurement noise. Our comparative studies confirm the superiority of our proposed FDI method when compared to the methods that are available in the literature.

Multifrequency InSAR height reconstruction through maximum likelihood estimation of local planes parameters.

PubMed

Pascazio, Vito; Schirinzi, Gilda

2002-01-01

In this paper, a technique that is able to reconstruct highly sloped and discontinuous terrain height profiles, starting from multifrequency wrapped phase acquired by interferometric synthetic aperture radar (SAR) systems, is presented. We propose an innovative unwrapping method, based on a maximum likelihood estimation technique, which uses multifrequency independent phase data, obtained by filtering the interferometric SAR raw data pair through nonoverlapping band-pass filters, and approximating the unknown surface by means of local planes. Since the method does not exploit the phase gradient, it assures the uniqueness of the solution, even in the case of highly sloped or piecewise continuous elevation patterns with strong discontinuities.

Modeling of electrical capacitance tomography with the use of complete electrode model

NASA Astrophysics Data System (ADS)

Fang, Weifu

2016-10-01

We introduce the complete electrode model in the modeling of electrical capacitance tomography (ECT), which extends the model with the commonly used model for electrodes. We show that the solution of the complete electrode model approaches the solution of the corresponding common electrode model as the impedance effect on the electrodes vanishes. We also derive the nonlinear relation between capacitance and permitivity and the sensitivity maps with respect to both the permittivity and the impedance constants, and present a finite difference scheme in polar coordinates for the case of circular ECT sensors that retains the continuity of displacement current with piecewise-constant permitivities.

Near-optimal, asymptotic tracking in control problems involving state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Markopoulos, N.; Calise, A. J.

1993-01-01

The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.

Robust and Quantized Wiener Filters for p-Point Spectral Classes.

DTIC Science & Technology

1980-01-01

REPORT DOCUMENTATION, __BEFORE COMPLETING FORM A. REPORT NUMBER ’ 12. GOVT ACCESSION NO. 3 . RECIPIENT’S CATALOG NUMBER AFOSR-TR- 80-0425z__...re School of Electrical Engineerin . 3 - , Philadelphia, PA 19104 ABSTRACT In Section III, we show that a piecewise const- ant filter also possesses...determining the optimum piecewise ters using a band-model for the PSD’s. Poor [ 3 , 4] constant filter. Then, for a particular class of then considered

Millimeter wave attenuation prediction using a piecewise uniform rain rate model

NASA Technical Reports Server (NTRS)

Persinger, R. R.; Stutzman, W. L.; Bostian, C. W.; Castle, R. E., Jr.

1980-01-01

A piecewise uniform rain rate distribution model is introduced as a quasi-physical model of real rain along earth-space millimeter wave propagation paths. It permits calculation of the total attenuation from specific attenuation in a simple fashion. The model predications are verified by comparison with direct attenuation measurements for several frequencies, elevation angles, and locations. Also, coupled with the Rice-Holmberg rain rate model, attenuation statistics are predicated from rainfall accumulation data.

Separated Component-Based Restoration of Speckled SAR Images

DTIC Science & Technology

2014-01-01

One of the simplest approaches for speckle noise reduction is known as multi-look processing. It involves non-coherently summing the independent...image is assumed to be piecewise smooth [21], [22], [23]. It has been shown that TV regular- ization often yields images with the stair -casing effect...as a function f , is to be decomposed into a sum of two components f = u+ v, where u represents the cartoon or geometric (i.e. piecewise smooth

Interface with weakly singular points always scatter

NASA Astrophysics Data System (ADS)

Li, Long; Hu, Guanghui; Yang, Jiansheng

2018-07-01

Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly singular point, we prove that the scattered field cannot vanish identically. This implies the absence of non-scattering energies for piecewise analytic interfaces with one singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.

Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT

NASA Astrophysics Data System (ADS)

Beretta, Elena; Micheletti, Stefano; Perotto, Simona; Santacesaria, Matteo

2018-01-01

In this paper, we develop a shape optimization-based algorithm for the electrical impedance tomography (EIT) problem of determining a piecewise constant conductivity on a polygonal partition from boundary measurements. The key tool is to use a distributed shape derivative of a suitable cost functional with respect to movements of the partition. Numerical simulations showing the robustness and accuracy of the method are presented for simulated test cases in two dimensions.

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

The steady aerodynamics of aerofoils with porosity gradients.

PubMed

Hajian, Rozhin; Jaworski, Justin W

2017-09-01

This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann-Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.

The steady aerodynamics of aerofoils with porosity gradients

NASA Astrophysics Data System (ADS)

Hajian, Rozhin; Jaworski, Justin W.

2017-09-01

This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann-Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.

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

Lee, E; Yuan, F; Templeton, A

Purpose: The ultimate goal of radiotherapy treatment planning is to find a treatment that will yield a high tumor-control-probability(TCP) with an acceptable normal-tissue-complication probability(NTCP). Yet most treatment planning today is not based upon optimization of TCPs and NTCPs, but rather upon meeting physical dose and volume constraints defined by the planner. We design treatment plans that optimize TCP directly and contrast them with the clinical dose-based plans. PET image is incorporated to evaluate gain in TCP for dose escalation. Methods: We build a nonlinear mixed integer programming optimization model that maximizes TCP directly while satisfying the dose requirements on themore » targeted organ and healthy tissues. The solution strategy first fits the TCP function with a piecewise-linear approximation, then solves the problem that maximizes the piecewise linear approximation of TCP, and finally performs a local neighborhood search to improve the TCP value. To gauge the feasibility, characteristics, and potential benefit of PET-image guided dose escalation, initial validation consists of fifteen cervical cancer HDR patient cases. These patients have all received prior 45Gy of external radiation dose. For both escalated strategies, we consider 35Gy PTV-dose, and two variations (37Gy-boost to BTV vs 40Gy-boost) to PET-image-pockets. Results: TCP for standard clinical plans range from 59.4% - 63.6%. TCP for dose-based PET-guided escalated-dose-plan ranges from 63.8%–98.6% for all patients; whereas TCP-optimized plans achieves over 91% for all patients. There is marginal difference in TCP among those with 37Gy-boosted vs 40Gy-boosted. There is no increase in rectum and bladder dose among all plans. Conclusion: Optimizing TCP directly results in highly conformed treatment plans. The TCP-optimized plan is individualized based on the biological PET-image of the patients. The TCP-optimization framework is generalizable and has been applied successfully to other external-beam delivery modalities. A clinical trial is on-going to gauge the clinical significance. Partially supported by the National Science Foundation.« less

Pseudochaos and anomalous transport: A study on saw-tooth map

NASA Astrophysics Data System (ADS)

Fan, Rong

The observation of chaotic dynamics in digital filter in late 1980s propelled the interest in piecewise linear map beyond the border of theoretical electrical engineering. Also, during last two decades, various physical models and phenomena, such as stochastic web and sticky orbits, not only broadened our knowledge of chaos but also urged us to further our understanding of meaning of chaos and randomness. In this dissertation, a piecewise linear kicked oscillator model: saw-tooth map, is studied as an example of pseudochaos. Physically, kicked oscillator model describes one-dimensional harmonic oscillator effected by delta-like kicks from external force source at certain fixed frequency. Starting from a special case of global periodicity, numerical investigations were carefully carried out in two cases that deviate from global periodicity. We observe the appearance of stochastic web structure and accompanying erratic dynamical behavior in the system that can't be fully explained by the classical Kolmogorov-Arnold-Moser theorem. Also anomalous transport occurs in both cases. We perform accurate analysis of Poincare recurrences and reconstruct the probability density function of Poincare recurrence times, which suggests a relation between the transport and the Poincare recurrence exponents. Saw-tooth map has non-uniform phase space, in which domains of regular dynamics and domains of chaotic dynamics are intertwined. The large-scale dynamics of the system is hugely impacted by the heterogeneity of the phase space, especially by the existence of hierarchy of periodic islands. We carefully study the characteristics of phase space and numerically compute fractal dimensions of the so-called exceptional set Delta in both cases. Our results suggest that the fractal dimension is strictly less than 2 and that the fractal structures are unifractal rather than multifractal. We present a phenomenological theoretical framework of Fractional Kinetic Equation (FKE) and Renormalization Group of Kinetics (RGK). FKE, which is fractional generalization of the Fokker-Planck-Kolmogorov equation, adopts the fractality of time and space and serves probabilistic description of chaos in Hamiltonian systems. RGK bridges the self-similar structure in phase space and large-scale behavior of the dynamics, and establishes relationships among fractality, transport and Poincare recurrences.

Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens.

PubMed

Métris, Aline; George, Susie M; Ropers, Delphine

2017-01-02

Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available, and the more abstract Boolean methods. Copyright © 2016 Elsevier B.V. All rights reserved.

Identification of piecewise affine systems based on fuzzy PCA-guided robust clustering technique

NASA Astrophysics Data System (ADS)

Khanmirza, Esmaeel; Nazarahari, Milad; Mousavi, Alireza

2016-12-01

Hybrid systems are a class of dynamical systems whose behaviors are based on the interaction between discrete and continuous dynamical behaviors. Since a general method for the analysis of hybrid systems is not available, some researchers have focused on specific types of hybrid systems. Piecewise affine (PWA) systems are one of the subsets of hybrid systems. The identification of PWA systems includes the estimation of the parameters of affine subsystems and the coefficients of the hyperplanes defining the partition of the state-input domain. In this paper, we have proposed a PWA identification approach based on a modified clustering technique. By using a fuzzy PCA-guided robust k-means clustering algorithm along with neighborhood outlier detection, the two main drawbacks of the well-known clustering algorithms, i.e., the poor initialization and the presence of outliers, are eliminated. Furthermore, this modified clustering technique enables us to determine the number of subsystems without any prior knowledge about system. In addition, applying the structure of the state-input domain, that is, considering the time sequence of input-output pairs, provides a more efficient clustering algorithm, which is the other novelty of this work. Finally, the proposed algorithm has been evaluated by parameter identification of an IGV servo actuator. Simulation together with experiment analysis has proved the effectiveness of the proposed method.

Self-locking degree-4 vertex origami structures

PubMed Central

Li, Suyi; Wang, K. W.

2016-01-01

A generic degree-4 vertex (4-vertex) origami possesses one continuous degree-of-freedom for rigid folding, and this folding process can be stopped when two of its facets bind together. Such facet-binding will induce self-locking so that the overall structure stays at a pre-specified configuration without additional locking elements or actuators. Self-locking offers many promising properties, such as programmable deformation ranges and piecewise stiffness jumps, that could significantly advance many adaptive structural systems. However, despite its excellent potential, the origami self-locking features have not been well studied, understood, and used. To advance the state of the art, this research conducts a comprehensive investigation on the principles of achieving and harnessing self-locking in 4-vertex origami structures. Especially, for the first time, this study expands the 4-vertex structure construction from single-component to dual-component designs and investigates their self-locking behaviours. By exploiting various tessellation designs, this research discovers that the dual-component designs offer the origami structures with extraordinary attributes that the single-component structures do not have, which include the existence of flat-folded locking planes, programmable locking points and deformability. Finally, proof-of-concept experiments investigate how self-locking can effectively induce piecewise stiffness jumps. The results of this research provide new scientific knowledge and a systematic framework for the design, analysis and utilization of self-locking origami structures for many potential engineering applications. PMID:27956889

Self-locking degree-4 vertex origami structures.

PubMed

Fang, Hongbin; Li, Suyi; Wang, K W

2016-11-01

A generic degree-4 vertex (4-vertex) origami possesses one continuous degree-of-freedom for rigid folding, and this folding process can be stopped when two of its facets bind together. Such facet-binding will induce self-locking so that the overall structure stays at a pre-specified configuration without additional locking elements or actuators. Self-locking offers many promising properties, such as programmable deformation ranges and piecewise stiffness jumps, that could significantly advance many adaptive structural systems. However, despite its excellent potential, the origami self-locking features have not been well studied, understood, and used. To advance the state of the art, this research conducts a comprehensive investigation on the principles of achieving and harnessing self-locking in 4-vertex origami structures. Especially, for the first time, this study expands the 4-vertex structure construction from single-component to dual-component designs and investigates their self-locking behaviours. By exploiting various tessellation designs, this research discovers that the dual-component designs offer the origami structures with extraordinary attributes that the single-component structures do not have, which include the existence of flat-folded locking planes, programmable locking points and deformability. Finally, proof-of-concept experiments investigate how self-locking can effectively induce piecewise stiffness jumps. The results of this research provide new scientific knowledge and a systematic framework for the design, analysis and utilization of self-locking origami structures for many potential engineering applications.

Log-normal frailty models fitted as Poisson generalized linear mixed models.

PubMed

Hirsch, Katharina; Wienke, Andreas; Kuss, Oliver

2016-12-01

The equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to "explode" the data set by the number of pieces. In this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. The simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. The suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Resonances in piecewise potentials and Supersymmetric Quantum Mechanics (SUSY-QM) for the construction of optical potentials

NASA Astrophysics Data System (ADS)

Orozco Cortés, Luis Fernando; Fernández García, Nicolás

2014-05-01

A method to obtain the general solution of any constant piecewise potential is presented, this is achieved by means of the analysis of the transfer matrices in each cutoff. The resonance phenomenon together with the supersymmetric quantum mechanics technique allow us to construct a wide family of complex potentials which can be used as theoretical models for optical systems. The method is applied to the particular case for which the potential function has six cutoff points.

Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

NASA Astrophysics Data System (ADS)

Alessandrini, Giovanni; de Hoop, Maarten V.; Gaburro, Romina

2017-12-01

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω\\subset{R}n when the so-called Neumann-to-Dirichlet map is locally given on a non-empty curved portion Σ of the boundary \\partialΩ . We prove that anisotropic conductivities that are a priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.

A Safe Cooperative Framework for Atmospheric Science Missions with Multiple Heterogeneous UAS using Piecewise Bezier Curves

NASA Technical Reports Server (NTRS)

Mehdi, S. Bilal; Puig-Navarro, Javier; Choe, Ronald; Cichella, Venanzio; Hovakimyan, Naira; Chandarana, Meghan; Trujillo, Anna; Rothhaar, Paul M.; Tran, Loc; Neilan, James H.;

[Analysis on the trend of long-term change of blood pressure in hypertensive patients treated with benazepril].

PubMed

Lu, Jun; Li, Li-Ming; He, Ping-Ping; Cao, Wei-Hua; Zhan, Si-Yan; Hu, Yong-Hua

2004-06-01

To introduce the application of mixed linear model in the analysis of secular trend of blood pressure under antihypertensive treatment. A community-based postmarketing surveillance of benazepril was conducted in 1831 essential hypertensive patients (age range from 35 to 88 years) in Shanghai. Data of blood pressure was analyzed every 3 months with mixed linear model to describe the secular trend of blood pressure and changes of age-specific and gender-specific. The changing trends of systolic blood pressure (SBP) and diastolic blood pressure (DBP) were found to fit the curvilinear models. A piecewise model was fit for pulse pressure (PP), i.e., curvilinear model in the first 9 months and linear model after 9 months of taking medication. Both blood pressure and its velocity gradually slowed down. There were significant variation for the curve parameters of intercept, slope, and acceleration. Blood pressure in patients with higher initial levels was persistently declining in the 3-year-treatment. However blood pressures of patients with relatively low initial levels remained low when dropped down to some degree. Elderly patients showed high SBP but low DBP, so as with higher PP. The velocity and sizes of blood pressure reductions increased with the initial level of blood pressure. Mixed linear model is flexible and robust when applied to the analysis of longitudinal data but with missing values and can also make the maximum use of available information.

Identification of Major Risk Sources for Surface Water Pollution by Risk Indexes (RI) in the Multi-Provincial Boundary Region of the Taihu Basin, China

PubMed Central

Yao, Hong; Li, Weixin; Qian, Xin

2015-01-01

Environmental safety in multi-district boundary regions has been one of the focuses in China and is mentioned many times in the Environmental Protection Act of 2014. Five types were categorized concerning the risk sources for surface water pollution in the multi-provincial boundary region of the Taihu basin: production enterprises, waste disposal sites, chemical storage sites, agricultural non-point sources and waterway transportations. Considering the hazard of risk sources, the purification property of environmental medium and the vulnerability of risk receptors, 52 specific attributes on the risk levels of each type of risk source were screened out. Continuous piecewise linear function model, expert consultation method and fuzzy integral model were used to calculate the integrated risk indexes (RI) to characterize the risk levels of pollution sources. In the studied area, 2716 pollution sources were characterized by RI values. There were 56 high-risk sources screened out as major risk sources, accounting for about 2% of the total. The numbers of sources with high-moderate, moderate, moderate-low and low pollution risk were 376, 1059, 101 and 1124, respectively, accounting for 14%, 38%, 5% and 41% of the total. The procedure proposed could be included in the integrated risk management systems of the multi-district boundary region of the Taihu basin. It could help decision makers to identify major risk sources in the risk prevention and reduction of surface water pollution. PMID:26308032

Identification of Major Risk Sources for Surface Water Pollution by Risk Indexes (RI) in the Multi-Provincial Boundary Region of the Taihu Basin, China.

PubMed

Yao, Hong; Li, Weixin; Qian, Xin

2015-08-21

Environmental safety in multi-district boundary regions has been one of the focuses in China and is mentioned many times in the Environmental Protection Act of 2014. Five types were categorized concerning the risk sources for surface water pollution in the multi-provincial boundary region of the Taihu basin: production enterprises, waste disposal sites, chemical storage sites, agricultural non-point sources and waterway transportations. Considering the hazard of risk sources, the purification property of environmental medium and the vulnerability of risk receptors, 52 specific attributes on the risk levels of each type of risk source were screened out. Continuous piecewise linear function model, expert consultation method and fuzzy integral model were used to calculate the integrated risk indexes (RI) to characterize the risk levels of pollution sources. In the studied area, 2716 pollution sources were characterized by RI values. There were 56 high-risk sources screened out as major risk sources, accounting for about 2% of the total. The numbers of sources with high-moderate, moderate, moderate-low and low pollution risk were 376, 1059, 101 and 1124, respectively, accounting for 14%, 38%, 5% and 41% of the total. The procedure proposed could be included in the integrated risk management systems of the multi-district boundary region of the Taihu basin. It could help decision makers to identify major risk sources in the risk prevention and reduction of surface water pollution.

Apparent multifractality of self-similar Lévy processes

NASA Astrophysics Data System (ADS)

Zamparo, Marco

2017-07-01

Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments are generally regarded as a sign of multifractality in the data. We show that, except for the Brownian motion, this method fails to disclose the correct monofractal nature of self-similar Lévy processes. We prove that for this class of processes it produces apparent multifractality characterised by a piecewise-linear scaling function with two different regimes, which match at the stability index of the considered process. This result is motivated by previous numerical evidence. It is obtained by introducing an appropriate stochastic normalisation which is able to cure empirical moments, without hiding their dependence on time, when moments they aim at estimating do not exist.

Hardware Neural Network for a Visual Inspection System

NASA Astrophysics Data System (ADS)

Chun, Seungwoo; Hayakawa, Yoshihiro; Nakajima, Koji

The visual inspection of defects in products is heavily dependent on human experience and instinct. In this situation, it is difficult to reduce the production costs and to shorten the inspection time and hence the total process time. Consequently people involved in this area desire an automatic inspection system. In this paper, we propose a hardware neural network, which is expected to provide high-speed operation for automatic inspection of products. Since neural networks can learn, this is a suitable method for self-adjustment of criteria for classification. To achieve high-speed operation, we use parallel and pipelining techniques. Furthermore, we use a piecewise linear function instead of a conventional activation function in order to save hardware resources. Consequently, our proposed hardware neural network achieved 6GCPS and 2GCUPS, which in our test sample proved to be sufficiently fast.

Determination of precipitation profiles from airborne passive microwave radiometric measurements

NASA Technical Reports Server (NTRS)

Kummerow, Christian; Hakkarinen, Ida M.; Pierce, Harold F.; Weinman, James A.

1991-01-01

This study presents the first quantitative retrievals of vertical profiles of precipitation derived from multispectral passive microwave radiometry. Measurements of microwave brightness temperature (Tb) obtained by a NASA high-altitude research aircraft are related to profiles of rainfall rate through a multichannel piecewise-linear statistical regression procedure. Statistics for Tb are obtained from a set of cloud radiative models representing a wide variety of convective, stratiform, and anvil structures. The retrieval scheme itself determines which cloud model best fits the observed meteorological conditions. Retrieved rainfall rate profiles are converted to equivalent radar reflectivity for comparison with observed reflectivities from a ground-based research radar. Results for two case studies, a stratiform rain situation and an intense convective thunderstorm, show that the radiometrically derived profiles capture the major features of the observed vertical structure of hydrometer density.

Evaluation of the CEAS model for barley yields in North Dakota and Minnesota

NASA Technical Reports Server (NTRS)

Barnett, T. L. (Principal Investigator)

1981-01-01

The CEAS yield model is based upon multiple regression analysis at the CRD and state levels. For the historical time series, yield is regressed on a set of variables derived from monthly mean temperature and monthly precipitation. Technological trend is represented by piecewise linear and/or quadriatic functions of year. Indicators of yield reliability obtained from a ten-year bootstrap test (1970-79) demonstrated that biases are small and performance as indicated by the root mean square errors are acceptable for intended application, however, model response for individual years particularly unusual years, is not very reliable and shows some large errors. The model is objective, adequate, timely, simple and not costly. It considers scientific knowledge on a broad scale but not in detail, and does not provide a good current measure of modeled yield reliability.

Control of transversal instabilities in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

2018-05-01

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

Estimation of Curve Tracing Time in Supercapacitor based PV Characterization

NASA Astrophysics Data System (ADS)

Basu Pal, Sudipta; Das Bhattacharya, Konika; Mukherjee, Dipankar; Paul, Debkalyan

2017-08-01

Smooth and noise-free characterisation of photovoltaic (PV) generators have been revisited with renewed interest in view of large size PV arrays making inroads into the urban sector of major developing countries. Such practice has recently been observed to be confronted by the use of a suitable data acquisition system and also the lack of a supporting theoretical analysis to justify the accuracy of curve tracing. However, the use of a selected bank of supercapacitors can mitigate the said problems to a large extent. Assuming a piecewise linear analysis of the V-I characteristics of a PV generator, an accurate analysis of curve plotting time has been possible. The analysis has been extended to consider the effect of equivalent series resistance of the supercapacitor leading to increased accuracy (90-95%) of curve plotting times.

An authenticated image encryption scheme based on chaotic maps and memory cellular automata

NASA Astrophysics Data System (ADS)

Bakhshandeh, Atieh; Eslami, Ziba

2013-06-01

This paper introduces a new image encryption scheme based on chaotic maps, cellular automata and permutation-diffusion architecture. In the permutation phase, a piecewise linear chaotic map is utilized to confuse the plain-image and in the diffusion phase, we employ the Logistic map as well as a reversible memory cellular automata to obtain an efficient and secure cryptosystem. The proposed method admits advantages such as highly secure diffusion mechanism, computational efficiency and ease of implementation. A novel property of the proposed scheme is its authentication ability which can detect whether the image is tampered during the transmission or not. This is particularly important in applications where image data or part of it contains highly sensitive information. Results of various analyses manifest high security of this new method and its capability for practical image encryption.

Applications of NASTRAN to nuclear problems

NASA Technical Reports Server (NTRS)

Spreeuw, E.

1972-01-01

The extent to which suitable solutions may be obtained for one physics problem and two engineering type problems is traced. NASTRAN appears to be a practical tool to solve one-group steady-state neutron diffusion equations. Transient diffusion analysis may be performed after new levels that allow time-dependent temperature calculations are developed. NASTRAN piecewise linear anlaysis may be applied to solve those plasticity problems for which a smooth stress-strain curve can be used to describe the nonlinear material behavior. The accuracy decreases when sharp transitions in the stress-strain relations are involved. Improved NASTRAN usefulness will be obtained when nonlinear material capabilities are extended to axisymmetric elements and to include provisions for time-dependent material properties and creep analysis. Rigid formats 3 and 5 proved to be very convenient for the buckling and normal-mode analysis of a nuclear fuel element.

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Experimental feedback linearisation of a vibrating system with a non-smooth nonlinearity

NASA Astrophysics Data System (ADS)

Lisitano, D.; Jiffri, S.; Bonisoli, E.; Mottershead, J. E.

2018-03-01

Input-output partial feedback linearisation is demonstrated experimentally for the first time on a system with non-smooth nonlinearity, a laboratory three degrees of freedom lumped mass system with a piecewise-linear spring. The output degree of freedom is located away from the nonlinearity so that the partial feedback linearisation possesses nonlinear internal dynamics. The dynamic behaviour of the linearised part is specified by eigenvalue assignment and an investigation of the zero dynamics is carried out to confirm stability of the overall system. A tuned numerical model is developed for use in the controller and to produce numerical outputs for comparison with experimental closed-loop results. A new limitation of the feedback linearisation method is discovered in the case of lumped mass systems - that the input and output must share the same degrees of freedom.

Low-frequency wideband vibration energy harvesting by using frequency up-conversion and quin-stable nonlinearity

NASA Astrophysics Data System (ADS)

Wang, Chen; Zhang, Qichang; Wang, Wei

2017-07-01

This work presents models and experiments of an impact-driven and frequency up-converted wideband piezoelectric-based vibration energy harvester with a quintuple-well potential induced by the combination effect of magnetic nonlinearity and mechanical piecewise-linearity. Analysis shows that the interwell motions during coupled vibration period enable to increase electrical power output in comparison to conventional frequency up-conversion technology. Besides, the quintuple-well potential with shallower potential wells could extend the harvester's operating bandwidth to lower frequencies. Experiments demonstrate our proposed approach can dramatically boost the measured power of the energy harvester as much as 35 times while its lower cut-off frequency is two times lower than that of a conventional counterpart. These results reveal our proposed approach shows promise for powering portable wireless smart devices from low-intensity, low-frequency vibration sources.

Impact of Many-Body Effects on Landau Levels in Graphene

NASA Astrophysics Data System (ADS)

Sonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C.

2018-05-01

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity vF. In contrast to the logarithmic divergence of vF at zero magnetic field, we find a piecewise linear scaling of vF as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

Control of mechanical systems by the mixed "time and expenditure" criterion

NASA Astrophysics Data System (ADS)

Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.

2018-05-01

The optimal controlled motion of a mechanical system, that is determined by the linear system ODE with constant coefficients and piecewise constant control components, is considered. The number of control switching points and the heights of control steps are considered as preset. The optimized functional is combination of classical time criteria and "Expenditure criteria", that is equal to the total area of all steps of all control components. In the absence of control, the solution of the system is equal to the sum of components (frequency components) corresponding to different eigenvalues of the matrix of the ODE system. Admissible controls are those that turn to zero (at a non predetermined time moment) the previously chosen frequency components of the solution. An algorithm for the finding of control switching points, based on the necessary minimum conditions for mixed criteria, is proposed.

Evaluation of the Williams-type model for barley yields in North Dakota and Minnesota

NASA Technical Reports Server (NTRS)

Barnett, T. L. (Principal Investigator)

1981-01-01

The Williams-type yield model is based on multiple regression analysis of historial time series data at CRD level pooled to regional level (groups of similar CRDs). Basic variables considered in the analysis include USDA yield, monthly mean temperature, monthly precipitation, soil texture and topographic information, and variables derived from these. Technologic trend is represented by piecewise linear and/or quadratic functions of year. Indicators of yield reliability obtained from a ten-year bootstrap test (1970-1979) demonstrate that biases are small and performance based on root mean square appears to be acceptable for the intended AgRISTARS large area applications. The model is objective, adequate, timely, simple, and not costly. It consideres scientific knowledge on a broad scale but not in detail, and does not provide a good current measure of modeled yield reliability.

Dynamic optimization approach for integrated supplier selection and tracking control of single product inventory system with product discount

NASA Astrophysics Data System (ADS)

Sutrisno; Widowati; Heru Tjahjana, R.

2017-01-01

In this paper, we propose a mathematical model in the form of dynamic/multi-stage optimization to solve an integrated supplier selection problem and tracking control problem of single product inventory system with product discount. The product discount will be stated as a piece-wise linear function. We use dynamic programming to solve this proposed optimization to determine the optimal supplier and the optimal product volume that will be purchased from the optimal supplier for each time period so that the inventory level tracks a reference trajectory given by decision maker with minimal total cost. We give a numerical experiment to evaluate the proposed model. From the result, the optimal supplier was determined for each time period and the inventory level follows the given reference well.

A numerical method for interface problems in elastodynamics

NASA Technical Reports Server (NTRS)

Mcghee, D. S.

1984-01-01

The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.

Trends in utilization of smoking cessation agents before and after the passage of FDA boxed warning in the United States.

PubMed

Shah, Drishti; Shah, Anuj; Tan, Xi; Sambamoorthi, Usha

2017-08-01

In 2009, the FDA required a black box warning (BBW) on bupropion and varenicline, the two commonly prescribed smoking cessation agents due to reports of adverse neuropsychiatric events. We investigated if there was a decline in use of bupropion and varenicline after the BBW by comparing the percent using these medications before and after BBW. We conducted a retrospective observational study using data from the Medical Expenditure Panel Survey from 2007 to 2014. The study sample consisted of adult smokers, who were advised by their physicians to quit smoking. We divided the time period into "pre-warning", "post-warning: immediate", and "post-warning: late." Unadjusted analysis using chi-square tests and adjusted analyses using logistic regressions were conducted to evaluate the change in bupropion and varenicline use before and after the BBW. Secondary analyses using piecewise regression were also conducted. On an average, 49.04% of smokers were advised by their physicians to quit smoking. We observed a statistically significant decline in varenicline use from 22.1% in year 2007 to 9.23% in 2014 (p value<0.001). In the logistic (Adjusted Odds Ratio=0.36, 95% CI=0.22-0.58) and piecewise regressions (Odds Ratio=0.64, 95% CI=0.41-0.99) smokers who were advised to quit smoking by their physicians were less likely to use varenicline in the immediate post-BBW period as compared to pre-BBW period. While the use of varenicline continued to be significantly low in the late post-BBW period (AOR=0.45, 95% CI=0.31-0.64) as compared to the pre-BBW period, the trend in use as seen in piecewise regression remained stable (OR=0.90, 95% CI=0.75-1.06). We did not observe significant differences in bupropion use between the pre- and post-BBW periods. The passage of the FDA boxed warning was associated with a significant decline in the use of varenicline, but not in the use of bupropion. Copyright © 2017 Elsevier B.V. All rights reserved.

Optimal GENCO bidding strategy

NASA Astrophysics Data System (ADS)

Gao, Feng

Electricity industries worldwide are undergoing a period of profound upheaval. The conventional vertically integrated mechanism is being replaced by a competitive market environment. Generation companies have incentives to apply novel technologies to lower production costs, for example: Combined Cycle units. Economic dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary Algorithms share a common mechanism, stochastic searching per generation. The stochastic property makes evolutionary algorithms robust and adaptive enough to solve a non-convex optimization problem. This research implements GA, EP, and PS algorithms for economic dispatch with Combined Cycle units, and makes a comparison with classical Mixed Integer Linear Programming. The electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models. This research identifies a proper SFE model, which can be applied to a multiple period situation. The equilibrium condition using discrete time optimal control is then developed for fuel resource constraints. Finally, the research discusses the issues of multiple equilibria and mixed strategies, which are caused by the transmission network. Additionally, an advantage of the proposed model for merchant transmission planning is discussed. A market simulator is a valuable training and evaluation tool to assist sellers, buyers, and regulators to understand market performance and make better decisions. A traditional optimization model may not be enough to consider the distributed, large-scale, and complex energy market. This research compares the performance and searching paths of different artificial life techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm (PS), and look for a proper method to emulate Generation Companies' (GENCOs) bidding strategies. After deregulation, GENCOs face risk and uncertainty associated with the fast-changing market environment. A profit-based bidding decision support system is critical for GENCOs to keep a competitive position in the new environment. Most past research do not pay special attention to the piecewise staircase characteristic of generator offer curves. This research proposes an optimal bidding strategy based on Parametric Linear Programming. The proposed algorithm is able to handle actual piecewise staircase energy offer curves. The proposed method is then extended to incorporate incomplete information based on Decision Analysis. Finally, the author develops an optimal bidding tool (GenBidding) and applies it to the RTS96 test system.

Exposure-response relationships for select cancer and non-cancer health outcomes in a cohort of U.S. firefighters from San Francisco, Chicago and Philadelphia (1950-2009).

PubMed

Daniels, Robert D; Bertke, Stephen; Dahm, Matthew M; Yiin, James H; Kubale, Travis L; Hales, Thomas R; Baris, Dalsu; Zahm, Shelia H; Beaumont, James J; Waters, Kathleen M; Pinkerton, Lynne E

2015-10-01

To examine exposure-response relationships between surrogates of firefighting exposure and select outcomes among previously studied US career firefighters. Eight cancer and four non-cancer outcomes were examined using conditional logistic regression. Incidence density sampling was used to match each case to 200 controls on attained age. Days accrued in firefighting assignments (exposed-days), run totals (fire-runs) and run times (fire-hours) were used as exposure surrogates. HRs comparing 75th and 25th centiles of lagged cumulative exposures were calculated using loglinear, linear, log-quadratic, power and restricted cubic spline general relative risk models. Piecewise constant models were used to examine risk differences by time since exposure, age at exposure and calendar period. Among 19,309 male firefighters eligible for the study, there were 1333 cancer deaths and 2609 cancer incidence cases. Significant positive associations between fire-hours and lung cancer mortality and incidence were evident. A similar relation between leukaemia mortality and fire-runs was also found. The lung cancer associations were nearly linear in cumulative exposure, while the association with leukaemia mortality was attenuated at higher exposure levels and greater for recent exposures. Significant negative associations were evident for the exposure surrogates and colorectal and prostate cancers, suggesting a healthy worker survivor effect possibly enhanced by medical screening. Lung cancer and leukaemia mortality risks were modestly increasing with firefighter exposures. These findings add to evidence of a causal association between firefighting and cancer. Nevertheless, small effects merit cautious interpretation. We plan to continue to follow the occurrence of disease and injury in this cohort. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Strain rate orientations near the Coso Geothermal Field

NASA Astrophysics Data System (ADS)

Ogasa, N. T.; Kaven, J. O.; Barbour, A. J.; von Huene, R.

2016-12-01

Many geothermal reservoirs derive their sustained capacity for heat exchange in large part due to continuous deformation of preexisting faults and fractures that permit permeability to be maintained. Similarly, enhanced geothermal systems rely on the creation of suitable permeability from fracture and faults networks to be viable. Stress measurements from boreholes or earthquake source mechanisms are commonly used to infer the tectonic conditions that drive deformation, but here we show that geodetic data can also be used. Specifically, we quantify variations in the horizontal strain rate tensor in the area surrounding the Coso Geothermal Field (CGF) by analyzing more than two decades of high accuracy differential GPS data from a network of 14 stations from the University of Nevada Reno Geodetic Laboratory. To handle offsets in the data, from equipment changes and coseismic deformation, we segment the data, perform a piecewise linear fit and take the average of each segment's strain rate to determine secular velocities at each station. With respect to North America, all stations tend to travel northwest at velocities ranging from 1 to 10 mm/yr. The nearest station to CGF shows anomalous motion compared to regional stations, which otherwise show a coherent increase in network velocity from the northeast to the southwest. We determine strain rates via linear approximation using GPS velocities in Cartesian reference frame due to the small area of our network. Principal strain rate components derived from this inversion show maximum extensional strain rates of 30 nanostrain/a occur at N87W with compressional strain rates of 37nanostrain/a at N3E. These results generally align with previous stress measurements from borehole breakouts, which indicate the least compressive horizontal principal stress is east-west oriented, and indicative of the basin and range tectonic setting. Our results suggest that the CGF represents an anomaly in the crustal deformation field, which may be influenced by the hydrothermal anomaly and possibly by the geothermal reservoir operations as well.

Assessing the impact of non-tidal atmospheric loading on a Kalman filter-based terrestrial reference frame

NASA Astrophysics Data System (ADS)

Abbondanza, Claudio; Altamimi, Zuheir; Chin, Toshio; Collilieux, Xavier; Dach, Rolf; Gross, Richard; Heflin, Michael; König, Rolf; Lemoine, Frank; Macmillan, Dan; Parker, Jay; van Dam, Tonie; Wu, Xiaoping

2014-05-01

The International Terrestrial Reference Frame (ITRF) adopts a piece-wise linear model to parameterize regularized station positions and velocities. The space-geodetic (SG) solutions from VLBI, SLR, GPS and DORIS used as input in the ITRF combination process account for tidal loading deformations, but ignore the non-tidal part. As a result, the non-linear signal observed in the time series of SG-derived station positions in part reflects non-tidal loading displacements not introduced in the SG data reduction. In this analysis, we assess the impact of non-tidal atmospheric loading (NTAL) corrections on the TRF computation. Focusing on the a-posteriori approach, (i) the NTAL model derived from the National Centre for Environmental Prediction (NCEP) surface pressure is removed from the SINEX files of the SG solutions used as inputs to the TRF determinations; (ii) adopting a Kalman-filter based approach, two distinct linear TRFs are estimated combining the 4 SG solutions with (corrected TRF solution) and without the NTAL displacements (standard TRF solution). Linear fits (offset and atmospheric velocity) of the NTAL displacements removed during step (i) are estimated accounting for the station position discontinuities introduced in the SG solutions and adopting different weighting strategies. The NTAL-derived (atmospheric) velocity fields are compared to those obtained from the TRF reductions during step (ii). The consistency between the atmospheric and the TRF-derived velocity fields is examined. We show how the presence of station position discontinuities in SG solutions degrades the agreement between the velocity fields and compare the effect of different weighting structure adopted while estimating the linear fits to the NTAL displacements. Finally, we evaluate the effect of restoring the atmospheric velocities determined through the linear fits of the NTAL displacements to the single-technique linear reference frames obtained by stacking the standard SG SINEX files. Differences between the velocity fields obtained restoring the NTAL displacements and the standard stacked linear reference frames are discussed.

Optimal guidance law development for an advanced launch system

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Hodges, Dewey H.; Leung, Martin S.; Bless, Robert R.

1991-01-01

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

Theory of Turing Patterns on Time Varying Networks.

PubMed

Petit, Julien; Lauwens, Ben; Fanelli, Duccio; Carletti, Timoteo

2017-10-06

The process of pattern formation for a multispecies model anchored on a time varying network is studied. A nonhomogeneous perturbation superposed to an homogeneous stable fixed point can be amplified following the Turing mechanism of instability, solely instigated by the network dynamics. By properly tuning the frequency of the imposed network evolution, one can make the examined system behave as its averaged counterpart, over a finite time window. This is the key observation to derive a closed analytical prediction for the onset of the instability in the time dependent framework. Continuously and piecewise constant periodic time varying networks are analyzed, setting the framework for the proposed approach. The extension to nonperiodic settings is also discussed.