On chaos synchronization and secure communication.

PubMed

Kinzel, W; Englert, A; Kanter, I

2010-01-28

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. This journal is © 2010 The Royal Society

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

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

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

Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

NASA Astrophysics Data System (ADS)

Huang, Yuechen; Li, Haiyang

2018-06-01

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

Computing exponentially faster: implementing a non-deterministic universal Turing machine using DNA

PubMed Central

Currin, Andrew; Korovin, Konstantin; Ababi, Maria; Roper, Katherine; Kell, Douglas B.; Day, Philip J.

2017-01-01

The theory of computer science is based around universal Turing machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of classical UTMs. For the most important class of problem in computer science, non-deterministic polynomial complete problems, non-deterministic UTMs (NUTMs) are theoretically exponentially faster than both classical UTMs and quantum mechanical UTMs (QUTMs). However, no attempt has previously been made to build an NUTM, and their construction has been regarded as impossible. Here, we demonstrate the first physical design of an NUTM. This design is based on Thue string rewriting systems, and thereby avoids the limitations of most previous DNA computing schemes: all the computation is local (simple edits to strings) so there is no need for communication, and there is no need to order operations. The design exploits DNA's ability to replicate to execute an exponential number of computational paths in P time. Each Thue rewriting step is embodied in a DNA edit implemented using a novel combination of polymerase chain reactions and site-directed mutagenesis. We demonstrate that the design works using both computational modelling and in vitro molecular biology experimentation: the design is thermodynamically favourable, microprogramming can be used to encode arbitrary Thue rules, all classes of Thue rule can be implemented, and non-deterministic rule implementation. In an NUTM, the resource limitation is space, which contrasts with classical UTMs and QUTMs where it is time. This fundamental difference enables an NUTM to trade space for time, which is significant for both theoretical computer science and physics. It is also of practical importance, for to quote Richard Feynman ‘there's plenty of room at the bottom’. This means that a desktop DNA NUTM could potentially utilize more processors than all the electronic computers in the world combined, and thereby outperform the world's current fastest supercomputer, while consuming a tiny fraction of its energy. PMID:28250099

Multi-scale dynamical behavior of spatially distributed systems: a deterministic point of view

NASA Astrophysics Data System (ADS)

Mangiarotti, S.; Le Jean, F.; Drapeau, L.; Huc, M.

2015-12-01

Physical and biophysical systems are spatially distributed systems. Their behavior can be observed or modelled spatially at various resolutions. In this work, a deterministic point of view is adopted to analyze multi-scale behavior taking a set of ordinary differential equation (ODE) as elementary part of the system.To perform analyses, scenes of study are thus generated based on ensembles of identical elementary ODE systems. Without any loss of generality, their dynamics is chosen chaotic in order to ensure sensitivity to initial conditions, that is, one fundamental property of atmosphere under instable conditions [1]. The Rössler system [2] is used for this purpose for both its topological and algebraic simplicity [3,4].Two cases are thus considered: the chaotic oscillators composing the scene of study are taken either independent, or in phase synchronization. Scale behaviors are analyzed considering the scene of study as aggregations (basically obtained by spatially averaging the signal) or as associations (obtained by concatenating the time series). The global modeling technique is used to perform the numerical analyses [5].One important result of this work is that, under phase synchronization, a scene of aggregated dynamics can be approximated by the elementary system composing the scene, but modifying its parameterization [6]. This is shown based on numerical analyses. It is then demonstrated analytically and generalized to a larger class of ODE systems. Preliminary applications to cereal crops observed from satellite are also presented.[1] Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141 (1963).[2] Rössler, An equation for continuous chaos, Phys. Lett. A, 57, 397-398 (1976).[3] Gouesbet & Letellier, Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets, Phys. Rev. E 49, 4955-4972 (1994).[4] Letellier, Roulin & Rössler, Inequivalent topologies of chaos in simple equations, Chaos, Solitons & Fractals, 28, 337-360 (2006).[5] Mangiarotti, Coudret, Drapeau, & Jarlan, Polynomial search and global modeling, Phys. Rev. E 86(4), 046205 (2012).[6] Mangiarotti, Modélisation globale et Caractérisation Topologique de dynamiques environnementales. Habilitation à Diriger des Recherches, Univ. Toulouse 3 (2014).

Optimal Alignment of Structures for Finite and Periodic Systems.

PubMed

Griffiths, Matthew; Niblett, Samuel P; Wales, David J

2017-10-10

Finding the optimal alignment between two structures is important for identifying the minimum root-mean-square distance (RMSD) between them and as a starting point for calculating pathways. Most current algorithms for aligning structures are stochastic, scale exponentially with the size of structure, and the performance can be unreliable. We present two complementary methods for aligning structures corresponding to isolated clusters of atoms and to condensed matter described by a periodic cubic supercell. The first method (Go-PERMDIST), a branch and bound algorithm, locates the global minimum RMSD deterministically in polynomial time. The run time increases for larger RMSDs. The second method (FASTOVERLAP) is a heuristic algorithm that aligns structures by finding the global maximum kernel correlation between them using fast Fourier transforms (FFTs) and fast SO(3) transforms (SOFTs). For periodic systems, FASTOVERLAP scales with the square of the number of identical atoms in the system, reliably finds the best alignment between structures that are not too distant, and shows significantly better performance than existing algorithms. The expected run time for Go-PERMDIST is longer than FASTOVERLAP for periodic systems. For finite clusters, the FASTOVERLAP algorithm is competitive with existing algorithms. The expected run time for Go-PERMDIST to find the global RMSD between two structures deterministically is generally longer than for existing stochastic algorithms. However, with an earlier exit condition, Go-PERMDIST exhibits similar or better performance.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing.

PubMed

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-10-23

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

NASA Astrophysics Data System (ADS)

Marandi, Alireza; Wang, Zhe; Takata, Kenta; Byer, Robert L.; Yamamoto, Yoshihisa

2014-12-01

Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.

A Parallel Biological Optimization Algorithm to Solve the Unbalanced Assignment Problem Based on DNA Molecular Computing

PubMed Central

Wang, Zhaocai; Pu, Jun; Cao, Liling; Tan, Jian

2015-01-01

The unbalanced assignment problem (UAP) is to optimally resolve the problem of assigning n jobs to m individuals (m < n), such that minimum cost or maximum profit obtained. It is a vitally important Non-deterministic Polynomial (NP) complete problem in operation management and applied mathematics, having numerous real life applications. In this paper, we present a new parallel DNA algorithm for solving the unbalanced assignment problem using DNA molecular operations. We reasonably design flexible-length DNA strands representing different jobs and individuals, take appropriate steps, and get the solutions of the UAP in the proper length range and O(mn) time. We extend the application of DNA molecular operations and simultaneity to simplify the complexity of the computation. PMID:26512650

A soft computing-based approach to optimise queuing-inventory control problem

NASA Astrophysics Data System (ADS)

Alaghebandha, Mohammad; Hajipour, Vahid

2015-04-01

In this paper, a multi-product continuous review inventory control problem within batch arrival queuing approach (MQr/M/1) is developed to find the optimal quantities of maximum inventory. The objective function is to minimise summation of ordering, holding and shortage costs under warehouse space, service level and expected lost-sales shortage cost constraints from retailer and warehouse viewpoints. Since the proposed model is Non-deterministic Polynomial-time hard, an efficient imperialist competitive algorithm (ICA) is proposed to solve the model. To justify proposed ICA, both ganetic algorithm and simulated annealing algorithm are utilised. In order to determine the best value of algorithm parameters that result in a better solution, a fine-tuning procedure is executed. Finally, the performance of the proposed ICA is analysed using some numerical illustrations.

Connectivity Restoration in Wireless Sensor Networks via Space Network Coding.

PubMed

Uwitonze, Alfred; Huang, Jiaqing; Ye, Yuanqing; Cheng, Wenqing

2017-04-20

The problem of finding the number and optimal positions of relay nodes for restoring the network connectivity in partitioned Wireless Sensor Networks (WSNs) is Non-deterministic Polynomial-time hard (NP-hard) and thus heuristic methods are preferred to solve it. This paper proposes a novel polynomial time heuristic algorithm, namely, Relay Placement using Space Network Coding (RPSNC), to solve this problem, where Space Network Coding, also called Space Information Flow (SIF), is a new research paradigm that studies network coding in Euclidean space, in which extra relay nodes can be introduced to reduce the cost of communication. Unlike contemporary schemes that are often based on Minimum Spanning Tree (MST), Euclidean Steiner Minimal Tree (ESMT) or a combination of MST with ESMT, RPSNC is a new min-cost multicast space network coding approach that combines Delaunay triangulation and non-uniform partitioning techniques for generating a number of candidate relay nodes, and then linear programming is applied for choosing the optimal relay nodes and computing their connection links with terminals. Subsequently, an equilibrium method is used to refine the locations of the optimal relay nodes, by moving them to balanced positions. RPSNC can adapt to any density distribution of relay nodes and terminals, as well as any density distribution of terminals. The performance and complexity of RPSNC are analyzed and its performance is validated through simulation experiments.

A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

NASA Astrophysics Data System (ADS)

Mycek, Paul; Contreras, Andres; Le Maître, Olivier; Sargsyan, Khachik; Rizzi, Francesco; Morris, Karla; Safta, Cosmin; Debusschere, Bert; Knio, Omar

2017-07-01

A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.

1998-01-01

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro; Abgrall, Remi

2014-11-01

Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients.

A robust and efficient stepwise regression method for building sparse polynomial chaos expansions

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

Abraham, Simon, E-mail: Simon.Abraham@ulb.ac.be; Raisee, Mehrdad; Ghorbaniasl, Ghader

2017-03-01

Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selectionmore » criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.« less

Does preprocessing change nonlinear measures of heart rate variability?

PubMed

Gomes, Murilo E D; Guimarães, Homero N; Ribeiro, Antônio L P; Aguirre, Luis A

2002-11-01

This work investigated if methods used to produce a uniformly sampled heart rate variability (HRV) time series significantly change the deterministic signature underlying the dynamics of such signals and some nonlinear measures of HRV. Two methods of preprocessing were used: the convolution of inverse interval function values with a rectangular window and the cubic polynomial interpolation. The HRV time series were obtained from 33 Wistar rats submitted to autonomic blockade protocols and from 17 healthy adults. The analysis of determinism was carried out by the method of surrogate data sets and nonlinear autoregressive moving average modelling and prediction. The scaling exponents alpha, alpha(1) and alpha(2) derived from the detrended fluctuation analysis were calculated from raw HRV time series and respective preprocessed signals. It was shown that the technique of cubic interpolation of HRV time series did not significantly change any nonlinear characteristic studied in this work, while the method of convolution only affected the alpha(1) index. The results suggested that preprocessed time series may be used to study HRV in the field of nonlinear dynamics.

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

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

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

2014-12-10

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

An improved spanning tree approach for the reliability analysis of supply chain collaborative network

NASA Astrophysics Data System (ADS)

Lam, C. Y.; Ip, W. H.

2012-11-01

A higher degree of reliability in the collaborative network can increase the competitiveness and performance of an entire supply chain. As supply chain networks grow more complex, the consequences of unreliable behaviour become increasingly severe in terms of cost, effort and time. Moreover, it is computationally difficult to calculate the network reliability of a Non-deterministic Polynomial-time hard (NP-hard) all-terminal network using state enumeration, as this may require a huge number of iterations for topology optimisation. Therefore, this paper proposes an alternative approach of an improved spanning tree for reliability analysis to help effectively evaluate and analyse the reliability of collaborative networks in supply chains and reduce the comparative computational complexity of algorithms. Set theory is employed to evaluate and model the all-terminal reliability of the improved spanning tree algorithm and present a case study of a supply chain used in lamp production to illustrate the application of the proposed approach.

Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

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

Murcia, Juan Pablo; Réthoré, Pierre-Elouan; Dimitrov, Nikolay

Polynomial surrogates are used to characterize the energy production and lifetime equivalent fatigue loads for different components of the DTU 10 MW reference wind turbine under realistic atmospheric conditions. The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations. A global sensitivity analysis shows that the turbulent inflow realization has a bigger impact on the total distribution of equivalent fatigue loads than the shear coefficient or yaw miss-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertaintymore » models and adds new variables like damage equivalent fatigue loads in different components of the turbine. These surrogate models can then be implemented inside other work-flows such as: estimation of the uncertainty in annual energy production due to wind resource variability and/or robust wind power plant layout optimization. It can be concluded that it is possible to capture the global behavior of a modern wind turbine and its uncertainty under realistic inflow conditions using polynomial response surfaces. In conclusion, the surrogates are a way to obtain power and load estimation under site specific characteristics without sharing the proprietary aeroelastic design.« less

Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

DOE PAGES

Murcia, Juan Pablo; Réthoré, Pierre-Elouan; Dimitrov, Nikolay; ...

2017-07-17

Polynomial surrogates are used to characterize the energy production and lifetime equivalent fatigue loads for different components of the DTU 10 MW reference wind turbine under realistic atmospheric conditions. The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations. A global sensitivity analysis shows that the turbulent inflow realization has a bigger impact on the total distribution of equivalent fatigue loads than the shear coefficient or yaw miss-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertaintymore » models and adds new variables like damage equivalent fatigue loads in different components of the turbine. These surrogate models can then be implemented inside other work-flows such as: estimation of the uncertainty in annual energy production due to wind resource variability and/or robust wind power plant layout optimization. It can be concluded that it is possible to capture the global behavior of a modern wind turbine and its uncertainty under realistic inflow conditions using polynomial response surfaces. In conclusion, the surrogates are a way to obtain power and load estimation under site specific characteristics without sharing the proprietary aeroelastic design.« less

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Study of the Influence of the Orientation of a 50-Hz Magnetic Field on Fetal Exposure Using Polynomial Chaos Decomposition

PubMed Central

Liorni, Ilaria; Parazzini, Marta; Fiocchi, Serena; Ravazzani, Paolo

2015-01-01

Human exposure modelling is a complex topic, because in a realistic exposure scenario, several parameters (e.g., the source, the orientation of incident fields, the morphology of subjects) vary and influence the dose. Deterministic dosimetry, so far used to analyze human exposure to electromagnetic fields (EMF), is highly time consuming if the previously-mentioned variations are considered. Stochastic dosimetry is an alternative method to build analytical approximations of exposure at a lower computational cost. In this study, it was used to assess the influence of magnetic flux density (B) orientation on fetal exposure at 50 Hz by polynomial chaos (PC). A PC expansion of induced electric field (E) in each fetal tissue at different gestational ages (GA) was built as a function of B orientation. Maximum E in each fetal tissue and at each GA was estimated for different exposure configurations and compared with the limits of the International Commission of Non-Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient tool to build accurate approximations of E in each fetal tissue. B orientation strongly influenced E, with a variability across tissues from 10% to 43% with respect to the mean value. However, varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010 at all GAs. PMID:26024363

Study of the influence of the orientation of a 50-Hz magnetic field on fetal exposure using polynomial chaos decomposition.

PubMed

Liorni, Ilaria; Parazzini, Marta; Fiocchi, Serena; Ravazzani, Paolo

2015-05-27

Human exposure modelling is a complex topic, because in a realistic exposure scenario, several parameters (e.g., the source, the orientation of incident fields, the morphology of subjects) vary and influence the dose. Deterministic dosimetry, so far used to analyze human exposure to electromagnetic fields (EMF), is highly time consuming if the previously-mentioned variations are considered. Stochastic dosimetry is an alternative method to build analytical approximations of exposure at a lower computational cost. In this study, it was used to assess the influence of magnetic flux density (B) orientation on fetal exposure at 50 Hz by polynomial chaos (PC). A PC expansion of induced electric field (E) in each fetal tissue at different gestational ages (GA) was built as a function of B orientation. Maximum E in each fetal tissue and at each GA was estimated for different exposure configurations and compared with the limits of the International Commission of Non-Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient tool to build accurate approximations of E in each fetal tissue. B orientation strongly influenced E, with a variability across tissues from 10% to 43% with respect to the mean value. However, varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010 at all GAs.

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing; Walker, Paul D.

2017-02-01

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

A hybrid algorithm optimization approach for machine loading problem in flexible manufacturing system

NASA Astrophysics Data System (ADS)

Kumar, Vijay M.; Murthy, ANN; Chandrashekara, K.

2012-05-01

The production planning problem of flexible manufacturing system (FMS) concerns with decisions that have to be made before an FMS begins to produce parts according to a given production plan during an upcoming planning horizon. The main aspect of production planning deals with machine loading problem in which selection of a subset of jobs to be manufactured and assignment of their operations to the relevant machines are made. Such problems are not only combinatorial optimization problems, but also happen to be non-deterministic polynomial-time-hard, making it difficult to obtain satisfactory solutions using traditional optimization techniques. In this paper, an attempt has been made to address the machine loading problem with objectives of minimization of system unbalance and maximization of throughput simultaneously while satisfying the system constraints related to available machining time and tool slot designing and using a meta-hybrid heuristic technique based on genetic algorithm and particle swarm optimization. The results reported in this paper demonstrate the model efficiency and examine the performance of the system with respect to measures such as throughput and system utilization.

Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro M.; Abgrall, Rémi

2016-06-01

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.

Design and development of thin quartz glass WFXT polynomial mirror shells by direct polishing

NASA Astrophysics Data System (ADS)

Proserpio, L.; Campana, S.; Citterio, O.; Civitani, M.; Combrinck, H.; Conconi, P.; Cotroneo, V.; Freeman, R.; Langstrof, P.; Mattaini, E.; Morton, R.; Oberle, B.; Pareschi, G.; Parodi, G.; Pels, C.; Schenk, C.; Stock, R.; Tagliaferri, G.

2010-07-01

The Wide Field X-ray Telescope (WFXT) is a medium class mission for X-ray surveys of the sky with an unprecedented area and sensitivity. In order to meet the effective area requirement, the design of the optical system is based on very thin mirror shells, with thicknesses in the 1-2 mm range. In order to get the desired angular resolution (10 arcsec requirement, 5 arcsec goal) across the entire 1x1 degree FOV (Field Of View), the design of the optical system is based on nested modified grazing incidence Wolter-I mirrors realized with polynomial profiles, focal plane curvature and plate scale corrections. This design guarantees an increased angular resolution at large off-axis angle with respect to the normally used Wolter I configuration, making WFXT ideal for survey purposes. The WFXT X-ray Telescope Assembly is composed by three identical mirror modules of 78 nested shells each, with diameter up to 1.1 m. The epoxy replication process with SiC shells has already been proved to be a valuable technology to meet the angular resolution requirement of 10 arcsec. To further mature the telescope manufacturing technology and to achieve the goal of 5 arcsec, a deterministic direct polishing method is under investigation. The direct polishing method has already been used for past missions (as Einstein, Rosat, Chandra): the technological challenge now is to apply it for almost ten times thinner shells. Under investigation is quartz glass (fused silica), a well-known material with good thermo-mechanical and polishability characteristics that could meet our goal in terms of mass and stiffness, with significant cost and time saving with respect to SiC. Our approach is based on two main steps: first quartz glass tubes available on the market are grinded to conical profiles, and second the obtained shells are polished to the required polynomial profiles by CNC (Computer Numerical Control) polishing machine. In this paper, the first results of the direct grinding and polishing of prototypes shells made by quartz glass with low thickness, representative of the WFXT optical design, are presented.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

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

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

Classification of Normal and Apoptotic Cells from Fluorescence Microscopy Images Using Generalized Polynomial Chaos and Level Set Function.

PubMed

Du, Yuncheng; Budman, Hector M; Duever, Thomas A

2016-06-01

Accurate automated quantitative analysis of living cells based on fluorescence microscopy images can be very useful for fast evaluation of experimental outcomes and cell culture protocols. In this work, an algorithm is developed for fast differentiation of normal and apoptotic viable Chinese hamster ovary (CHO) cells. For effective segmentation of cell images, a stochastic segmentation algorithm is developed by combining a generalized polynomial chaos expansion with a level set function-based segmentation algorithm. This approach provides a probabilistic description of the segmented cellular regions along the boundary, from which it is possible to calculate morphological changes related to apoptosis, i.e., the curvature and length of a cell's boundary. These features are then used as inputs to a support vector machine (SVM) classifier that is trained to distinguish between normal and apoptotic viable states of CHO cell images. The use of morphological features obtained from the stochastic level set segmentation of cell images in combination with the trained SVM classifier is more efficient in terms of differentiation accuracy as compared with the original deterministic level set method.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

Design and development by direct polishing of the WFXT thin polynomial mirror shells

NASA Astrophysics Data System (ADS)

Proserpio, L.; Campana, S.; Citterio, O.; Civitani, M.; Combrinck, H.; Conconi, P.; Cotroneo, V.; Freeman, R.; Mattini, E.; Langstrof, P.; Morton, R.; Motta, G.; Oberle, O.; Pareschi, G.; Parodi, G.; Pels, C.; Schenk, C.; Stock, R.; Tagliaferri, G.

2017-11-01

The Wide Field X-ray Telescope (WFXT) is a medium class mission proposed to address key questions about cosmic origins and physics of the cosmos through an unprecedented survey of the sky in the soft X-ray band (0.2-6 keV) [1], [2]. In order to get the desired angular resolution of 10 arcsec (5 arcsec goal) on the entire 1 degrees Field Of View (FOV), the design of the optical system is based on nested grazing-incidence polynomial profiles mirrors, and assumes a focal plane curvature and plate scale corrections among the shells. This design guarantees an increased angular resolution also at large off-axis positions with respect to the usually adopted Wolter I configuration. In order to meet the requirements in terms of mass and effective area (less than 1200 kg, 6000 cm2 @ 1 keV), the nested shells are thin and made of quartz glass. The telescope assembly is composed by three identical modules of 78 nested shells each, with diameter up to 1.1 m, length in the range of 200-440 mm and thickness of less than 2.2 mm. At this regard, a deterministic direct polishing method is under investigation to manufacture the WFXT thin grazing-incidence mirrors made of quartz. The direct polishing method has already been used for past missions (as Einstein, Rosat, Chandra) but based on much thicker shells (10 mm ore more). The technological challenge for WFXT is to apply the same approach but for 510 times thinner shells. The proposed approach is based on two main steps: first, quartz glass tubes available on the market are ground to conical profiles; second the pre-shaped shells are polished to the required polynomial profiles using a CNC polishing machine. In this paper, preliminary results on the direct grinding and polishing of prototypes shells made by quartz glass with low thickness, representative of the WFXT optical design, are presented.

Sythesis of MCMC and Belief Propagation

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

Ahn, Sungsoo; Chertkov, Michael; Shin, Jinwoo

Markov Chain Monte Carlo (MCMC) and Belief Propagation (BP) are the most popular algorithms for computational inference in Graphical Models (GM). In principle, MCMC is an exact probabilistic method which, however, often suffers from exponentially slow mixing. In contrast, BP is a deterministic method, which is typically fast, empirically very successful, however in general lacking control of accuracy over loopy graphs. In this paper, we introduce MCMC algorithms correcting the approximation error of BP, i.e., we provide a way to compensate for BP errors via a consecutive BP-aware MCMC. Our framework is based on the Loop Calculus (LC) approach whichmore » allows to express the BP error as a sum of weighted generalized loops. Although the full series is computationally intractable, it is known that a truncated series, summing up all 2-regular loops, is computable in polynomial-time for planar pair-wise binary GMs and it also provides a highly accurate approximation empirically. Motivated by this, we first propose a polynomial-time approximation MCMC scheme for the truncated series of general (non-planar) pair-wise binary models. Our main idea here is to use the Worm algorithm, known to provide fast mixing in other (related) problems, and then design an appropriate rejection scheme to sample 2-regular loops. Furthermore, we also design an efficient rejection-free MCMC scheme for approximating the full series. The main novelty underlying our design is in utilizing the concept of cycle basis, which provides an efficient decomposition of the generalized loops. In essence, the proposed MCMC schemes run on transformed GM built upon the non-trivial BP solution, and our experiments show that this synthesis of BP and MCMC outperforms both direct MCMC and bare BP schemes.« less

Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model.

PubMed

Smirnova, Alexandra; deCamp, Linda; Chowell, Gerardo

2017-05-02

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov's) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014-2015 Ebola epidemic in West Africa.

Aeroelastic Uncertainty Quantification Studies Using the S4T Wind Tunnel Model

NASA Technical Reports Server (NTRS)

Nikbay, Melike; Heeg, Jennifer

2017-01-01

This paper originates from the joint efforts of an aeroelastic study team in the Applied Vehicle Technology Panel from NATO Science and Technology Organization, with the Task Group number AVT-191, titled "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." We present aeroelastic uncertainty quantification studies using the SemiSpan Supersonic Transport wind tunnel model at the NASA Langley Research Center. The aeroelastic study team decided treat both structural and aerodynamic input parameters as uncertain and represent them as samples drawn from statistical distributions, propagating them through aeroelastic analysis frameworks. Uncertainty quantification processes require many function evaluations to asses the impact of variations in numerous parameters on the vehicle characteristics, rapidly increasing the computational time requirement relative to that required to assess a system deterministically. The increased computational time is particularly prohibitive if high-fidelity analyses are employed. As a remedy, the Istanbul Technical University team employed an Euler solver in an aeroelastic analysis framework, and implemented reduced order modeling with Polynomial Chaos Expansion and Proper Orthogonal Decomposition to perform the uncertainty propagation. The NASA team chose to reduce the prohibitive computational time by employing linear solution processes. The NASA team also focused on determining input sample distributions.

Characterizing the topology of probabilistic biological networks.

PubMed

Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2013-01-01

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

Computation of probabilistic hazard maps and source parameter estimation for volcanic ash transport and dispersion

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

Madankan, R.; Pouget, S.; Singla, P., E-mail: psingla@buffalo.edu

Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This papermore » presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.« less

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

Time-Varying Delay Estimation Applied to the Surface Electromyography Signals Using the Parametric Approach

NASA Astrophysics Data System (ADS)

Luu, Gia Thien; Boualem, Abdelbassit; Duy, Tran Trung; Ravier, Philippe; Butteli, Olivier

Muscle Fiber Conduction Velocity (MFCV) can be calculated from the time delay between the surface electromyographic (sEMG) signals recorded by electrodes aligned with the fiber direction. In order to take into account the non-stationarity during the dynamic contraction (the most daily life situation) of the data, the developed methods have to consider that the MFCV changes over time, which induces time-varying delays and the data is non-stationary (change of Power Spectral Density (PSD)). In this paper, the problem of TVD estimation is considered using a parametric method. First, the polynomial model of TVD has been proposed. Then, the TVD model parameters are estimated by using a maximum likelihood estimation (MLE) strategy solved by a deterministic optimization technique (Newton) and stochastic optimization technique, called simulated annealing (SA). The performance of the two techniques is also compared. We also derive two appropriate Cramer-Rao Lower Bounds (CRLB) for the estimated TVD model parameters and for the TVD waveforms. Monte-Carlo simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the variance obtained is close to the derived CRBs. A comparison with non-parametric approaches of the TVD estimation is also presented and shows the superiority of the method proposed.

Efficient sampling of parsimonious inversion histories with application to genome rearrangement in Yersinia.

PubMed

Miklós, István; Darling, Aaron E

2009-06-22

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called "MC4Inversion." We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique.

Nested polynomial trends for the improvement of Gaussian process-based predictors

NASA Astrophysics Data System (ADS)

Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.

2017-10-01

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Time-series modeling and prediction of global monthly absolute temperature for environmental decision making

NASA Astrophysics Data System (ADS)

Ye, Liming; Yang, Guixia; Van Ranst, Eric; Tang, Huajun

2013-03-01

A generalized, structural, time series modeling framework was developed to analyze the monthly records of absolute surface temperature, one of the most important environmental parameters, using a deterministicstochastic combined (DSC) approach. Although the development of the framework was based on the characterization of the variation patterns of a global dataset, the methodology could be applied to any monthly absolute temperature record. Deterministic processes were used to characterize the variation patterns of the global trend and the cyclic oscillations of the temperature signal, involving polynomial functions and the Fourier method, respectively, while stochastic processes were employed to account for any remaining patterns in the temperature signal, involving seasonal autoregressive integrated moving average (SARIMA) models. A prediction of the monthly global surface temperature during the second decade of the 21st century using the DSC model shows that the global temperature will likely continue to rise at twice the average rate of the past 150 years. The evaluation of prediction accuracy shows that DSC models perform systematically well against selected models of other authors, suggesting that DSC models, when coupled with other ecoenvironmental models, can be used as a supplemental tool for short-term (˜10-year) environmental planning and decision making.

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

NASA Astrophysics Data System (ADS)

Chen, Zhixiang; Fu, Bin

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.

PubMed

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-08-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks

PubMed Central

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-01-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is “non-intrusive” and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design. PMID:26317784

Uncertainty Quantification of Non-linear Oscillation Triggering in a Multi-injector Liquid-propellant Rocket Combustion Chamber

NASA Astrophysics Data System (ADS)

Popov, Pavel; Sideris, Athanasios; Sirignano, William

2014-11-01

We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.

Topology optimization under stochastic stiffness

NASA Astrophysics Data System (ADS)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations for the response quantities allow for efficient and accurate calculation of sensitivities of response statistics with respect to the design variables. The proposed methods are shown to be successful at generating robust optimal topologies. Examples from topology optimization in continuum and discrete domains (truss structures) under uncertainty are presented. It is also shown that proposed methods lead to significant computational savings when compared to Monte Carlo-based optimization which involve multiple formations and inversions of the global stiffness matrix and that results obtained from the proposed method are in excellent agreement with those obtained from a Monte Carlo-based optimization algorithm.

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

Tang, Kunkun, E-mail: ktg@illinois.edu; Inria Bordeaux – Sud-Ouest, Team Cardamom, 200 avenue de la Vieille Tour, 33405 Talence; Congedo, Pietro M.

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable formore » real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.« less

Superconducting Qubit (transmon) coupled to Surface Acoustic Waves (SAWs)

NASA Astrophysics Data System (ADS)

Guo, Lingzhen; Johansson, Göran

We work on a hybrid system, which couples the transmon in circuit QED to the propagating mechanical modes of Surface Acoustic Waves (SAWs). This is an analogue of circuit QED system but replacing the microwave photons by SAW phonons. We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders of magnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially follows a polynomial decay law instead of an exponential one, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. The time delay gives rise to novel features in the reflection, transmission, power spectra, and second-order correlation functions of the system. We show that the giant atom can generate entangled phonon pairs, which may have applications in quantum communication. L.G. acknowledges financial support from Carl-Zeiss Stiftung (0563-2.8/508/2).

The Fixed-Links Model in Combination with the Polynomial Function as a Tool for Investigating Choice Reaction Time Data

ERIC Educational Resources Information Center

Schweizer, Karl

2006-01-01

A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

Robust Structural Analysis and Design of Distributed Control Systems to Prevent Zero Dynamics Attacks

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

Weerakkody, Sean; Liu, Xiaofei; Sinopoli, Bruno

We consider the design and analysis of robust distributed control systems (DCSs) to ensure the detection of integrity attacks. DCSs are often managed by independent agents and are implemented using a diverse set of sensors and controllers. However, the heterogeneous nature of DCSs along with their scale leave such systems vulnerable to adversarial behavior. To mitigate this reality, we provide tools that allow operators to prevent zero dynamics attacks when as many as p agents and sensors are corrupted. Such a design ensures attack detectability in deterministic systems while removing the threat of a class of stealthy attacks in stochasticmore » systems. To achieve this goal, we use graph theory to obtain necessary and sufficient conditions for the presence of zero dynamics attacks in terms of the structural interactions between agents and sensors. We then formulate and solve optimization problems which minimize communication networks while also ensuring a resource limited adversary cannot perform a zero dynamics attacks. Polynomial time algorithms for design and analysis are provided.« less

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

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

NASA Astrophysics Data System (ADS)

Doha, E. H.

2002-02-01

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

Probabilistic risk assessment for CO2 storage in geological formations: robust design and support for decision making under uncertainty

NASA Astrophysics Data System (ADS)

Oladyshkin, Sergey; Class, Holger; Helmig, Rainer; Nowak, Wolfgang

2010-05-01

CO2 storage in geological formations is currently being discussed intensively as a technology for mitigating CO2 emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis and for stochastic approaches based on brute-force repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a orthogonal basis of higher-order polynomials to approximate dependence on uncertain parameters (porosity, permeability etc.) and design parameters (injection rate, depth etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs of the non-linear system that minimize failure probability and provide valuable support for risk-informed management decisions. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al. Computational Geosciences 13, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speedup by a factor of 100 compared to Monte Carlo simulation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO2 injection, including uncertainty in the analysis leads to a systematic and significant shift of predicted leakage rates towards higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios. This implies that, neglecting uncertainty can be a strong simplification for modeling CO2 injection, and the consequences can be stronger than when neglecting several physical phenomena (e.g. phase transition, convective mixing, capillary forces etc.). The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. Keywords: polynomial chaos; CO2 storage; multiphase flow; porous media; risk assessment; uncertainty; integrative response surfaces

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia

PubMed Central

Darling, Aaron E.

2009-01-01

Inversions are among the most common mutations acting on the order and orientation of genes in a genome, and polynomial-time algorithms exist to obtain a minimal length series of inversions that transform one genome arrangement to another. However, the minimum length series of inversions (the optimal sorting path) is often not unique as many such optimal sorting paths exist. If we assume that all optimal sorting paths are equally likely, then statistical inference on genome arrangement history must account for all such sorting paths and not just a single estimate. No deterministic polynomial algorithm is known to count the number of optimal sorting paths nor sample from the uniform distribution of optimal sorting paths. Here, we propose a stochastic method that uniformly samples the set of all optimal sorting paths. Our method uses a novel formulation of parallel Markov chain Monte Carlo. In practice, our method can quickly estimate the total number of optimal sorting paths. We introduce a variant of our approach in which short inversions are modeled to be more likely, and we show how the method can be used to estimate the distribution of inversion lengths and breakpoint usage in pathogenic Yersinia pestis. The proposed method has been implemented in a program called “MC4Inversion.” We draw comparison of MC4Inversion to the sampler implemented in BADGER and a previously described importance sampling (IS) technique. We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER and the IS technique and simultaneously avoids bias inherent in the IS technique. PMID:20333186

WFXT Technology Overview

NASA Astrophysics Data System (ADS)

Pareschi, G.; Campana, S.

The Wide Field X-ray Telescope (WFXT) is a medium class mission for X-ray surveys of the sky with an unprecedented area and sensitivity. In order to meet the effective area requirement, the design of the optical system is based on very thin mirror shells, with thicknesses in the 1-2 mm range. In order to get the desired angular resolution (10 arcsec requirement, 5 arcsec goal) across the entire 1× 1 degree FOV (Field Of View), the design of the optical system is based on nested modified grazing incidence Wolter-I mirrors realized with polynomial profiles, focal plane curvature and plate scale corrections. This design guarantees an increased angular resolution at large off-axis angle with respect to the normally used Wolter I configuration, making WFXT ideal for survey purposes. The WFXT X-ray Telescope Assembly is composed by three identical mirror modules of 78 nested shells each, with diameter up to 1.1 m. The epoxy replication process with SiC shells has already been proved to be a valuable technology to meet the angular resolution requirement of 10 arcsec. To further mature the telescope manufacturing technology and to achieve the goal of 5 arcsec, we are considering different materials for the mirror shells with particular care to quartz glass (fused silica), a well-known material with good thermo-mechanical and polishability characteristics that could meet our goal in terms of mass and stiffness, with significant cost and time saving with respect to SiC. To bring the mirror shells to the needed accuracy a deterministic direct polishing method for the mirror shells is under investigation. A direct polishing method has already been used for past missions (as Einstein, Rosat, Chandra): the technological challenge now is to apply it for almost ten times thinner shells. Our approach is based on two main steps: first quartz glass tubes available on the market are grinded to conical profiles, and second the obtained shells are polished to the required polynomial profiles by Computer Numerical Control (CNC) polishing machine.

On the coefficients of differentiated expansions of ultraspherical polynomials

NASA Technical Reports Server (NTRS)

Karageorghis, Andreas; Phillips, Timothy N.

1989-01-01

A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

Human brain detects short-time nonlinear predictability in the temporal fine structure of deterministic chaotic sounds

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakada, Tsutomu

2013-04-01

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

On the optimal selection of interpolation methods for groundwater contouring: An example of propagation of uncertainty regarding inter-aquifer exchange

NASA Astrophysics Data System (ADS)

Ohmer, Marc; Liesch, Tanja; Goeppert, Nadine; Goldscheider, Nico

2017-11-01

The selection of the best possible method to interpolate a continuous groundwater surface from point data of groundwater levels is a controversial issue. In the present study four deterministic and five geostatistical interpolation methods (global polynomial interpolation, local polynomial interpolation, inverse distance weighting, radial basis function, simple-, ordinary-, universal-, empirical Bayesian and co-Kriging) and six error statistics (ME, MAE, MAPE, RMSE, RMSSE, Pearson R) were examined for a Jurassic karst aquifer and a Quaternary alluvial aquifer. We investigated the possible propagation of uncertainty of the chosen interpolation method on the calculation of the estimated vertical groundwater exchange between the aquifers. Furthermore, we validated the results with eco-hydrogeological data including the comparison between calculated groundwater depths and geographic locations of karst springs, wetlands and surface waters. These results show, that calculated inter-aquifer exchange rates based on different interpolations of groundwater potentials may vary greatly depending on the chosen interpolation method (by factor >10). Therefore, the choice of an interpolation method should be made with care, taking different error measures as well as additional data for plausibility control into account. The most accurate results have been obtained with co-Kriging incorporating secondary data (e.g. topography, river levels).

Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs

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

Karagiannis, Georgios; Lin, Guang

2014-02-15

Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesianmore » model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.« less

Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2016-11-01

This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.

Effect of sample volume on metastable zone width and induction time

NASA Astrophysics Data System (ADS)

Kubota, Noriaki

2012-04-01

The metastable zone width (MSZW) and the induction time, measured for a large sample (say>0.1 L) are reproducible and deterministic, while, for a small sample (say<1 mL), these values are irreproducible and stochastic. Such behaviors of MSZW and induction time were theoretically discussed both with stochastic and deterministic models. Equations for the distribution of stochastic MSZW and induction time were derived. The average values of stochastic MSZW and induction time both decreased with an increase in sample volume, while, the deterministic MSZW and induction time remained unchanged. Such different behaviors with variation in sample volume were explained in terms of detection sensitivity of crystallization events. The average values of MSZW and induction time in the stochastic model were compared with the deterministic MSZW and induction time, respectively. Literature data reported for paracetamol aqueous solution were explained theoretically with the presented models.

A comparison of VLSI architectures for time and transform domain decoding of Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Deutsch, L. J.; Satorius, E. H.; Reed, I. S.

1988-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial needed to decode a Reed-Solomon (RS) code. It is shown that this algorithm can be used for both time and transform domain decoding by replacing its initial conditions with the Forney syndromes and the erasure locator polynomial. By this means both the errata locator polynomial and the errate evaluator polynomial can be obtained with the Euclidean algorithm. With these ideas, both time and transform domain Reed-Solomon decoders for correcting errors and erasures are simplified and compared. As a consequence, the architectures of Reed-Solomon decoders for correcting both errors and erasures can be made more modular, regular, simple, and naturally suitable for VLSI implementation.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Development a heuristic method to locate and allocate the medical centers to minimize the earthquake relief operation time.

PubMed

Aghamohammadi, Hossein; Saadi Mesgari, Mohammad; Molaei, Damoon; Aghamohammadi, Hasan

2013-01-01

Location-allocation is a combinatorial optimization problem, and is defined as Non deterministic Polynomial Hard (NP) hard optimization. Therefore, solution of such a problem should be shifted from exact to heuristic or Meta heuristic due to the complexity of the problem. Locating medical centers and allocating injuries of an earthquake to them has high importance in earthquake disaster management so that developing a proper method will reduce the time of relief operation and will consequently decrease the number of fatalities. This paper presents the development of a heuristic method based on two nested genetic algorithms to optimize this location allocation problem by using the abilities of Geographic Information System (GIS). In the proposed method, outer genetic algorithm is applied to the location part of the problem and inner genetic algorithm is used to optimize the resource allocation. The final outcome of implemented method includes the spatial location of new required medical centers. The method also calculates that how many of the injuries at each demanding point should be taken to any of the existing and new medical centers as well. The results of proposed method showed high performance of designed structure to solve a capacitated location-allocation problem that may arise in a disaster situation when injured people has to be taken to medical centers in a reasonable time.

Inverse kinematic problem for a random gradient medium in geometric optics approximation

NASA Astrophysics Data System (ADS)

Petersen, N. V.

1990-03-01

Scattering at random inhomogeneities in a gradient medium results in systematic deviations of the rays and travel times of refracted body waves from those corresponding to the deterministic velocity component. The character of the difference depends on the parameters of the deterministic and random velocity component. However, at great distances to the source, independently of the velocity parameters (weakly or strongly inhomogeneous medium), the most probable depth of the ray turning point is smaller than that corresponding to the deterministic velocity component, the most probable travel times also being lower. The relative uncertainty in the deterministic velocity component, derived from the mean travel times using methods developed for laterally homogeneous media (for instance, the Herglotz-Wiechert method), is systematic in character, but does not exceed the contrast of velocity inhomogeneities by magnitude. The gradient of the deterministic velocity component has a significant effect on the travel-time fluctuations. The variance at great distances to the source is mainly controlled by shallow inhomogeneities. The travel-time flucutations are studied only for weakly inhomogeneous media.

Constant-Round Concurrent Zero Knowledge From Falsifiable Assumptions

DTIC Science & Technology

2013-01-01

assumptions (e.g., [DS98, Dam00, CGGM00, Gol02, PTV12, GJO+12]), or in alternative models (e.g., super -polynomial-time simulation [Pas03b, PV10]). In the...T (·)-time computations, where T (·) is some “nice” (slightly) super -polynomial function (e.g., T (n) = nlog log logn). We refer to such proof...put a cap on both using a (slightly) super -polynomial function, and thus to guarantee soundness of the concurrent zero-knowledge protocol, we need

Multiple zeros of polynomials

NASA Technical Reports Server (NTRS)

Wood, C. A.

1974-01-01

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Learning polynomial feedforward neural networks by genetic programming and backpropagation.

PubMed

Nikolaev, N Y; Iba, H

2003-01-01

This paper presents an approach to learning polynomial feedforward neural networks (PFNNs). The approach suggests, first, finding the polynomial network structure by means of a population-based search technique relying on the genetic programming paradigm, and second, further adjustment of the best discovered network weights by an especially derived backpropagation algorithm for higher order networks with polynomial activation functions. These two stages of the PFNN learning process enable us to identify networks with good training as well as generalization performance. Empirical results show that this approach finds PFNN which outperform considerably some previous constructive polynomial network algorithms on processing benchmark time series.

Reachability Analysis in Probabilistic Biological Networks.

PubMed

Gabr, Haitham; Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2015-01-01

Extra-cellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources), which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extra-cellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bi-variate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real data sets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods. Availability: All the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/PReach/.

Learning oncogenetic networks by reducing to mixed integer linear programming.

PubMed

Shahrabi Farahani, Hossein; Lagergren, Jens

2013-01-01

Cancer can be a result of accumulation of different types of genetic mutations such as copy number aberrations. The data from tumors are cross-sectional and do not contain the temporal order of the genetic events. Finding the order in which the genetic events have occurred and progression pathways are of vital importance in understanding the disease. In order to model cancer progression, we propose Progression Networks, a special case of Bayesian networks, that are tailored to model disease progression. Progression networks have similarities with Conjunctive Bayesian Networks (CBNs) [1],a variation of Bayesian networks also proposed for modeling disease progression. We also describe a learning algorithm for learning Bayesian networks in general and progression networks in particular. We reduce the hard problem of learning the Bayesian and progression networks to Mixed Integer Linear Programming (MILP). MILP is a Non-deterministic Polynomial-time complete (NP-complete) problem for which very good heuristics exists. We tested our algorithm on synthetic and real cytogenetic data from renal cell carcinoma. We also compared our learned progression networks with the networks proposed in earlier publications. The software is available on the website https://bitbucket.org/farahani/diprog.

A Lifetime Maximization Relay Selection Scheme in Wireless Body Area Networks.

PubMed

Zhang, Yu; Zhang, Bing; Zhang, Shi

2017-06-02

Network Lifetime is one of the most important metrics in Wireless Body Area Networks (WBANs). In this paper, a relay selection scheme is proposed under the topology constrains specified in the IEEE 802.15.6 standard to maximize the lifetime of WBANs through formulating and solving an optimization problem where relay selection of each node acts as optimization variable. Considering the diversity of the sensor nodes in WBANs, the optimization problem takes not only energy consumption rate but also energy difference among sensor nodes into account to improve the network lifetime performance. Since it is Non-deterministic Polynomial-hard (NP-hard) and intractable, a heuristic solution is then designed to rapidly address the optimization. The simulation results indicate that the proposed relay selection scheme has better performance in network lifetime compared with existing algorithms and that the heuristic solution has low time complexity with only a negligible performance degradation gap from optimal value. Furthermore, we also conduct simulations based on a general WBAN model to comprehensively illustrate the advantages of the proposed algorithm. At the end of the evaluation, we validate the feasibility of our proposed scheme via an implementation discussion.

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

DOE PAGES

Chen, Zheng; Liu, Liu; Mu, Lin

2017-05-03

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof ofmore » the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.« less

On a sparse pressure-flow rate condensation of rigid circulation models

PubMed Central

Schiavazzi, D. E.; Hsia, T. Y.; Marsden, A. L.

2015-01-01

Cardiovascular simulation has shown potential value in clinical decision-making, providing a framework to assess changes in hemodynamics produced by physiological and surgical alterations. State-of-the-art predictions are provided by deterministic multiscale numerical approaches coupling 3D finite element Navier Stokes simulations to lumped parameter circulation models governed by ODEs. Development of next-generation stochastic multiscale models whose parameters can be learned from available clinical data under uncertainty constitutes a research challenge made more difficult by the high computational cost typically associated with the solution of these models. We present a methodology for constructing reduced representations that condense the behavior of 3D anatomical models using outlet pressure-flow polynomial surrogates, based on multiscale model solutions spanning several heart cycles. Relevance vector machine regression is compared with maximum likelihood estimation, showing that sparse pressure/flow rate approximations offer superior performance in producing working surrogate models to be included in lumped circulation networks. Sensitivities of outlets flow rates are also quantified through a Sobol’ decomposition of their total variance encoded in the orthogonal polynomial expansion. Finally, we show that augmented lumped parameter models including the proposed surrogates accurately reproduce the response of multiscale models they were derived from. In particular, results are presented for models of the coronary circulation with closed loop boundary conditions and the abdominal aorta with open loop boundary conditions. PMID:26671219

A parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1993-01-01

A parallel algorithm, called polysection, is presented for computing the eigenvalues of a symmetric tridiagonal matrix. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The signs of the polynomials at the interval endpoints are determined a priori and used to guarantee that all zeros are found. The use of finite-precision arithmetic may result in multiple zeros; however, in this case, the intervals coalesce and their number determines exactly the multiplicity of the zero. For an N x N matrix the eigenvalues can be determined in O(log-squared N) time with N-squared processors and O(N) time with N processors. The method is compared with a parallel variant of bisection that requires O(N-squared) time on a single processor, O(N) time with N processors, and O(log N) time with N-squared processors.

Pulse transmission transmitter including a higher order time derivate filter

DOEpatents

Dress, Jr., William B.; Smith, Stephen F.

2003-09-23

Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission transmitter includes: a clock; a pseudorandom polynomial generator coupled to the clock, the pseudorandom polynomial generator having a polynomial load input; an exclusive-OR gate coupled to the pseudorandom polynomial generator, the exclusive-OR gate having a serial data input; a programmable delay circuit coupled to both the clock and the exclusive-OR gate; a pulse generator coupled to the programmable delay circuit; and a higher order time derivative filter coupled to the pulse generator. The systems and methods significantly reduce lower-frequency emissions from pulse transmission spread-spectrum communication modes, which reduces potentially harmful interference to existing radio frequency services and users and also simultaneously permit transmission of multiple data bits by utilizing specific pulse shapes.

Hybrid deterministic/stochastic simulation of complex biochemical systems.

PubMed

Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina

2017-11-21

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by complex networks of chemical reactions involving genes, proteins, and enzymes. Accurate computational models are indispensable means for understanding the mechanisms behind the evolution of a complex system, not always explored with wet lab experiments. To serve their purpose, computational models, however, should be able to describe and simulate the complexity of a biological system in many of its aspects. Moreover, it should be implemented by efficient algorithms requiring the shortest possible execution time, to avoid enlarging excessively the time elapsing between data analysis and any subsequent experiment. Besides the features of their topological structure, the complexity of biological networks also refers to their dynamics, that is often non-linear and stiff. The stiffness is due to the presence of molecular species whose abundance fluctuates by many orders of magnitude. A fully stochastic simulation of a stiff system is computationally time-expensive. On the other hand, continuous models are less costly, but they fail to capture the stochastic behaviour of small populations of molecular species. We introduce a new efficient hybrid stochastic-deterministic computational model and the software tool MoBioS (MOlecular Biology Simulator) implementing it. The mathematical model of MoBioS uses continuous differential equations to describe the deterministic reactions and a Gillespie-like algorithm to describe the stochastic ones. Unlike the majority of current hybrid methods, the MoBioS algorithm divides the reactions' set into fast reactions, moderate reactions, and slow reactions and implements a hysteresis switching between the stochastic model and the deterministic model. Fast reactions are approximated as continuous-deterministic processes and modelled by deterministic rate equations. Moderate reactions are those whose reaction waiting time is greater than the fast reaction waiting time but smaller than the slow reaction waiting time. A moderate reaction is approximated as a stochastic (deterministic) process if it was classified as a stochastic (deterministic) process at the time at which it crosses the threshold of low (high) waiting time. A Gillespie First Reaction Method is implemented to select and execute the slow reactions. The performances of MoBios were tested on a typical example of hybrid dynamics: that is the DNA transcription regulation. The simulated dynamic profile of the reagents' abundance and the estimate of the error introduced by the fully deterministic approach were used to evaluate the consistency of the computational model and that of the software tool.

Dynamical Localization for Unitary Anderson Models

NASA Astrophysics Data System (ADS)

Hamza, Eman; Joye, Alain; Stolz, Günter

2009-11-01

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.

Design optimization and uncertainty quantification for aeromechanics forced response of a turbomachinery blade

NASA Astrophysics Data System (ADS)

Modgil, Girish A.

Gas turbine engines for aerospace applications have evolved dramatically over the last 50 years through the constant pursuit for better specific fuel consumption, higher thrust-to-weight ratio, lower noise and emissions all while maintaining reliability and affordability. An important step in enabling these improvements is a forced response aeromechanics analysis involving structural dynamics and aerodynamics of the turbine. It is well documented that forced response vibration is a very critical problem in aircraft engine design, causing High Cycle Fatigue (HCF). Pushing the envelope on engine design has led to increased forced response problems and subsequently an increased risk of HCF failure. Forced response analysis is used to assess design feasibility of turbine blades for HCF using a material limit boundary set by the Goodman Diagram envelope that combines the effects of steady and vibratory stresses. Forced response analysis is computationally expensive, time consuming and requires multi-domain experts to finalize a result. As a consequence, high-fidelity aeromechanics analysis is performed deterministically and is usually done at the end of the blade design process when it is very costly to make significant changes to geometry or aerodynamic design. To address uncertainties in the system (engine operating point, temperature distribution, mistuning, etc.) and variability in material properties, designers apply conservative safety factors in the traditional deterministic approach, which leads to bulky designs. Moreover, using a deterministic approach does not provide a calculated risk of HCF failure. This thesis describes a process that begins with the optimal aerodynamic design of a turbomachinery blade developed using surrogate models of high-fidelity analyses. The resulting optimal blade undergoes probabilistic evaluation to generate aeromechanics results that provide a calculated likelihood of failure from HCF. An existing Rolls-Royce High Work Single Stage (HWSS) turbine blisk provides a baseline to demonstrate the process. The generalized polynomial chaos (gPC) toolbox which was developed includes sampling methods and constructs polynomial approximations. The toolbox provides not only the means for uncertainty quantification of the final blade design, but also facilitates construction of the surrogate models used for the blade optimization. This paper shows that gPC , with a small number of samples, achieves very fast rates of convergence and high accuracy in describing probability distributions without loss of detail in the tails . First, an optimization problem maximizes stage efficiency using turbine aerodynamic design rules as constraints; the function evaluations for this optimization are surrogate models from detailed 3D steady Computational Fluid Dynamics (CFD) analyses. The resulting optimal shape provides a starting point for the 3D high-fidelity aeromechanics (unsteady CFD and 3D Finite Element Analysis (FEA)) UQ study assuming three uncertain input parameters. This investigation seeks to find the steady and vibratory stresses associated with the first torsion mode for the HWSS turbine blisk near maximum operating speed of the engine. Using gPC to provide uncertainty estimates of the steady and vibratory stresses enables the creation of a Probabilistic Goodman Diagram, which - to the authors' best knowledge - is the first of its kind using high fidelity aeromechanics for turbomachinery blades. The Probabilistic Goodman Diagram enables turbine blade designers to make more informed design decisions and it allows the aeromechanics expert to assess quantitatively the risk associated with HCF for any mode crossing based on high fidelity simulations.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Stitching interferometry of a full cylinder without using overlap areas

NASA Astrophysics Data System (ADS)

Peng, Junzheng; Chen, Dingfu; Yu, Yingjie

2017-08-01

Traditional stitching interferometry requires finding out the overlap correspondence and computing the discrepancies in the overlap regions, which makes it complex and time-consuming to obtain the 360° form map of a cylinder. In this paper, we develop a cylinder stitching model based on a new set of orthogonal polynomials, termed Legendre Fourier (LF) polynomials. With these polynomials, individual subaperture data can be expanded as a composition of the inherent form of a partial cylinder surface and additional misalignment parameters. Then the 360° form map can be acquired by simultaneously fitting all subaperture data with the LF polynomials. A metal shaft was measured to experimentally verify the proposed method. In contrast to traditional stitching interferometry, our technique does not require overlapping of adjacent subapertures, thus significantly reducing the measurement time and making the stitching algorithm simple.

An Online Gravity Modeling Method Applied for High Precision Free-INS

PubMed Central

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-01-01

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. PMID:27669261

An Online Gravity Modeling Method Applied for High Precision Free-INS.

PubMed

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-09-23

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS.

Stochastic Models in the DORIS Position Time Series: Estimates from the IDS Contribution to the ITRF2014

NASA Astrophysics Data System (ADS)

Klos, A.; Bogusz, J.; Moreaux, G.

2017-12-01

This research focuses on the investigation of the deterministic and stochastic parts of the DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) weekly coordinate time series from the IDS contribution to the ITRF2014A set of 90 stations was divided into three groups depending on when the data was collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations (these three sum up to produce the Polynomial Trend Model) and a stochastic part, all being resolved with Maximum Likelihood Estimation (MLE). We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations, meaning that the most recent data are the most reliable ones. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. We examined five different noise models to be applied to the stochastic part of the DORIS time series: a pure white noise (WN), a pure power-law noise (PL), a combination of white and power-law noise (WNPL), an autoregressive process of first order (AR(1)) and a Generalized Gauss Markov model (GGM). From our study it arises that the PL process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from AR(1) to pure PL with few stations characterized by a positive spectral index.

Bayesian B-spline mapping for dynamic quantitative traits.

PubMed

Xing, Jun; Li, Jiahan; Yang, Runqing; Zhou, Xiaojing; Xu, Shizhong

2012-04-01

Owing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.

Near Real-Time Closed-Loop Optimal Control Feedback for Spacecraft Attitude Maneuvers

DTIC Science & Technology

2009-03-01

60 3.8 Positive ωi Static Thrust Fan Characterization Polynomial Coefficients . . 62 3.9 Negative ωi Static Thrust Fan...Characterization Polynomial Coefficients . 62 4.1 Coefficients for SimSAT II’s Air Drag Polynomial Function . . . . . . . . . . . 78 5.1 OLOC Simulation...maneuver. Researchers using OCT identified that naturally occurring aerodynamic drag and gravity forces could be exploited in such a way that the CMGs

Ridge Polynomial Neural Network with Error Feedback for Time Series Forecasting

PubMed Central

Ghazali, Rozaida; Herawan, Tutut

2016-01-01

Time series forecasting has gained much attention due to its many practical applications. Higher-order neural network with recurrent feedback is a powerful technique that has been used successfully for time series forecasting. It maintains fast learning and the ability to learn the dynamics of the time series over time. Network output feedback is the most common recurrent feedback for many recurrent neural network models. However, not much attention has been paid to the use of network error feedback instead of network output feedback. In this study, we propose a novel model, called Ridge Polynomial Neural Network with Error Feedback (RPNN-EF) that incorporates higher order terms, recurrence and error feedback. To evaluate the performance of RPNN-EF, we used four univariate time series with different forecasting horizons, namely star brightness, monthly smoothed sunspot numbers, daily Euro/Dollar exchange rate, and Mackey-Glass time-delay differential equation. We compared the forecasting performance of RPNN-EF with the ordinary Ridge Polynomial Neural Network (RPNN) and the Dynamic Ridge Polynomial Neural Network (DRPNN). Simulation results showed an average 23.34% improvement in Root Mean Square Error (RMSE) with respect to RPNN and an average 10.74% improvement with respect to DRPNN. That means that using network errors during training helps enhance the overall forecasting performance for the network. PMID:27959927

Ridge Polynomial Neural Network with Error Feedback for Time Series Forecasting.

PubMed

Waheeb, Waddah; Ghazali, Rozaida; Herawan, Tutut

2016-01-01

Time series forecasting has gained much attention due to its many practical applications. Higher-order neural network with recurrent feedback is a powerful technique that has been used successfully for time series forecasting. It maintains fast learning and the ability to learn the dynamics of the time series over time. Network output feedback is the most common recurrent feedback for many recurrent neural network models. However, not much attention has been paid to the use of network error feedback instead of network output feedback. In this study, we propose a novel model, called Ridge Polynomial Neural Network with Error Feedback (RPNN-EF) that incorporates higher order terms, recurrence and error feedback. To evaluate the performance of RPNN-EF, we used four univariate time series with different forecasting horizons, namely star brightness, monthly smoothed sunspot numbers, daily Euro/Dollar exchange rate, and Mackey-Glass time-delay differential equation. We compared the forecasting performance of RPNN-EF with the ordinary Ridge Polynomial Neural Network (RPNN) and the Dynamic Ridge Polynomial Neural Network (DRPNN). Simulation results showed an average 23.34% improvement in Root Mean Square Error (RMSE) with respect to RPNN and an average 10.74% improvement with respect to DRPNN. That means that using network errors during training helps enhance the overall forecasting performance for the network.

Service-Oriented Architecture (SOA) Instantiation within a Hard Real-Time, Deterministic Combat System Environment

ERIC Educational Resources Information Center

Moreland, James D., Jr

2013-01-01

This research investigates the instantiation of a Service-Oriented Architecture (SOA) within a hard real-time (stringent time constraints), deterministic (maximum predictability) combat system (CS) environment. There are numerous stakeholders across the U.S. Department of the Navy who are affected by this development, and therefore the system…

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

The viability of ADVANTG deterministic method for synthetic radiography generation

NASA Astrophysics Data System (ADS)

Bingham, Andrew; Lee, Hyoung K.

2018-07-01

Fast simulation techniques to generate synthetic radiographic images of high resolution are helpful when new radiation imaging systems are designed. However, the standard stochastic approach requires lengthy run time with poorer statistics at higher resolution. The investigation of the viability of a deterministic approach to synthetic radiography image generation was explored. The aim was to analyze a computational time decrease over the stochastic method. ADVANTG was compared to MCNP in multiple scenarios including a small radiography system prototype, to simulate high resolution radiography images. By using ADVANTG deterministic code to simulate radiography images the computational time was found to decrease 10 to 13 times compared to the MCNP stochastic approach while retaining image quality.

Positive dwell time algorithm with minimum equal extra material removal in deterministic optical surfacing technology.

PubMed

Li, Longxiang; Xue, Donglin; Deng, Weijie; Wang, Xu; Bai, Yang; Zhang, Feng; Zhang, Xuejun

2017-11-10

In deterministic computer-controlled optical surfacing, accurate dwell time execution by computer numeric control machines is crucial in guaranteeing a high-convergence ratio for the optical surface error. It is necessary to consider the machine dynamics limitations in the numerical dwell time algorithms. In this paper, these constraints on dwell time distribution are analyzed, and a model of the equal extra material removal is established. A positive dwell time algorithm with minimum equal extra material removal is developed. Results of simulations based on deterministic magnetorheological finishing demonstrate the necessity of considering machine dynamics performance and illustrate the validity of the proposed algorithm. Indeed, the algorithm effectively facilitates the determinacy of sub-aperture optical surfacing processes.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony; Munoz, Cesar

2015-01-01

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Eastman, W. L.; Reed, I. S.

1987-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Probabilistic volcanic hazard assessments of Pyroclastic Density Currents: ongoing practices and future perspectives

NASA Astrophysics Data System (ADS)

Tierz, Pablo; Sandri, Laura; Ramona Stefanescu, Elena; Patra, Abani; Marzocchi, Warner; Costa, Antonio; Sulpizio, Roberto

2014-05-01

Explosive volcanoes and, especially, Pyroclastic Density Currents (PDCs) pose an enormous threat to populations living in the surroundings of volcanic areas. Difficulties in the modeling of PDCs are related to (i) very complex and stochastic physical processes, intrinsic to their occurrence, and (ii) to a lack of knowledge about how these processes actually form and evolve. This means that there are deep uncertainties (namely, of aleatory nature due to point (i) above, and of epistemic nature due to point (ii) above) associated to the study and forecast of PDCs. Consequently, the assessment of their hazard is better described in terms of probabilistic approaches rather than by deterministic ones. What is actually done to assess probabilistic hazard from PDCs is to couple deterministic simulators with statistical techniques that can, eventually, supply probabilities and inform about the uncertainties involved. In this work, some examples of both PDC numerical simulators (Energy Cone and TITAN2D) and uncertainty quantification techniques (Monte Carlo sampling -MC-, Polynomial Chaos Quadrature -PCQ- and Bayesian Linear Emulation -BLE-) are presented, and their advantages, limitations and future potential are underlined. The key point in choosing a specific method leans on the balance between its related computational cost, the physical reliability of the simulator and the pursued target of the hazard analysis (type of PDCs considered, time-scale selected for the analysis, particular guidelines received from decision-making agencies, etc.). Although current numerical and statistical techniques have brought important advances in probabilistic volcanic hazard assessment from PDCs, some of them may be further applicable to more sophisticated simulators. In addition, forthcoming improvements could be focused on three main multidisciplinary directions: 1) Validate the simulators frequently used (through comparison with PDC deposits and other simulators), 2) Decrease simulator runtimes (whether by increasing the knowledge about the physical processes or by doing more efficient programming, parallelization, ...) and 3) Improve uncertainty quantification techniques.

Deterministic quantum splitter based on time-reversed Hong-Ou-Mandel interference

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

Chen, Jun; Lee, Kim Fook; Kumar, Prem

2007-09-15

By utilizing a fiber-based indistinguishable photon-pair source in the 1.55 {mu}m telecommunications band [J. Chen et al., Opt. Lett. 31, 2798 (2006)], we present the first, to the best of our knowledge, deterministic quantum splitter based on the principle of time-reversed Hong-Ou-Mandel quantum interference. The deterministically separated identical photons' indistinguishability is then verified by using a conventional Hong-Ou-Mandel quantum interference, which exhibits a near-unity dip visibility of 94{+-}1%, making this quantum splitter useful for various quantum information processing applications.

Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng

2016-03-01

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

Stochastic uncertainty analysis for unconfined flow systems

USGS Publications Warehouse

Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming

2006-01-01

A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.

Realistic Simulation for Body Area and Body-To-Body Networks

PubMed Central

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D’Errico, Raffaele

2016-01-01

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices. PMID:27104537

Realistic Simulation for Body Area and Body-To-Body Networks.

PubMed

Alam, Muhammad Mahtab; Ben Hamida, Elyes; Ben Arbia, Dhafer; Maman, Mickael; Mani, Francesco; Denis, Benoit; D'Errico, Raffaele

2016-04-20

In this paper, we present an accurate and realistic simulation for body area networks (BAN) and body-to-body networks (BBN) using deterministic and semi-deterministic approaches. First, in the semi-deterministic approach, a real-time measurement campaign is performed, which is further characterized through statistical analysis. It is able to generate link-correlated and time-varying realistic traces (i.e., with consistent mobility patterns) for on-body and body-to-body shadowing and fading, including body orientations and rotations, by means of stochastic channel models. The full deterministic approach is particularly targeted to enhance IEEE 802.15.6 proposed channel models by introducing space and time variations (i.e., dynamic distances) through biomechanical modeling. In addition, it helps to accurately model the radio link by identifying the link types and corresponding path loss factors for line of sight (LOS) and non-line of sight (NLOS). This approach is particularly important for links that vary over time due to mobility. It is also important to add that the communication and protocol stack, including the physical (PHY), medium access control (MAC) and networking models, is developed for BAN and BBN, and the IEEE 802.15.6 compliance standard is provided as a benchmark for future research works of the community. Finally, the two approaches are compared in terms of the successful packet delivery ratio, packet delay and energy efficiency. The results show that the semi-deterministic approach is the best option; however, for the diversity of the mobility patterns and scenarios applicable, biomechanical modeling and the deterministic approach are better choices.

Computational complexity of ecological and evolutionary spatial dynamics

PubMed Central

Ibsen-Jensen, Rasmus; Chatterjee, Krishnendu; Nowak, Martin A.

2015-01-01

There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant) will take over a resident population? We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP). PMID:26644569

Investigating and Modelling Effects of Climatically and Hydrologically Indicators on the Urmia Lake Coastline Changes Using Time Series Analysis

NASA Astrophysics Data System (ADS)

Ahmadijamal, M.; Hasanlou, M.

2017-09-01

Study of hydrological parameters of lakes and examine the variation of water level to operate management on water resources are important. The purpose of this study is to investigate and model the Urmia Lake water level changes due to changes in climatically and hydrological indicators that affects in the process of level variation and area of this lake. For this purpose, Landsat satellite images, hydrological data, the daily precipitation, the daily surface evaporation and the daily discharge in total of the lake basin during the period of 2010-2016 have been used. Based on time-series analysis that is conducted on individual data independently with same procedure, to model variation of Urmia Lake level, we used polynomial regression technique and combined polynomial with periodic behavior. In the first scenario, we fit a multivariate linear polynomial to our datasets and determining RMSE, NRSME and R² value. We found that fourth degree polynomial can better fit to our datasets with lowest RMSE value about 9 cm. In the second scenario, we combine polynomial with periodic behavior for modeling. The second scenario has superiority comparing to the first one, by RMSE value about 3 cm.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Deterministic generation of remote entanglement with active quantum feedback

DOE PAGES

Martin, Leigh; Motzoi, Felix; Li, Hanhan; ...

2015-12-10

We develop and study protocols for deterministic remote entanglement generation using quantum feedback, without relying on an entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can bemore » modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Lastly, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.« less

On the coefficients of integrated expansions of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2006-03-01

A new formula expressing explicitly the integrals of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another new explicit formula relating the Bessel coefficients of an expansion for infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is also established. An application of these formulae for solving ordinary differential equations with varying coefficients is discussed.

Optimal control and Galois theory

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

Zelikin, M I; Kiselev, D D; Lokutsievskiy, L V

2013-11-30

An important role is played in the solution of a class of optimal control problems by a certain special polynomial of degree 2(n−1) with integer coefficients. The linear independence of a family of k roots of this polynomial over the field Q implies the existence of a solution of the original problem with optimal control in the form of an irrational winding of a k-dimensional Clifford torus, which is passed in finite time. In the paper, we prove that for n≤15 one can take an arbitrary positive integer not exceeding [n/2] for k. The apparatus developed in the paper is applied to the systems ofmore » Chebyshev-Hermite polynomials and generalized Chebyshev-Laguerre polynomials. It is proved that for such polynomials of degree 2m every subsystem of [(m+1)/2] roots with pairwise distinct squares is linearly independent over the field Q. Bibliography: 11 titles.« less

Design of polynomial fuzzy observer-controller for nonlinear systems with state delay: sum of squares approach

NASA Astrophysics Data System (ADS)

Gassara, H.; El Hajjaji, A.; Chaabane, M.

2017-07-01

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.

Polynomial complexity despite the fermionic sign

NASA Astrophysics Data System (ADS)

Rossi, R.; Prokof'ev, N.; Svistunov, B.; Van Houcke, K.; Werner, F.

2017-04-01

It is commonly believed that in unbiased quantum Monte Carlo approaches to fermionic many-body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with a recently introduced Monte Carlo algorithm (see Rossi R., arXiv:1612.05184), the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.

A conforming spectral collocation strategy for Stokes flow through a channel contraction

NASA Technical Reports Server (NTRS)

Phillips, Timothy N.; Karageorghis, Andreas

1989-01-01

A formula expressing the coefficients of an expansion of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

Maximum likelihood decoding of Reed Solomon Codes

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

Sudan, M.

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore » decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.« less

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model

PubMed Central

Nené, Nuno R.; Dunham, Alistair S.; Illingworth, Christopher J. R.

2018-01-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. PMID:29500183

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

Yang, Y M; Bush, K; Han, B

Purpose: Accurate and fast dose calculation is a prerequisite of precision radiation therapy in modern photon and particle therapy. While Monte Carlo (MC) dose calculation provides high dosimetric accuracy, the drastically increased computational time hinders its routine use. Deterministic dose calculation methods are fast, but problematic in the presence of tissue density inhomogeneity. We leverage the useful features of deterministic methods and MC to develop a hybrid dose calculation platform with autonomous utilization of MC and deterministic calculation depending on the local geometry, for optimal accuracy and speed. Methods: Our platform utilizes a Geant4 based “localized Monte Carlo” (LMC) methodmore » that isolates MC dose calculations only to volumes that have potential for dosimetric inaccuracy. In our approach, additional structures are created encompassing heterogeneous volumes. Deterministic methods calculate dose and energy fluence up to the volume surfaces, where the energy fluence distribution is sampled into discrete histories and transported using MC. Histories exiting the volume are converted back into energy fluence, and transported deterministically. By matching boundary conditions at both interfaces, deterministic dose calculation account for dose perturbations “downstream” of localized heterogeneities. Hybrid dose calculation was performed for water and anthropomorphic phantoms. Results: We achieved <1% agreement between deterministic and MC calculations in the water benchmark for photon and proton beams, and dose differences of 2%–15% could be observed in heterogeneous phantoms. The saving in computational time (a factor ∼4–7 compared to a full Monte Carlo dose calculation) was found to be approximately proportional to the volume of the heterogeneous region. Conclusion: Our hybrid dose calculation approach takes advantage of the computational efficiency of deterministic method and accuracy of MC, providing a practical tool for high performance dose calculation in modern RT. The approach is generalizable to all modalities where heterogeneities play a large role, notably particle therapy.« less

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Processing short-term and long-term information with a combination of polynomial approximation techniques and time-delay neural networks.

PubMed

Fuchs, Erich; Gruber, Christian; Reitmaier, Tobias; Sick, Bernhard

2009-09-01

Neural networks are often used to process temporal information, i.e., any kind of information related to time series. In many cases, time series contain short-term and long-term trends or behavior. This paper presents a new approach to capture temporal information with various reference periods simultaneously. A least squares approximation of the time series with orthogonal polynomials will be used to describe short-term trends contained in a signal (average, increase, curvature, etc.). Long-term behavior will be modeled with the tapped delay lines of a time-delay neural network (TDNN). This network takes the coefficients of the orthogonal expansion of the approximating polynomial as inputs such considering short-term and long-term information efficiently. The advantages of the method will be demonstrated by means of artificial data and two real-world application examples, the prediction of the user number in a computer network and online tool wear classification in turning.

Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.

PubMed

Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

2011-10-01

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Polynomial approximation of the Lense-Thirring rigid precession frequency

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Motta, Sara

2018-05-01

We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low-frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of ≈70 in the range of minutes.

Segmented Polynomial Models in Quasi-Experimental Research.

ERIC Educational Resources Information Center

Wasik, John L.

1981-01-01

The use of segmented polynomial models is explained. Examples of design matrices of dummy variables are given for the least squares analyses of time series and discontinuity quasi-experimental research designs. Linear combinations of dummy variable vectors appear to provide tests of effects in the two quasi-experimental designs. (Author/BW)

Appropriate time scales for nonlinear analyses of deterministic jump systems

NASA Astrophysics Data System (ADS)

Suzuki, Tomoya

2011-06-01

In the real world, there are many phenomena that are derived from deterministic systems but which fluctuate with nonuniform time intervals. This paper discusses the appropriate time scales that can be applied to such systems to analyze their properties. The financial markets are an example of such systems wherein price movements fluctuate with nonuniform time intervals. However, it is common to apply uniform time scales such as 1-min data and 1-h data to study price movements. This paper examines the validity of such time scales by using surrogate data tests to ascertain whether the deterministic properties of the original system can be identified from uniform sampled data. The results show that uniform time samplings are often inappropriate for nonlinear analyses. However, for other systems such as neural spikes and Internet traffic packets, which produce similar outputs, uniform time samplings are quite effective in extracting the system properties. Nevertheless, uniform samplings often generate overlapping data, which can cause false rejections of surrogate data tests.

Computational algebraic geometry for statistical modeling FY09Q2 progress.

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

Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

2009-03-01

This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones inmore » more detail; the next section provides an overview of the project and how the current progress fits into it.« less

Direct solution for thermal stresses in a nose cap under an arbitrary axisymmetric temperature distribution

NASA Technical Reports Server (NTRS)

Davis, Randall C.

1988-01-01

The design of a nose cap for a hypersonic vehicle is an iterative process requiring a rapid, easy to use and accurate stress analysis. The objective of this paper is to develop such a stress analysis technique from a direct solution of the thermal stress equations for a spherical shell. The nose cap structure is treated as a thin spherical shell with an axisymmetric temperature distribution. The governing differential equations are solved by expressing the stress solution to the thermoelastic equations in terms of a series of derivatives of the Legendre polynomials. The process of finding the coefficients for the series solution in terms of the temperature distribution is generalized by expressing the temperature along the shell and through the thickness as a polynomial in the spherical angle coordinate. Under this generalization the orthogonality property of the Legendre polynomials leads to a sequence of integrals involving powers of the spherical shell coordinate times the derivative of the Legendre polynomials. The coefficients of the temperature polynomial appear outside of these integrals. Thus, the integrals are evaluated only once and their values tabulated for use with any arbitrary polynomial temperature distribution.

Model-based estimates of long-term persistence of induced HPV antibodies: a flexible subject-specific approach.

PubMed

Aregay, Mehreteab; Shkedy, Ziv; Molenberghs, Geert; David, Marie-Pierre; Tibaldi, Fabián

2013-01-01

In infectious diseases, it is important to predict the long-term persistence of vaccine-induced antibodies and to estimate the time points where the individual titers are below the threshold value for protection. This article focuses on HPV-16/18, and uses a so-called fractional-polynomial model to this effect, derived in a data-driven fashion. Initially, model selection was done from among the second- and first-order fractional polynomials on the one hand and from the linear mixed model on the other. According to a functional selection procedure, the first-order fractional polynomial was selected. Apart from the fractional polynomial model, we also fitted a power-law model, which is a special case of the fractional polynomial model. Both models were compared using Akaike's information criterion. Over the observation period, the fractional polynomials fitted the data better than the power-law model; this, of course, does not imply that it fits best over the long run, and hence, caution ought to be used when prediction is of interest. Therefore, we point out that the persistence of the anti-HPV responses induced by these vaccines can only be ascertained empirically by long-term follow-up analysis.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model.

PubMed

Nené, Nuno R; Dunham, Alistair S; Illingworth, Christopher J R

2018-05-01

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model. Copyright © 2018 Nené et al.

Consensus seeking in a network of discrete-time linear agents with communication noises

NASA Astrophysics Data System (ADS)

Wang, Yunpeng; Cheng, Long; Hou, Zeng-Guang; Tan, Min; Zhou, Chao; Wang, Ming

2015-07-01

This paper studies the mean square consensus of discrete-time linear time-invariant multi-agent systems with communication noises. A distributed consensus protocol, which is composed of the agent's own state feedback and the relative states between the agent and its neighbours, is proposed. A time-varying consensus gain a[k] is applied to attenuate the effect of noises which inherits in the inaccurate measurement of relative states with neighbours. A polynomial, namely 'parameter polynomial', is constructed. And its coefficients are the parameters in the feedback gain vector of the proposed protocol. It turns out that the parameter polynomial plays an important role in guaranteeing the consensus of linear multi-agent systems. By the proposed protocol, necessary and sufficient conditions for mean square consensus are presented under different topology conditions: (1) if the communication topology graph has a spanning tree and every node in the graph has at least one parent node, then the mean square consensus can be achieved if and only if ∑∞k = 0a[k] = ∞, ∑∞k = 0a2[k] < ∞ and all roots of the parameter polynomial are in the unit circle; (2) if the communication topology graph has a spanning tree and there exits one node without any parent node (the leader-follower case), then the mean square consensus can be achieved if and only if ∑∞k = 0a[k] = ∞, limk → ∞a[k] = 0 and all roots of the parameter polynomial are in the unit circle; (3) if the communication topology graph does not have a spanning tree, then the mean square consensus can never be achieved. Finally, one simulation example on the multiple aircrafts system is provided to validate the theoretical analysis.

Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; AliShaykhian, Gholam

2010-01-01

We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.

A chaotic model for the plague epidemic that has occurred in Bombay at the end of the 19th century

NASA Astrophysics Data System (ADS)

Mangiarotti, Sylvain

2015-04-01

The plague epidemic that has occurred in Bombay at the end of the 19th century was detected in 1896. One year before, an Advisory Committee had been appointed by the Secretary of State for India, the Royal Society, and the Lister Institute. This Committee made numerous investigations and gathered a large panel of data including the number of people attacked and died from the plague, records of rat and flea populations, as well as meteorological records of temperature and humidity [1]. The global modeling technique [2] aims to obtain low dimensional models able to simulate the observed cycles from time series. As far as we know, this technique has been tried only to one case of epidemiological analysis (the whooping cough infection) based on a discrete formulation [3]. In the present work, the continuous time formulation of this technique is used to analyze the time evolution of the plague epidemic from this data set. One low dimensional model (three variables) is obtained exhibiting a limit cycle of period-5. A chaotic behavior could be derived from this model by tuning the model parameters. It provides a strong argument for a dynamical behavior that can be approximated by low dimensional deterministic equations. This model also provides an empirical argument for chaos in epidemics. [1] Verjbitski D. T., Bannerman W. B. & Kápadiâ R. T., 1908. Reports on Plague Investigations in India (May,1908), The Journal of Hygiene, 8(2), 161 -308. [2] Mangiarotti S., Coudret R., Drapeau L. & Jarlan L., 2012. Polynomial search and Global modelling: two algorithms for modeling chaos. Physical Review E, 86(4), 046205. [3] Boudjema G. & Cazelles B., 2003. Extraction of nonlinear dynamics from short and noisy time series. Chaos, Solitons and Fractals, 12, 2051-2069.

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials

PubMed Central

Corteel, Sylvie; Williams, Lauren K.

2010-01-01

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities α and γ, and they may exit and enter at the right with probabilities β and δ. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials. PMID:20348417

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials.

PubMed

Corteel, Sylvie; Williams, Lauren K

2010-04-13

We introduce some combinatorial objects called staircase tableaux, which have cardinality 4(n)n!, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities alpha and gamma, and they may exit and enter at the right with probabilities beta and delta. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials.

Polynomial-Time Algorithms for Building a Consensus MUL-Tree

PubMed Central

Cui, Yun; Jansson, Jesper

2012-01-01

Abstract A multi-labeled phylogenetic tree, or MUL-tree, is a generalization of a phylogenetic tree that allows each leaf label to be used many times. MUL-trees have applications in biogeography, the study of host–parasite cospeciation, gene evolution studies, and computer science. Here, we consider the problem of inferring a consensus MUL-tree that summarizes a given set of conflicting MUL-trees, and present the first polynomial-time algorithms for solving it. In particular, we give a straightforward, fast algorithm for building a strict consensus MUL-tree for any input set of MUL-trees with identical leaf label multisets, as well as a polynomial-time algorithm for building a majority rule consensus MUL-tree for the special case where every leaf label occurs at most twice. We also show that, although it is NP-hard to find a majority rule consensus MUL-tree in general, the variant that we call the singular majority rule consensus MUL-tree can be constructed efficiently whenever it exists. PMID:22963134

Polynomial-time algorithms for building a consensus MUL-tree.

PubMed

Cui, Yun; Jansson, Jesper; Sung, Wing-Kin

2012-09-01

A multi-labeled phylogenetic tree, or MUL-tree, is a generalization of a phylogenetic tree that allows each leaf label to be used many times. MUL-trees have applications in biogeography, the study of host-parasite cospeciation, gene evolution studies, and computer science. Here, we consider the problem of inferring a consensus MUL-tree that summarizes a given set of conflicting MUL-trees, and present the first polynomial-time algorithms for solving it. In particular, we give a straightforward, fast algorithm for building a strict consensus MUL-tree for any input set of MUL-trees with identical leaf label multisets, as well as a polynomial-time algorithm for building a majority rule consensus MUL-tree for the special case where every leaf label occurs at most twice. We also show that, although it is NP-hard to find a majority rule consensus MUL-tree in general, the variant that we call the singular majority rule consensus MUL-tree can be constructed efficiently whenever it exists.

A weighted least squares estimation of the polynomial regression model on paddy production in the area of Kedah and Perlis

NASA Astrophysics Data System (ADS)

Musa, Rosliza; Ali, Zalila; Baharum, Adam; Nor, Norlida Mohd

2017-08-01

The linear regression model assumes that all random error components are identically and independently distributed with constant variance. Hence, each data point provides equally precise information about the deterministic part of the total variation. In other words, the standard deviations of the error terms are constant over all values of the predictor variables. When the assumption of constant variance is violated, the ordinary least squares estimator of regression coefficient lost its property of minimum variance in the class of linear and unbiased estimators. Weighted least squares estimation are often used to maximize the efficiency of parameter estimation. A procedure that treats all of the data equally would give less precisely measured points more influence than they should have and would give highly precise points too little influence. Optimizing the weighted fitting criterion to find the parameter estimates allows the weights to determine the contribution of each observation to the final parameter estimates. This study used polynomial model with weighted least squares estimation to investigate paddy production of different paddy lots based on paddy cultivation characteristics and environmental characteristics in the area of Kedah and Perlis. The results indicated that factors affecting paddy production are mixture fertilizer application cycle, average temperature, the squared effect of average rainfall, the squared effect of pest and disease, the interaction between acreage with amount of mixture fertilizer, the interaction between paddy variety and NPK fertilizer application cycle and the interaction between pest and disease and NPK fertilizer application cycle.

Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures

PubMed Central

Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.

2014-01-01

Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295

Deterministic and stochastic CTMC models from Zika disease transmission

NASA Astrophysics Data System (ADS)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Deterministic chaos in an ytterbium-doped mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Mélo, Lucas B. A.; Palacios, Guillermo F. R.; Carelli, Pedro V.; Acioli, Lúcio H.; Rios Leite, José R.; de Miranda, Marcio H. G.

2018-05-01

We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rossler map. A positive Lyapunov exponent $\\lambda = 0.14$ confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

Explicit analytical expression for the condition number of polynomials in power form

NASA Astrophysics Data System (ADS)

Rack, Heinz-Joachim

2017-07-01

In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

Analytical solution of tt¯ dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-03-01

The top quark antiquark production system in the dilepton decay channel is described by a set of equations which is nonlinear in the unknown neutrino momenta. Its most precise and least time consuming solution is of major importance for measurements of top quark properties like the top quark mass and tt¯ spin correlations. The initial system of equations can be transformed into two polynomial equations with two unknowns by means of elementary algebraic operations. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation is solved analytically.

The past, present and future of cyber-physical systems: a focus on models.

PubMed

Lee, Edward A

2015-02-26

This paper is about better engineering of cyber-physical systems (CPSs) through better models. Deterministic models have historically proven extremely useful and arguably form the kingpin of the industrial revolution and the digital and information technology revolutions. Key deterministic models that have proven successful include differential equations, synchronous digital logic and single-threaded imperative programs. Cyber-physical systems, however, combine these models in such a way that determinism is not preserved. Two projects show that deterministic CPS models with faithful physical realizations are possible and practical. The first project is PRET, which shows that the timing precision of synchronous digital logic can be practically made available at the software level of abstraction. The second project is Ptides (programming temporally-integrated distributed embedded systems), which shows that deterministic models for distributed cyber-physical systems have practical faithful realizations. These projects are existence proofs that deterministic CPS models are possible and practical.

The Past, Present and Future of Cyber-Physical Systems: A Focus on Models

PubMed Central

Lee, Edward A.

2015-01-01

This paper is about better engineering of cyber-physical systems (CPSs) through better models. Deterministic models have historically proven extremely useful and arguably form the kingpin of the industrial revolution and the digital and information technology revolutions. Key deterministic models that have proven successful include differential equations, synchronous digital logic and single-threaded imperative programs. Cyber-physical systems, however, combine these models in such a way that determinism is not preserved. Two projects show that deterministic CPS models with faithful physical realizations are possible and practical. The first project is PRET, which shows that the timing precision of synchronous digital logic can be practically made available at the software level of abstraction. The second project is Ptides (programming temporally-integrated distributed embedded systems), which shows that deterministic models for distributed cyber-physical systems have practical faithful realizations. These projects are existence proofs that deterministic CPS models are possible and practical. PMID:25730486

Non-intrusive uncertainty quantification of computational fluid dynamics simulations: notes on the accuracy and efficiency

NASA Astrophysics Data System (ADS)

Zimoń, Małgorzata; Sawko, Robert; Emerson, David; Thompson, Christopher

2017-11-01

Uncertainty quantification (UQ) is increasingly becoming an indispensable tool for assessing the reliability of computational modelling. Efficient handling of stochastic inputs, such as boundary conditions, physical properties or geometry, increases the utility of model results significantly. We discuss the application of non-intrusive generalised polynomial chaos techniques in the context of fluid engineering simulations. Deterministic and Monte Carlo integration rules are applied to a set of problems, including ordinary differential equations and the computation of aerodynamic parameters subject to random perturbations. In particular, we analyse acoustic wave propagation in a heterogeneous medium to study the effects of mesh resolution, transients, number and variability of stochastic inputs. We consider variants of multi-level Monte Carlo and perform a novel comparison of the methods with respect to numerical and parametric errors, as well as computational cost. The results provide a comprehensive view of the necessary steps in UQ analysis and demonstrate some key features of stochastic fluid flow systems.

Generalized Detectability for Discrete Event Systems

PubMed Central

Shu, Shaolong; Lin, Feng

2011-01-01

In our previous work, we investigated detectability of discrete event systems, which is defined as the ability to determine the current and subsequent states of a system based on observation. For different applications, we defined four types of detectabilities: (weak) detectability, strong detectability, (weak) periodic detectability, and strong periodic detectability. In this paper, we extend our results in three aspects. (1) We extend detectability from deterministic systems to nondeterministic systems. Such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems. (2) We develop polynomial algorithms to check strong detectability. The previous algorithms are based on observer whose construction is of exponential complexity, while the new algorithms are based on a new automaton called detector. (3) We extend detectability to D-detectability. While detectability requires determining the exact state of a system, D-detectability relaxes this requirement by asking only to distinguish certain pairs of states. With these extensions, the theory on detectability of discrete event systems becomes more applicable in solving many practical problems. PMID:21691432

Uncertainty quantification-based robust aerodynamic optimization of laminar flow nacelle

NASA Astrophysics Data System (ADS)

Xiong, Neng; Tao, Yang; Liu, Zhiyong; Lin, Jun

2018-05-01

The aerodynamic performance of laminar flow nacelle is highly sensitive to uncertain working conditions, especially the surface roughness. An efficient robust aerodynamic optimization method on the basis of non-deterministic computational fluid dynamic (CFD) simulation and Efficient Global Optimization (EGO)algorithm was employed. A non-intrusive polynomial chaos method is used in conjunction with an existing well-verified CFD module to quantify the uncertainty propagation in the flow field. This paper investigates the roughness modeling behavior with the γ-Ret shear stress transport model including modeling flow transition and surface roughness effects. The roughness effects are modeled to simulate sand grain roughness. A Class-Shape Transformation-based parametrical description of the nacelle contour as part of an automatic design evaluation process is presented. A Design-of-Experiments (DoE) was performed and surrogate model by Kriging method was built. The new design nacelle process demonstrates that significant improvements of both mean and variance of the efficiency are achieved and the proposed method can be applied to laminar flow nacelle design successfully.

Deterministic Factors Overwhelm Stochastic Environmental Fluctuations as Drivers of Jellyfish Outbreaks.

PubMed

Benedetti-Cecchi, Lisandro; Canepa, Antonio; Fuentes, Veronica; Tamburello, Laura; Purcell, Jennifer E; Piraino, Stefano; Roberts, Jason; Boero, Ferdinando; Halpin, Patrick

2015-01-01

Jellyfish outbreaks are increasingly viewed as a deterministic response to escalating levels of environmental degradation and climate extremes. However, a comprehensive understanding of the influence of deterministic drivers and stochastic environmental variations favouring population renewal processes has remained elusive. This study quantifies the deterministic and stochastic components of environmental change that lead to outbreaks of the jellyfish Pelagia noctiluca in the Mediterranen Sea. Using data of jellyfish abundance collected at 241 sites along the Catalan coast from 2007 to 2010 we: (1) tested hypotheses about the influence of time-varying and spatial predictors of jellyfish outbreaks; (2) evaluated the relative importance of stochastic vs. deterministic forcing of outbreaks through the environmental bootstrap method; and (3) quantified return times of extreme events. Outbreaks were common in May and June and less likely in other summer months, which resulted in a negative relationship between outbreaks and SST. Cross- and along-shore advection by geostrophic flow were important concentrating forces of jellyfish, but most outbreaks occurred in the proximity of two canyons in the northern part of the study area. This result supported the recent hypothesis that canyons can funnel P. noctiluca blooms towards shore during upwelling. This can be a general, yet unappreciated mechanism leading to outbreaks of holoplanktonic jellyfish species. The environmental bootstrap indicated that stochastic environmental fluctuations have negligible effects on return times of outbreaks. Our analysis emphasized the importance of deterministic processes leading to jellyfish outbreaks compared to the stochastic component of environmental variation. A better understanding of how environmental drivers affect demographic and population processes in jellyfish species will increase the ability to anticipate jellyfish outbreaks in the future.

Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter

NASA Astrophysics Data System (ADS)

Bisnovatyi-Kogan, G. S.; Glushikhina, M. V.

2018-04-01

The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman-Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron-electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron-electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8.

Probabilistic vs. deterministic fiber tracking and the influence of different seed regions to delineate cerebellar-thalamic fibers in deep brain stimulation.

PubMed

Schlaier, Juergen R; Beer, Anton L; Faltermeier, Rupert; Fellner, Claudia; Steib, Kathrin; Lange, Max; Greenlee, Mark W; Brawanski, Alexander T; Anthofer, Judith M

2017-06-01

This study compared tractography approaches for identifying cerebellar-thalamic fiber bundles relevant to planning target sites for deep brain stimulation (DBS). In particular, probabilistic and deterministic tracking of the dentate-rubro-thalamic tract (DRTT) and differences between the spatial courses of the DRTT and the cerebello-thalamo-cortical (CTC) tract were compared. Six patients with movement disorders were examined by magnetic resonance imaging (MRI), including two sets of diffusion-weighted images (12 and 64 directions). Probabilistic and deterministic tractography was applied on each diffusion-weighted dataset to delineate the DRTT. Results were compared with regard to their sensitivity in revealing the DRTT and additional fiber tracts and processing time. Two sets of regions-of-interests (ROIs) guided deterministic tractography of the DRTT or the CTC, respectively. Tract distances to an atlas-based reference target were compared. Probabilistic fiber tracking with 64 orientations detected the DRTT in all twelve hemispheres. Deterministic tracking detected the DRTT in nine (12 directions) and in only two (64 directions) hemispheres. Probabilistic tracking was more sensitive in detecting additional fibers (e.g. ansa lenticularis and medial forebrain bundle) than deterministic tracking. Probabilistic tracking lasted substantially longer than deterministic. Deterministic tracking was more sensitive in detecting the CTC than the DRTT. CTC tracts were located adjacent but consistently more posterior to DRTT tracts. These results suggest that probabilistic tracking is more sensitive and robust in detecting the DRTT but harder to implement than deterministic approaches. Although sensitivity of deterministic tracking is higher for the CTC than the DRTT, targets for DBS based on these tracts likely differ. © 2017 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method.

PubMed

Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay

2017-11-01

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Cubic Polynomials with Real or Complex Coefficients: The Full Picture

ERIC Educational Resources Information Center

Bardell, Nicholas S.

2016-01-01

The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance…

Defense of Cyber Infrastructures Against Cyber-Physical Attacks Using Game-Theoretic Models

DOE PAGES

Rao, Nageswara S. V.; Poole, Stephen W.; Ma, Chris Y. T.; ...

2015-04-06

The operation of cyber infrastructures relies on both cyber and physical components, which are subject to incidental and intentional degradations of different kinds. Within the context of network and computing infrastructures, we study the strategic interactions between an attacker and a defender using game-theoretic models that take into account both cyber and physical components. The attacker and defender optimize their individual utilities expressed as sums of cost and system terms. First, we consider a Boolean attack-defense model, wherein the cyber and physical sub-infrastructures may be attacked and reinforced as individual units. Second, we consider a component attack-defense model wherein theirmore » components may be attacked and defended, and the infrastructure requires minimum numbers of both to function. We show that the Nash equilibrium under uniform costs in both cases is computable in polynomial time, and it provides high-level deterministic conditions for the infrastructure survival. When probabilities of successful attack and defense, and of incidental failures are incorporated into the models, the results favor the attacker but otherwise remain qualitatively similar. This approach has been motivated and validated by our experiences with UltraScience Net infrastructure, which was built to support high-performance network experiments. In conclusion, the analytical results, however, are more general, and we apply them to simplified models of cloud and high-performance computing infrastructures.« less

Defense of Cyber Infrastructures Against Cyber-Physical Attacks Using Game-Theoretic Models

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

Rao, Nageswara S. V.; Poole, Stephen W.; Ma, Chris Y. T.

The operation of cyber infrastructures relies on both cyber and physical components, which are subject to incidental and intentional degradations of different kinds. Within the context of network and computing infrastructures, we study the strategic interactions between an attacker and a defender using game-theoretic models that take into account both cyber and physical components. The attacker and defender optimize their individual utilities expressed as sums of cost and system terms. First, we consider a Boolean attack-defense model, wherein the cyber and physical sub-infrastructures may be attacked and reinforced as individual units. Second, we consider a component attack-defense model wherein theirmore » components may be attacked and defended, and the infrastructure requires minimum numbers of both to function. We show that the Nash equilibrium under uniform costs in both cases is computable in polynomial time, and it provides high-level deterministic conditions for the infrastructure survival. When probabilities of successful attack and defense, and of incidental failures are incorporated into the models, the results favor the attacker but otherwise remain qualitatively similar. This approach has been motivated and validated by our experiences with UltraScience Net infrastructure, which was built to support high-performance network experiments. In conclusion, the analytical results, however, are more general, and we apply them to simplified models of cloud and high-performance computing infrastructures.« less

Defense of Cyber Infrastructures Against Cyber-Physical Attacks Using Game-Theoretic Models.

PubMed

Rao, Nageswara S V; Poole, Stephen W; Ma, Chris Y T; He, Fei; Zhuang, Jun; Yau, David K Y

2016-04-01

The operation of cyber infrastructures relies on both cyber and physical components, which are subject to incidental and intentional degradations of different kinds. Within the context of network and computing infrastructures, we study the strategic interactions between an attacker and a defender using game-theoretic models that take into account both cyber and physical components. The attacker and defender optimize their individual utilities, expressed as sums of cost and system terms. First, we consider a Boolean attack-defense model, wherein the cyber and physical subinfrastructures may be attacked and reinforced as individual units. Second, we consider a component attack-defense model wherein their components may be attacked and defended, and the infrastructure requires minimum numbers of both to function. We show that the Nash equilibrium under uniform costs in both cases is computable in polynomial time, and it provides high-level deterministic conditions for the infrastructure survival. When probabilities of successful attack and defense, and of incidental failures, are incorporated into the models, the results favor the attacker but otherwise remain qualitatively similar. This approach has been motivated and validated by our experiences with UltraScience Net infrastructure, which was built to support high-performance network experiments. The analytical results, however, are more general, and we apply them to simplified models of cloud and high-performance computing infrastructures. © 2015 Society for Risk Analysis.

Power of one nonclean qubit

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke; Nishimura, Harumichi

2017-04-01

The one-clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single qubit of the initial state is pure and others are maximally mixed. Although the model is not universal, it can efficiently solve several problems whose classical efficient solutions are not known. Furthermore, it was recently shown that if the one-clean qubit model is classically efficiently simulated, the polynomial hierarchy collapses to the second level. A disadvantage of the one-clean qubit model is, however, that the clean qubit is too clean: for example, in realistic NMR experiments, polarizations are not high enough to have the perfectly pure qubit. In this paper, we consider a more realistic one-clean qubit model, where the clean qubit is not clean, but depolarized. We first show that, for any polarization, a multiplicative-error calculation of the output probability distribution of the model is possible in a classical polynomial time if we take an appropriately large multiplicative error. The result is in strong contrast with that of the ideal one-clean qubit model where the classical efficient multiplicative-error calculation (or even the sampling) with the same amount of error causes the collapse of the polynomial hierarchy. We next show that, for any polarization lower-bounded by an inverse polynomial, a classical efficient sampling (in terms of a sufficiently small multiplicative error or an exponentially small additive error) of the output probability distribution of the model is impossible unless BQP (bounded error quantum polynomial time) is contained in the second level of the polynomial hierarchy, which suggests the hardness of the classical efficient simulation of the one nonclean qubit model.

A class of generalized Ginzburg-Landau equations with random switching

NASA Astrophysics Data System (ADS)

Wu, Zheng; Yin, George; Lei, Dongxia

2018-09-01

This paper focuses on a class of generalized Ginzburg-Landau equations with random switching. In our formulation, the nonlinear term is allowed to have higher polynomial growth rate than the usual cubic polynomials. The random switching is modeled by a continuous-time Markov chain with a finite state space. First, an explicit solution is obtained. Then properties such as stochastic-ultimate boundedness and permanence of the solution processes are investigated. Finally, two-time-scale models are examined leading to a reduction of complexity.

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

NASA Astrophysics Data System (ADS)

Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan

2018-05-01

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.

Distinct Sources of Deterministic and Stochastic Components of Action Timing Decisions in Rodent Frontal Cortex.

PubMed

Murakami, Masayoshi; Shteingart, Hanan; Loewenstein, Yonatan; Mainen, Zachary F

2017-05-17

The selection and timing of actions are subject to determinate influences such as sensory cues and internal state as well as to effectively stochastic variability. Although stochastic choice mechanisms are assumed by many theoretical models, their origin and mechanisms remain poorly understood. Here we investigated this issue by studying how neural circuits in the frontal cortex determine action timing in rats performing a waiting task. Electrophysiological recordings from two regions necessary for this behavior, medial prefrontal cortex (mPFC) and secondary motor cortex (M2), revealed an unexpected functional dissociation. Both areas encoded deterministic biases in action timing, but only M2 neurons reflected stochastic trial-by-trial fluctuations. This differential coding was reflected in distinct timescales of neural dynamics in the two frontal cortical areas. These results suggest a two-stage model in which stochastic components of action timing decisions are injected by circuits downstream of those carrying deterministic bias signals. Copyright © 2017 Elsevier Inc. All rights reserved.

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

PubMed

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

PubMed Central

Li, Degui; Li, Runze

2016-01-01

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory. PMID:27667894

Experimental demonstration on the deterministic quantum key distribution based on entangled photons.

PubMed

Chen, Hua; Zhou, Zhi-Yuan; Zangana, Alaa Jabbar Jumaah; Yin, Zhen-Qiang; Wu, Juan; Han, Yun-Guang; Wang, Shuang; Li, Hong-Wei; He, De-Yong; Tawfeeq, Shelan Khasro; Shi, Bao-Sen; Guo, Guang-Can; Chen, Wei; Han, Zheng-Fu

2016-02-10

As an important resource, entanglement light source has been used in developing quantum information technologies, such as quantum key distribution(QKD). There are few experiments implementing entanglement-based deterministic QKD protocols since the security of existing protocols may be compromised in lossy channels. In this work, we report on a loss-tolerant deterministic QKD experiment which follows a modified "Ping-Pong"(PP) protocol. The experiment results demonstrate for the first time that a secure deterministic QKD session can be fulfilled in a channel with an optical loss of 9 dB, based on a telecom-band entangled photon source. This exhibits a conceivable prospect of ultilizing entanglement light source in real-life fiber-based quantum communications.

Experimental demonstration on the deterministic quantum key distribution based on entangled photons

PubMed Central

Chen, Hua; Zhou, Zhi-Yuan; Zangana, Alaa Jabbar Jumaah; Yin, Zhen-Qiang; Wu, Juan; Han, Yun-Guang; Wang, Shuang; Li, Hong-Wei; He, De-Yong; Tawfeeq, Shelan Khasro; Shi, Bao-Sen; Guo, Guang-Can; Chen, Wei; Han, Zheng-Fu

2016-01-01

As an important resource, entanglement light source has been used in developing quantum information technologies, such as quantum key distribution(QKD). There are few experiments implementing entanglement-based deterministic QKD protocols since the security of existing protocols may be compromised in lossy channels. In this work, we report on a loss-tolerant deterministic QKD experiment which follows a modified “Ping-Pong”(PP) protocol. The experiment results demonstrate for the first time that a secure deterministic QKD session can be fulfilled in a channel with an optical loss of 9 dB, based on a telecom-band entangled photon source. This exhibits a conceivable prospect of ultilizing entanglement light source in real-life fiber-based quantum communications. PMID:26860582

Fitting by Orthonormal Polynomials of Silver Nanoparticles Spectroscopic Data

NASA Astrophysics Data System (ADS)

Bogdanova, Nina; Koleva, Mihaela

2018-02-01

Our original Orthonormal Polynomial Expansion Method (OPEM) in one-dimensional version is applied for first time to describe the silver nanoparticles (NPs) spectroscopic data. The weights for approximation include experimental errors in variables. In this way we construct orthonormal polynomial expansion for approximating the curve on a non equidistant point grid. The corridors of given data and criteria define the optimal behavior of searched curve. The most important subinterval of spectra data is investigated, where the minimum (surface plasmon resonance absorption) is looking for. This study describes the Ag nanoparticles produced by laser approach in a ZnO medium forming a AgNPs/ZnO nanocomposite heterostructure.

HOMFLYPT polynomial is the best quantifier for topological cascades of vortex knots

NASA Astrophysics Data System (ADS)

Ricca, Renzo L.; Liu, Xin

2018-02-01

In this paper we derive and compare numerical sequences obtained by adapted polynomials such as HOMFLYPT, Jones and Alexander-Conway for the topological cascade of vortex torus knots and links that progressively untie by a single reconnection event at a time. Two cases are considered: the alternate sequence of knots and co-oriented links (with positive crossings) and the sequence of two-component links with oppositely oriented components (negative crossings). New recurrence equations are derived and sequences of numerical values are computed. In all cases the adapted HOMFLYPT polynomial proves to be the best quantifier for the topological cascade of torus knots and links.

Venus radar mapper attitude reference quaternion

NASA Technical Reports Server (NTRS)

Lyons, D. T.

1986-01-01

Polynomial functions of time are used to specify the components of the quaternion which represents the nominal attitude of the Venus Radar mapper spacecraft during mapping. The following constraints must be satisfied in order to obtain acceptable synthetic array radar data: the nominal attitude function must have a large dynamic range, the sensor orientation must be known very accurately, the attitude reference function must use as little memory as possible, and the spacecraft must operate autonomously. Fitting polynomials to the components of the desired quaternion function is a straightforward method for providing a very dynamic nominal attitude using a minimum amount of on-board computer resources. Although the attitude from the polynomials may not be exactly the one requested by the radar designers, the polynomial coefficients are known, so they do not contribute to the attitude uncertainty. Frequent coefficient updates are not required, so the spacecraft can operate autonomously.

Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

NASA Astrophysics Data System (ADS)

Sánchez-Vizuet, Tonatiuh; Cerfon, Antoine J.

2018-02-01

We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.

INTEGRATED PROBABILISTIC AND DETERMINISTIC MODELING TECHNIQUES IN ESTIMATING EXPOSURE TO WATER-BORNE CONTAMINANTS: PART 2 PHARMACOKINETIC MODELING

EPA Science Inventory

The Total Exposure Model (TEM) uses deterministic and stochastic methods to estimate the exposure of a person performing daily activities of eating, drinking, showering, and bathing. There were 250 time histories generated, by subject with activities, for the three exposure ro...

Rigorous RG Algorithms and Area Laws for Low Energy Eigenstates in 1D

NASA Astrophysics Data System (ADS)

Arad, Itai; Landau, Zeph; Vazirani, Umesh; Vidick, Thomas

2017-11-01

One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance (Landau et al. in Nat Phys, 2015) gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unsolved, including whether there exist efficient algorithms when the ground space is degenerate (and of polynomial dimension in the system size), or for the polynomially many lowest energy states, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly( n) degenerate ground spaces and an n O(log n) algorithm for the poly( n) lowest energy states (under a mild density condition). For these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is {\\tilde{O}(nM(n))} , where M( n) is the time required to multiply two n × n matrices.

Monte Carlo simulation of induction time and metastable zone width; stochastic or deterministic?

NASA Astrophysics Data System (ADS)

Kubota, Noriaki

2018-03-01

The induction time and metastable zone width (MSZW) measured for small samples (say 1 mL or less) both scatter widely. Thus, these two are observed as stochastic quantities. Whereas, for large samples (say 1000 mL or more), the induction time and MSZW are observed as deterministic quantities. The reason for such experimental differences is investigated with Monte Carlo simulation. In the simulation, the time (under isothermal condition) and supercooling (under polythermal condition) at which a first single crystal is detected are defined as the induction time t and the MSZW ΔT for small samples, respectively. The number of crystals just at the moment of t and ΔT is unity. A first crystal emerges at random due to the intrinsic nature of nucleation, accordingly t and ΔT become stochastic. For large samples, the time and supercooling at which the number density of crystals N/V reaches a detector sensitivity (N/V)det are defined as t and ΔT for isothermal and polythermal conditions, respectively. The points of t and ΔT are those of which a large number of crystals have accumulated. Consequently, t and ΔT become deterministic according to the law of large numbers. Whether t and ΔT may stochastic or deterministic in actual experiments should not be attributed to change in nucleation mechanisms in molecular level. It could be just a problem caused by differences in the experimental definition of t and ΔT.

Thermodynamic characterization of networks using graph polynomials

NASA Astrophysics Data System (ADS)

Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.

2015-09-01

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.

Analysis of correlations and search for evidence of deterministic chaos in rhythmic motor control by the human brain

NASA Astrophysics Data System (ADS)

Roberts, Sean; Eykholt, R.; Thaut, Michael H.

2000-08-01

We investigate rhythmic finger tapping in both the presence and the absence of a metronome. We examine both the time intervals between taps and the time lags between the stimulus tones from the metronome and the response taps by the subject. We analyze the correlations in these data sets, and we search for evidence of deterministic chaos, as opposed to randomness, in the fluctuations.

Effect of Uncertainty on Deterministic Runway Scheduling

NASA Technical Reports Server (NTRS)

Gupta, Gautam; Malik, Waqar; Jung, Yoon C.

2012-01-01

Active runway scheduling involves scheduling departures for takeoffs and arrivals for runway crossing subject to numerous constraints. This paper evaluates the effect of uncertainty on a deterministic runway scheduler. The evaluation is done against a first-come- first-serve scheme. In particular, the sequence from a deterministic scheduler is frozen and the times adjusted to satisfy all separation criteria; this approach is tested against FCFS. The comparison is done for both system performance (throughput and system delay) and predictability, and varying levels of congestion are considered. The modeling of uncertainty is done in two ways: as equal uncertainty in availability at the runway as for all aircraft, and as increasing uncertainty for later aircraft. Results indicate that the deterministic approach consistently performs better than first-come-first-serve in both system performance and predictability.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Computing border bases using mutant strategies

NASA Astrophysics Data System (ADS)

Ullah, E.; Abbas Khan, S.

2014-01-01

Border bases, a generalization of Gröbner bases, have actively been addressed during recent years due to their applicability to industrial problems. In cryptography and coding theory a useful application of border based is to solve zero-dimensional systems of polynomial equations over finite fields, which motivates us for developing optimizations of the algorithms that compute border bases. In 2006, Kehrein and Kreuzer formulated the Border Basis Algorithm (BBA), an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In 2007, J. Ding et al. introduced mutant strategies bases on finding special lower degree polynomials in the ideal. The mutant strategies aim to distinguish special lower degree polynomials (mutants) from the other polynomials and give them priority in the process of generating new polynomials in the ideal. In this paper we develop hybrid algorithms that use the ideas of J. Ding et al. involving the concept of mutants to optimize the Border Basis Algorithm for solving systems of polynomial equations over finite fields. In particular, we recall a version of the Border Basis Algorithm which is actually called the Improved Border Basis Algorithm and propose two hybrid algorithms, called MBBA and IMBBA. The new mutants variants provide us space efficiency as well as time efficiency. The efficiency of these newly developed hybrid algorithms is discussed using standard cryptographic examples.

A DETERMINISTIC GEOMETRIC REPRESENTATION OF TEMPORAL RAINFALL: SENSITIVITY ANALYSIS FOR A STORM IN BOSTON. (R824780)

EPA Science Inventory

In an earlier study, Puente and Obregón [Water Resour. Res. 32(1996)2825] reported on the usage of a deterministic fractal–multifractal (FM) methodology to faithfully describe an 8.3 h high-resolution rainfall time series in Boston, gathered every 15 s ...

Utilization Bound of Non-preemptive Fixed Priority Schedulers

NASA Astrophysics Data System (ADS)

Park, Moonju; Chae, Jinseok

It is known that the schedulability of a non-preemptive task set with fixed priority can be determined in pseudo-polynomial time. However, since Rate Monotonic scheduling is not optimal for non-preemptive scheduling, the applicability of existing polynomial time tests that provide sufficient schedulability conditions, such as Liu and Layland's bound, is limited. This letter proposes a new sufficient condition for non-preemptive fixed priority scheduling that can be used for any fixed priority assignment scheme. It is also shown that the proposed schedulability test has a tighter utilization bound than existing test methods.

Discrete-Time Deterministic $Q$ -Learning: A Novel Convergence Analysis.

PubMed

Wei, Qinglai; Lewis, Frank L; Sun, Qiuye; Yan, Pengfei; Song, Ruizhuo

2017-05-01

In this paper, a novel discrete-time deterministic Q -learning algorithm is developed. In each iteration of the developed Q -learning algorithm, the iterative Q function is updated for all the state and control spaces, instead of updating for a single state and a single control in traditional Q -learning algorithm. A new convergence criterion is established to guarantee that the iterative Q function converges to the optimum, where the convergence criterion of the learning rates for traditional Q -learning algorithms is simplified. During the convergence analysis, the upper and lower bounds of the iterative Q function are analyzed to obtain the convergence criterion, instead of analyzing the iterative Q function itself. For convenience of analysis, the convergence properties for undiscounted case of the deterministic Q -learning algorithm are first developed. Then, considering the discounted factor, the convergence criterion for the discounted case is established. Neural networks are used to approximate the iterative Q function and compute the iterative control law, respectively, for facilitating the implementation of the deterministic Q -learning algorithm. Finally, simulation results and comparisons are given to illustrate the performance of the developed algorithm.

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

NASA Astrophysics Data System (ADS)

Khataybeh, S. N.; Hashim, I.

2018-04-01

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

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Trend analysis of Arctic sea ice extent

NASA Astrophysics Data System (ADS)

Silva, M. E.; Barbosa, S. M.; Antunes, Luís; Rocha, Conceição

2009-04-01

The extent of Arctic sea ice is a fundamental parameter of Arctic climate variability. In the context of climate change, the area covered by ice in the Arctic is a particularly useful indicator of recent changes in the Arctic environment. Climate models are in near universal agreement that Arctic sea ice extent will decline through the 21st century as a consequence of global warming and many studies predict a ice free Arctic as soon as 2012. Time series of satellite passive microwave observations allow to assess the temporal changes in the extent of Arctic sea ice. Much of the analysis of the ice extent time series, as in most climate studies from observational data, have been focussed on the computation of deterministic linear trends by ordinary least squares. However, many different processes, including deterministic, unit root and long-range dependent processes can engender trend like features in a time series. Several parametric tests have been developed, mainly in econometrics, to discriminate between stationarity (no trend), deterministic trend and stochastic trends. Here, these tests are applied in the trend analysis of the sea ice extent time series available at National Snow and Ice Data Center. The parametric stationary tests, Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and the KPSS, do not support an overall deterministic trend in the time series of Arctic sea ice extent. Therefore, alternative parametrizations such as long-range dependence should be considered for characterising long-term Arctic sea ice variability.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography

NASA Astrophysics Data System (ADS)

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography.

PubMed

Xie, Hong-Bo; Dokos, Socrates

2013-06-01

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

Deterministic and efficient quantum cryptography based on Bell's theorem

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

Chen Zengbing; Pan Jianwei; Physikalisches Institut, Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg

2006-05-15

We propose a double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation, and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similar to the six-state protocol, under individual attacks. Our scheme allows a robust implementation under the current technology.

Extraction of angle deterministic signals in the presence of stationary speed fluctuations with cyclostationary blind source separation

NASA Astrophysics Data System (ADS)

Delvecchio, S.; Antoni, J.

2012-02-01

This paper addresses the use of a cyclostationary blind source separation algorithm (namely RRCR) to extract angle deterministic signals from mechanical rotating machines in presence of stationary speed fluctuations. This means that only phase fluctuations while machine is running in steady-state conditions are considered while run-up or run-down speed variations are not taken into account. The machine is also supposed to run in idle conditions so non-stationary phenomena due to the load are not considered. It is theoretically assessed that in such operating conditions the deterministic (periodic) signal in the angle domain becomes cyclostationary at first and second orders in the time domain. This fact justifies the use of the RRCR algorithm, which is able to directly extract the angle deterministic signal from the time domain without performing any kind of interpolation. This is particularly valuable when angular resampling fails because of uncontrolled speed fluctuations. The capability of the proposed approach is verified by means of simulated and actual vibration signals captured on a pneumatic screwdriver handle. In this particular case not only the extraction of the angle deterministic part can be performed but also the separation of the main sources of excitation (i.e. motor shaft imbalance, epyciloidal gear meshing and air pressure forces) affecting the user hand during operations.

An Extension of the Time-Spectral Method to Overset Solvers

NASA Technical Reports Server (NTRS)

Leffell, Joshua Isaac; Murman, Scott M.; Pulliam, Thomas

2013-01-01

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Linear and evolutionary polynomial regression models to forecast coastal dynamics: Comparison and reliability assessment

NASA Astrophysics Data System (ADS)

Bruno, Delia Evelina; Barca, Emanuele; Goncalves, Rodrigo Mikosz; de Araujo Queiroz, Heithor Alexandre; Berardi, Luigi; Passarella, Giuseppe

2018-01-01

In this paper, the Evolutionary Polynomial Regression data modelling strategy has been applied to study small scale, short-term coastal morphodynamics, given its capability for treating a wide database of known information, non-linearly. Simple linear and multilinear regression models were also applied to achieve a balance between the computational load and reliability of estimations of the three models. In fact, even though it is easy to imagine that the more complex the model, the more the prediction improves, sometimes a "slight" worsening of estimations can be accepted in exchange for the time saved in data organization and computational load. The models' outcomes were validated through a detailed statistical, error analysis, which revealed a slightly better estimation of the polynomial model with respect to the multilinear model, as expected. On the other hand, even though the data organization was identical for the two models, the multilinear one required a simpler simulation setting and a faster run time. Finally, the most reliable evolutionary polynomial regression model was used in order to make some conjecture about the uncertainty increase with the extension of extrapolation time of the estimation. The overlapping rate between the confidence band of the mean of the known coast position and the prediction band of the estimated position can be a good index of the weakness in producing reliable estimations when the extrapolation time increases too much. The proposed models and tests have been applied to a coastal sector located nearby Torre Colimena in the Apulia region, south Italy.

Algorithm for Compressing Time-Series Data

NASA Technical Reports Server (NTRS)

Hawkins, S. Edward, III; Darlington, Edward Hugo

2012-01-01

An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

Deterministic chaos in entangled eigenstates

NASA Astrophysics Data System (ADS)

Schlegel, K. G.; Förster, S.

2008-05-01

We investigate the problem of deterministic chaos in connection with entangled states using the Bohmian formulation of quantum mechanics. We show for a two particle system in a harmonic oscillator potential, that in a case of entanglement and three energy eigen-values the maximum Lyapunov-parameters of a representative ensemble of trajectories for large times develops to a narrow positive distribution, which indicates nearly complete chaotic dynamics. We also present in short results from two time-dependent systems, the anisotropic and the Rabi oscillator.

Satellite Orbit Theory for a Small Computer.

DTIC Science & Technology

1983-12-15

them across the pass. . Both sets of interpolating polynomials are finally used to provide osculating orbital elements at arbitrary times during the...polyno-iials are established for themt across the mass. Both sets of inter- polating polynomials are finally used to provide osculating orbital elements ...high Drecisicn orbital elements at epoch, a correspond ing set of initial mean eleme-nts must be determined for the samianalytical model. It is importan

Predicting Physical Time Series Using Dynamic Ridge Polynomial Neural Networks

PubMed Central

Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir

2014-01-01

Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques. PMID:25157950

Predicting physical time series using dynamic ridge polynomial neural networks.

PubMed

Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir

2014-01-01

Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques.

Sensor selection cost optimisation for tracking structurally cyclic systems: a P-order solution

NASA Astrophysics Data System (ADS)

Doostmohammadian, M.; Zarrabi, H.; Rabiee, H. R.

2017-08-01

Measurements and sensing implementations impose certain cost in sensor networks. The sensor selection cost optimisation is the problem of minimising the sensing cost of monitoring a physical (or cyber-physical) system. Consider a given set of sensors tracking states of a dynamical system for estimation purposes. For each sensor assume different costs to measure different (realisable) states. The idea is to assign sensors to measure states such that the global cost is minimised. The number and selection of sensor measurements need to ensure the observability to track the dynamic state of the system with bounded estimation error. The main question we address is how to select the state measurements to minimise the cost while satisfying the observability conditions. Relaxing the observability condition for structurally cyclic systems, the main contribution is to propose a graph theoretic approach to solve the problem in polynomial time. Note that polynomial time algorithms are suitable for large-scale systems as their running time is upper-bounded by a polynomial expression in the size of input for the algorithm. We frame the problem as a linear sum assignment with solution complexity of ?.

Online Removal of Baseline Shift with a Polynomial Function for Hemodynamic Monitoring Using Near-Infrared Spectroscopy.

PubMed

Zhao, Ke; Ji, Yaoyao; Li, Yan; Li, Ting

2018-01-21

Near-infrared spectroscopy (NIRS) has become widely accepted as a valuable tool for noninvasively monitoring hemodynamics for clinical and diagnostic purposes. Baseline shift has attracted great attention in the field, but there has been little quantitative study on baseline removal. Here, we aimed to study the baseline characteristics of an in-house-built portable medical NIRS device over a long time (>3.5 h). We found that the measured baselines all formed perfect polynomial functions on phantom tests mimicking human bodies, which were identified by recent NIRS studies. More importantly, our study shows that the fourth-order polynomial function acted to distinguish performance with stable and low-computation-burden fitting calibration (R-square >0.99 for all probes) among second- to sixth-order polynomials, evaluated by the parameters R-square, sum of squares due to error, and residual. This study provides a straightforward, efficient, and quantitatively evaluated solution for online baseline removal for hemodynamic monitoring using NIRS devices.

Peculiarities of stochastic regime of Arctic ice cover time evolution over 1987-2014 from microwave satellite sounding on the basis of NASA team 2 algorithm

NASA Astrophysics Data System (ADS)

Raev, M. D.; Sharkov, E. A.; Tikhonov, V. V.; Repina, I. A.; Komarova, N. Yu.

2015-12-01

The GLOBAL-RT database (DB) is composed of long-term radio heat multichannel observation data received from DMSP F08-F17 satellites; it is permanently supplemented with new data on the Earth's exploration from the space department of the Space Research Institute, Russian Academy of Sciences. Arctic ice-cover areas for regions higher than 60° N latitude were calculated using the DB polar version and NASA Team 2 algorithm, which is widely used in foreign scientific literature. According to the analysis of variability of Arctic ice cover during 1987-2014, 2 months were selected when the Arctic ice cover was maximal (February) and minimal (September), and the average ice cover area was calculated for these months. Confidence intervals of the average values are in the 95-98% limits. Several approximations are derived for the time dependences of the ice-cover maximum and minimum over the period under study. Regression dependences were calculated for polynomials from the first degree (linear) to sextic. It was ascertained that the minimal root-mean-square error of deviation from the approximated curve sharply decreased for the biquadratic polynomial and then varied insignificantly: from 0.5593 for the polynomial of third degree to 0.4560 for the biquadratic polynomial. Hence, the commonly used strictly linear regression with a negative time gradient for the September Arctic ice cover minimum over 30 years should be considered incorrect.

Improved teaching-learning-based and JAYA optimization algorithms for solving flexible flow shop scheduling problems

NASA Astrophysics Data System (ADS)

Buddala, Raviteja; Mahapatra, Siba Sankar

2017-11-01

Flexible flow shop (or a hybrid flow shop) scheduling problem is an extension of classical flow shop scheduling problem. In a simple flow shop configuration, a job having `g' operations is performed on `g' operation centres (stages) with each stage having only one machine. If any stage contains more than one machine for providing alternate processing facility, then the problem becomes a flexible flow shop problem (FFSP). FFSP which contains all the complexities involved in a simple flow shop and parallel machine scheduling problems is a well-known NP-hard (Non-deterministic polynomial time) problem. Owing to high computational complexity involved in solving these problems, it is not always possible to obtain an optimal solution in a reasonable computation time. To obtain near-optimal solutions in a reasonable computation time, a large variety of meta-heuristics have been proposed in the past. However, tuning algorithm-specific parameters for solving FFSP is rather tricky and time consuming. To address this limitation, teaching-learning-based optimization (TLBO) and JAYA algorithm are chosen for the study because these are not only recent meta-heuristics but they do not require tuning of algorithm-specific parameters. Although these algorithms seem to be elegant, they lose solution diversity after few iterations and get trapped at the local optima. To alleviate such drawback, a new local search procedure is proposed in this paper to improve the solution quality. Further, mutation strategy (inspired from genetic algorithm) is incorporated in the basic algorithm to maintain solution diversity in the population. Computational experiments have been conducted on standard benchmark problems to calculate makespan and computational time. It is found that the rate of convergence of TLBO is superior to JAYA. From the results, it is found that TLBO and JAYA outperform many algorithms reported in the literature and can be treated as efficient methods for solving the FFSP.

Real-Time Curvature Defect Detection on Outer Surfaces Using Best-Fit Polynomial Interpolation

PubMed Central

Golkar, Ehsan; Prabuwono, Anton Satria; Patel, Ahmed

2012-01-01

This paper presents a novel, real-time defect detection system, based on a best-fit polynomial interpolation, that inspects the conditions of outer surfaces. The defect detection system is an enhanced feature extraction method that employs this technique to inspect the flatness, waviness, blob, and curvature faults of these surfaces. The proposed method has been performed, tested, and validated on numerous pipes and ceramic tiles. The results illustrate that the physical defects such as abnormal, popped-up blobs are recognized completely, and that flames, waviness, and curvature faults are detected simultaneously. PMID:23202186

Tool wear modeling using abductive networks

NASA Astrophysics Data System (ADS)

Masory, Oren

1992-09-01

A tool wear model based on Abductive Networks, which consists of a network of `polynomial' nodes, is described. The model relates the cutting parameters, components of the cutting force, and machining time to flank wear. Thus real time measurements of the cutting force can be used to monitor the machining process. The model is obtained by a training process in which the connectivity between the network's nodes and the polynomial coefficients of each node are determined by optimizing a performance criteria. Actual wear measurements of coated and uncoated carbide inserts were used for training and evaluating the established model.

Optical solver of combinatorial problems: nanotechnological approach.

PubMed

Cohen, Eyal; Dolev, Shlomi; Frenkel, Sergey; Kryzhanovsky, Boris; Palagushkin, Alexandr; Rosenblit, Michael; Zakharov, Victor

2013-09-01

We present an optical computing system to solve NP-hard problems. As nano-optical computing is a promising venue for the next generation of computers performing parallel computations, we investigate the application of submicron, or even subwavelength, computing device designs. The system utilizes a setup of exponential sized masks with exponential space complexity produced in polynomial time preprocessing. The masks are later used to solve the problem in polynomial time. The size of the masks is reduced to nanoscaled density. Simulations were done to choose a proper design, and actual implementations show the feasibility of such a system.

Event-Triggered Fault Detection of Nonlinear Networked Systems.

PubMed

Li, Hongyi; Chen, Ziran; Wu, Ligang; Lam, Hak-Keung; Du, Haiping

2017-04-01

This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOSs) and can be solved by SOS tools in MATLAB environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

Parameter Estimation in Epidemiology: from Simple to Complex Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Ballesteros, Sebastién; Boto, João Pedro; Kooi, Bob W.; Mateus, Luís; Stollenwerk, Nico

2011-09-01

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models like multi-strain dynamics to describe the virus-host interaction in dengue fever, even most recently developed parameter estimation techniques, like maximum likelihood iterated filtering, come to their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

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.

A dimension-wise analysis method for the structural-acoustic system with interval parameters

NASA Astrophysics Data System (ADS)

Xu, Menghui; Du, Jianke; Wang, Chong; Li, Yunlong

2017-04-01

The interval structural-acoustic analysis is mainly accomplished by interval and subinterval perturbation methods. Potential limitations for these intrusive methods include overestimation or interval translation effect for the former and prohibitive computational cost for the latter. In this paper, a dimension-wise analysis method is thus proposed to overcome these potential limitations. In this method, a sectional curve of the system response surface along each input dimensionality is firstly extracted, the minimal and maximal points of which are identified based on its Legendre polynomial approximation. And two input vectors, i.e. the minimal and maximal input vectors, are dimension-wisely assembled by the minimal and maximal points of all sectional curves. Finally, the lower and upper bounds of system response are computed by deterministic finite element analysis at the two input vectors. Two numerical examples are studied to demonstrate the effectiveness of the proposed method and show that, compared to the interval and subinterval perturbation method, a better accuracy is achieved without much compromise on efficiency by the proposed method, especially for nonlinear problems with large interval parameters.

Mixed Legendre moments and discrete scattering cross sections for anisotropy representation

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

Calloo, A.; Vidal, J. F.; Le Tellier, R.

2012-07-01

This paper deals with the resolution of the integro-differential form of the Boltzmann transport equation for neutron transport in nuclear reactors. In multigroup theory, deterministic codes use transfer cross sections which are expanded on Legendre polynomials. This modelling leads to negative values of the transfer cross section for certain scattering angles, and hence, the multigroup scattering source term is wrongly computed. The first part compares the convergence of 'Legendre-expanded' cross sections with respect to the order used with the method of characteristics (MOC) for Pressurised Water Reactor (PWR) type cells. Furthermore, the cross section is developed using piecewise-constant functions, whichmore » better models the multigroup transfer cross section and prevents the occurrence of any negative value for it. The second part focuses on the method of solving the transport equation with the above-mentioned piecewise-constant cross sections for lattice calculations for PWR cells. This expansion thereby constitutes a 'reference' method to compare the conventional Legendre expansion to, and to determine its pertinence when applied to reactor physics calculations. (authors)« less

multiUQ: An intrusive uncertainty quantification tool for gas-liquid multiphase flows

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2017-11-01

Uncertainty quantification (UQ) can improve our understanding of the sensitivity of gas-liquid multiphase flows to variability about inflow conditions and fluid properties, creating a valuable tool for engineers. While non-intrusive UQ methods (e.g., Monte Carlo) are simple and robust, the cost associated with these techniques can render them unrealistic. In contrast, intrusive UQ techniques modify the governing equations by replacing deterministic variables with stochastic variables, adding complexity, but making UQ cost effective. Our numerical framework, called multiUQ, introduces an intrusive UQ approach for gas-liquid flows, leveraging a polynomial chaos expansion of the stochastic variables: density, momentum, pressure, viscosity, and surface tension. The gas-liquid interface is captured using a conservative level set approach, including a modified reinitialization equation which is robust and quadrature free. A least-squares method is leveraged to compute the stochastic interface normal and curvature needed in the continuum surface force method for surface tension. The solver is tested by applying uncertainty to one or two variables and verifying results against the Monte Carlo approach. NSF Grant #1511325.

Deterministic analysis of extrinsic and intrinsic noise in an epidemiological model.

PubMed

Bayati, Basil S

2016-05-01

We couple a stochastic collocation method with an analytical expansion of the canonical epidemiological master equation to analyze the effects of both extrinsic and intrinsic noise. It is shown that depending on the distribution of the extrinsic noise, the master equation yields quantitatively different results compared to using the expectation of the distribution for the stochastic parameter. This difference is incident to the nonlinear terms in the master equation, and we show that the deviation away from the expectation of the extrinsic noise scales nonlinearly with the variance of the distribution. The method presented here converges linearly with respect to the number of particles in the system and exponentially with respect to the order of the polynomials used in the stochastic collocation calculation. This makes the method presented here more accurate than standard Monte Carlo methods, which suffer from slow, nonmonotonic convergence. In epidemiological terms, the results show that extrinsic fluctuations should be taken into account since they effect the speed of disease breakouts and that the gamma distribution should be used to model the basic reproductive number.

Optimization Under Uncertainty for Wake Steering Strategies

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

Quick, Julian; Annoni, Jennifer; King, Ryan N

Offsetting turbines' yaw orientations from incoming wind is a powerful tool that may be leveraged to reduce undesirable wake effects on downstream turbines. First, we examine a simple two-turbine case to gain intuition as to how inflow direction uncertainty affects the optimal solution. The turbines are modeled with unidirectional inflow such that one turbine directly wakes the other, using ten rotor diameter spacing. We perform optimization under uncertainty (OUU) via a parameter sweep of the front turbine. The OUU solution generally prefers less steering. We then do this optimization for a 60-turbine wind farm with unidirectional inflow, varying the degreemore » of inflow uncertainty and approaching this OUU problem by nesting a polynomial chaos expansion uncertainty quantification routine within an outer optimization. We examined how different levels of uncertainty in the inflow direction effect the ratio of the expected values of deterministic and OUU solutions for steering strategies in the large wind farm, assuming the directional uncertainty used to reach said OUU solution (this ratio is defined as the value of the stochastic solution or VSS).« less

A stochastic model for correlated protein motions

NASA Astrophysics Data System (ADS)

Karain, Wael I.; Qaraeen, Nael I.; Ajarmah, Basem

2006-06-01

A one-dimensional Langevin-type stochastic difference equation is used to find the deterministic and Gaussian contributions of time series representing the projections of a Bovine Pancreatic Trypsin Inhibitor (BPTI) protein molecular dynamics simulation along different eigenvector directions determined using principal component analysis. The deterministic part shows a distinct nonlinear behavior only for eigenvectors contributing significantly to the collective protein motion.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Habitat connectivity and in-stream vegetation control temporal variability of benthic invertebrate communities.

PubMed

Huttunen, K-L; Mykrä, H; Oksanen, J; Astorga, A; Paavola, R; Muotka, T

2017-05-03

One of the key challenges to understanding patterns of β diversity is to disentangle deterministic patterns from stochastic ones. Stochastic processes may mask the influence of deterministic factors on community dynamics, hindering identification of the mechanisms causing variation in community composition. We studied temporal β diversity (among-year dissimilarity) of macroinvertebrate communities in near-pristine boreal streams across 14 years. To assess whether the observed β diversity deviates from that expected by chance, and to identify processes (deterministic vs. stochastic) through which different explanatory factors affect community variability, we used a null model approach. We observed that at the majority of sites temporal β diversity was low indicating high community stability. When stochastic variation was unaccounted for, connectivity was the only variable explaining temporal β diversity, with weakly connected sites exhibiting higher community variability through time. After accounting for stochastic effects, connectivity lost importance, suggesting that it was related to temporal β diversity via random colonization processes. Instead, β diversity was best explained by in-stream vegetation, community variability decreasing with increasing bryophyte cover. These results highlight the potential of stochastic factors to dampen the influence of deterministic processes, affecting our ability to understand and predict changes in biological communities through time.

Dual Roles for Spike Signaling in Cortical Neural Populations

PubMed Central

Ballard, Dana H.; Jehee, Janneke F. M.

2011-01-01

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding. PMID:21687798

Kernelization

NASA Astrophysics Data System (ADS)

Fomin, Fedor V.

Preprocessing (data reduction or kernelization) as a strategy of coping with hard problems is universally used in almost every implementation. The history of preprocessing, like applying reduction rules simplifying truth functions, can be traced back to the 1950's [6]. A natural question in this regard is how to measure the quality of preprocessing rules proposed for a specific problem. For a long time the mathematical analysis of polynomial time preprocessing algorithms was neglected. The basic reason for this anomaly was that if we start with an instance I of an NP-hard problem and can show that in polynomial time we can replace this with an equivalent instance I' with |I'| < |I| then that would imply P=NP in classical complexity.

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

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

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

Discrete Deterministic and Stochastic Petri Nets

NASA Technical Reports Server (NTRS)

Zijal, Robert; Ciardo, Gianfranco

1996-01-01

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

Hybrid stochastic and deterministic simulations of calcium blips.

PubMed

Rüdiger, S; Shuai, J W; Huisinga, W; Nagaiah, C; Warnecke, G; Parker, I; Falcke, M

2007-09-15

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.

Application of overlay modeling and control with Zernike polynomials in an HVM environment

NASA Astrophysics Data System (ADS)

Ju, JaeWuk; Kim, MinGyu; Lee, JuHan; Nabeth, Jeremy; Jeon, Sanghuck; Heo, Hoyoung; Robinson, John C.; Pierson, Bill

2016-03-01

Shrinking technology nodes and smaller process margins require improved photolithography overlay control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for both intra-field and inter-field models and the model coefficients are sent to an advanced process control (APC) system operating in an XY Cartesian basis. Dampened overlay corrections, typically via exponentially or linearly weighted moving average in time, are then retrieved from the APC system to apply on the scanner in XY Cartesian form for subsequent lot exposure. The goal of the above method is to process lots with corrections that target the least possible overlay misregistration in steady state as well as in change point situations. In this study, we model overlay errors on product using Zernike polynomials with same fitting capability as the process of reference (POR) to represent the wafer-level terms, and use the standard Cartesian polynomials to represent the field-level terms. APC calculations for wafer-level correction are performed in Zernike basis while field-level calculations use standard XY Cartesian basis. Finally, weighted wafer-level correction terms are converted to XY Cartesian space in order to be applied on the scanner, along with field-level corrections, for future wafer exposures. Since Zernike polynomials have the property of being orthogonal in the unit disk we are able to reduce the amount of collinearity between terms and improve overlay stability. Our real time Zernike modeling and feedback evaluation was performed on a 20-lot dataset in a high volume manufacturing (HVM) environment. The measured on-product results were compared to POR and showed a 7% reduction in overlay variation including a 22% terms variation. This led to an on-product raw overlay Mean + 3Sigma X&Y improvement of 5% and resulted in 0.1% yield improvement.

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Dumbser, Michael

2016-01-01

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER schemes provide less oscillatory solutions when compared to ADER finite volume schemes based on the reconstruction in conserved variables, especially for the RMHD and the Baer-Nunziato equations. For the RHD and RMHD equations, the overall accuracy is improved and the CPU time is reduced by about 25 %. Because of its increased accuracy and due to the reduced computational cost, we recommend to use this version of ADER as the standard one in the relativistic framework. At the end of the paper, the new approach has also been extended to ADER-DG schemes on space-time adaptive grids (AMR).

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

PubMed

Mahajan, Virendra N

2012-06-20

In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as they do not represent balanced aberrations for such a system.

Diffusion in Deterministic Interacting Lattice Systems

NASA Astrophysics Data System (ADS)

Medenjak, Marko; Klobas, Katja; Prosen, Tomaž

2017-09-01

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

Deterministic filtering of breakdown flashing at telecom wavelengths

NASA Astrophysics Data System (ADS)

Marini, Loris; Camphausen, Robin; Eggleton, Benjamin J.; Palomba, Stefano

2017-11-01

Breakdown flashes are undesired photo-emissions from the active area of single-photon avalanche photo-diodes. They arise from radiative recombinations of hot carriers generated during an avalanche and can induce crosstalk, compromise the measurement of optical quantum states, and hinder the security of quantum communications. Although the spectrum of this emission extends over hundreds of nanometers, active quenching may lead to a smaller uncertainty in the time of emission, thus enabling deterministic filtering. Our results pave the way to broadband interference mitigation in time-correlated single-photon applications.

Dynamic response analysis of structure under time-variant interval process model

NASA Astrophysics Data System (ADS)

Xia, Baizhan; Qin, Yuan; Yu, Dejie; Jiang, Chao

2016-10-01

Due to the aggressiveness of the environmental factor, the variation of the dynamic load, the degeneration of the material property and the wear of the machine surface, parameters related with the structure are distinctly time-variant. Typical model for time-variant uncertainties is the random process model which is constructed on the basis of a large number of samples. In this work, we propose a time-variant interval process model which can be effectively used to deal with time-variant uncertainties with limit information. And then two methods are presented for the dynamic response analysis of the structure under the time-variant interval process model. The first one is the direct Monte Carlo method (DMCM) whose computational burden is relative high. The second one is the Monte Carlo method based on the Chebyshev polynomial expansion (MCM-CPE) whose computational efficiency is high. In MCM-CPE, the dynamic response of the structure is approximated by the Chebyshev polynomials which can be efficiently calculated, and then the variational range of the dynamic response is estimated according to the samples yielded by the Monte Carlo method. To solve the dependency phenomenon of the interval operation, the affine arithmetic is integrated into the Chebyshev polynomial expansion. The computational effectiveness and efficiency of MCM-CPE is verified by two numerical examples, including a spring-mass-damper system and a shell structure.

An effective PSO-based memetic algorithm for flow shop scheduling.

PubMed

Liu, Bo; Wang, Ling; Jin, Yi-Hui

2007-02-01

This paper proposes an effective particle swarm optimization (PSO)-based memetic algorithm (MA) for the permutation flow shop scheduling problem (PFSSP) with the objective to minimize the maximum completion time, which is a typical non-deterministic polynomial-time (NP) hard combinatorial optimization problem. In the proposed PSO-based MA (PSOMA), both PSO-based searching operators and some special local searching operators are designed to balance the exploration and exploitation abilities. In particular, the PSOMA applies the evolutionary searching mechanism of PSO, which is characterized by individual improvement, population cooperation, and competition to effectively perform exploration. On the other hand, the PSOMA utilizes several adaptive local searches to perform exploitation. First, to make PSO suitable for solving PFSSP, a ranked-order value rule based on random key representation is presented to convert the continuous position values of particles to job permutations. Second, to generate an initial swarm with certain quality and diversity, the famous Nawaz-Enscore-Ham (NEH) heuristic is incorporated into the initialization of population. Third, to balance the exploration and exploitation abilities, after the standard PSO-based searching operation, a new local search technique named NEH_1 insertion is probabilistically applied to some good particles selected by using a roulette wheel mechanism with a specified probability. Fourth, to enrich the searching behaviors and to avoid premature convergence, a simulated annealing (SA)-based local search with multiple different neighborhoods is designed and incorporated into the PSOMA. Meanwhile, an effective adaptive meta-Lamarckian learning strategy is employed to decide which neighborhood to be used in SA-based local search. Finally, to further enhance the exploitation ability, a pairwise-based local search is applied after the SA-based search. Simulation results based on benchmarks demonstrate the effectiveness of the PSOMA. Additionally, the effects of some parameters on optimization performances are also discussed.

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

Combinatorial Reliability and Repair

DTIC Science & Technology

1992-07-01

Press, Oxford, 1987. [2] G. Gordon and L. Traldi, Generalized activities and the Tutte polynomial, Discrete Math . 85 (1990), 167-176. [3] A. B. Huseby, A...Chromatic polynomials and network reliability, Discrete Math . 67 (1987), 57-79. [7] A. Satayanarayana and R. K. Wood, A linear-time algorithm for comput- ing...K-terminal reliability in series-parallel networks, SIAM J. Comput. 14 (1985), 818-832. [8] L. Traldi, Generalized activities and K-terminal reliability, Discrete Math . 96 (1991), 131-149. 4

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

A Novel Multi-Receiver Signcryption Scheme with Complete Anonymity.

PubMed

Pang, Liaojun; Yan, Xuxia; Zhao, Huiyang; Hu, Yufei; Li, Huixian

2016-01-01

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender's anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided.

Byzantine-fault tolerant self-stabilizing protocol for distributed clock synchronization systems

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R. (Inventor)

2010-01-01

A rapid Byzantine self-stabilizing clock synchronization protocol that self-stabilizes from any state, tolerates bursts of transient failures, and deterministically converges within a linear convergence time with respect to the self-stabilization period. Upon self-stabilization, all good clocks proceed synchronously. The Byzantine self-stabilizing clock synchronization protocol does not rely on any assumptions about the initial state of the clocks. Furthermore, there is neither a central clock nor an externally generated pulse system. The protocol converges deterministically, is scalable, and self-stabilizes in a short amount of time. The convergence time is linear with respect to the self-stabilization period.

Sandia Higher Order Elements (SHOE) v 0.5 alpha

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

2013-09-24

SHOE is research code for characterizing and visualizing higher-order finite elements; it contains a framework for defining classes of interpolation techniques and element shapes; methods for interpolating triangular, quadrilateral, tetrahedral, and hexahedral cells using Lagrange and Legendre polynomial bases of arbitrary order; methods to decompose each element into domains of constant gradient flow (using a polynomial solver to identify critical points); and an isocontouring technique that uses this decomposition to guarantee topological correctness. Please note that this is an alpha release of research software and that some time has passed since it was actively developed; build- and run-time issues likelymore » exist.« less

Orbital component extraction by time-variant sinusoidal modeling.

NASA Astrophysics Data System (ADS)

Sinnesael, Matthias; Zivanovic, Miroslav; De Vleeschouwer, David; Claeys, Philippe; Schoukens, Johan

2016-04-01

Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on the (Fast) Fourier Transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic makes it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. Here, we circumvent this drawback by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach has been proven useful to characterize audio signals (music and speech), which are non-stationary in nature (Zivanovic and Schoukens, 2010, 2012). Paleoclimate proxy signals and audio signals have in nature similar dynamics; the only difference is the frequency relationship between the different components. A harmonic frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, the latter difference is irrelevant for the problem at hand. Using a sliding window approach, the model captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretation, whereas the latter are estimated by means of linear least-squares. As an output, the model provides the orbital component waveform, either in the depth or time domain. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns can be used to reconstruct changes in accumulation rate, whereas amplitude modulation can be used to reconstruct e.g. eccentricity-modulated precession. The time-variant sinusoidal model is applied to well-established Pleistocene benthic isotope records to evaluate its performance. Zivanovic M. and Schoukens J. (2010) On The Polynomial Approximation for Time-Variant Harmonic Signal Modeling. IEEE Transactions On Audio, Speech, and Language Processing vol. 19, no. 3, pp. 458-467. Doi: 10.1109/TASL.2010.2049673. Zivanovic M. and Schoukens J. (2012) Single and Piecewise Polynomials for Modeling of Pitched Sounds. IEEE Transactions On Audio, Speech, and Language Processing vol. 20, no. 4, pp. 1270-1281. Doi: 10.1109/TASL.2011.2174228.

Optimal Robust Motion Controller Design Using Multiobjective Genetic Algorithm

PubMed Central

Svečko, Rajko

2014-01-01

This paper describes the use of a multiobjective genetic algorithm for robust motion controller design. Motion controller structure is based on a disturbance observer in an RIC framework. The RIC approach is presented in the form with internal and external feedback loops, in which an internal disturbance rejection controller and an external performance controller must be synthesised. This paper involves novel objectives for robustness and performance assessments for such an approach. Objective functions for the robustness property of RIC are based on simple even polynomials with nonnegativity conditions. Regional pole placement method is presented with the aims of controllers' structures simplification and their additional arbitrary selection. Regional pole placement involves arbitrary selection of central polynomials for both loops, with additional admissible region of the optimized pole location. Polynomial deviation between selected and optimized polynomials is measured with derived performance objective functions. A multiobjective function is composed of different unrelated criteria such as robust stability, controllers' stability, and time-performance indexes of closed loops. The design of controllers and multiobjective optimization procedure involve a set of the objectives, which are optimized simultaneously with a genetic algorithm—differential evolution. PMID:24987749

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation

NASA Astrophysics Data System (ADS)

Oruç, Ömer

2018-04-01

In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.

New realisation of Preisach model using adaptive polynomial approximation

NASA Astrophysics Data System (ADS)

Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young

2012-09-01

Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

Extended Islands of Tractability for Parsimony Haplotyping

NASA Astrophysics Data System (ADS)

Fleischer, Rudolf; Guo, Jiong; Niedermeier, Rolf; Uhlmann, Johannes; Wang, Yihui; Weller, Mathias; Wu, Xi

Parsimony haplotyping is the problem of finding a smallest size set of haplotypes that can explain a given set of genotypes. The problem is NP-hard, and many heuristic and approximation algorithms as well as polynomial-time solvable special cases have been discovered. We propose improved fixed-parameter tractability results with respect to the parameter "size of the target haplotype set" k by presenting an O *(k 4k )-time algorithm. This also applies to the practically important constrained case, where we can only use haplotypes from a given set. Furthermore, we show that the problem becomes polynomial-time solvable if the given set of genotypes is complete, i.e., contains all possible genotypes that can be explained by the set of haplotypes.

A comparison between space-time video descriptors

NASA Astrophysics Data System (ADS)

Costantini, Luca; Capodiferro, Licia; Neri, Alessandro

2013-02-01

The description of space-time patches is a fundamental task in many applications such as video retrieval or classification. Each space-time patch can be described by using a set of orthogonal functions that represent a subspace, for example a sphere or a cylinder, within the patch. In this work, our aim is to investigate the differences between the spherical descriptors and the cylindrical descriptors. In order to compute the descriptors, the 3D spherical and cylindrical Zernike polynomials are employed. This is important because both the functions are based on the same family of polynomials, and only the symmetry is different. Our experimental results show that the cylindrical descriptor outperforms the spherical descriptor. However, the performances of the two descriptors are similar.

Equivalences of the multi-indexed orthogonal polynomials

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

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Deterministic influences exceed dispersal effects on hydrologically-connected microbiomes: Deterministic assembly of hyporheic microbiomes

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

Graham, Emily B.; Crump, Alex R.; Resch, Charles T.

2017-03-28

Subsurface zones of groundwater and surface water mixing (hyporheic zones) are regions of enhanced rates of biogeochemical cycling, yet ecological processes governing hyporheic microbiome composition and function through space and time remain unknown. We sampled attached and planktonic microbiomes in the Columbia River hyporheic zone across seasonal hydrologic change, and employed statistical null models to infer mechanisms generating temporal changes in microbiomes within three hydrologically-connected, physicochemically-distinct geographic zones (inland, nearshore, river). We reveal that microbiomes remain dissimilar through time across all zones and habitat types (attached vs. planktonic) and that deterministic assembly processes regulate microbiome composition in all data subsets.more » The consistent presence of heterotrophic taxa and members of the Planctomycetes-Verrucomicrobia-Chlamydiae (PVC) superphylum nonetheless suggests common selective pressures for physiologies represented in these groups. Further, co-occurrence networks were used to provide insight into taxa most affected by deterministic assembly processes. We identified network clusters to represent groups of organisms that correlated with seasonal and physicochemical change. Extended network analyses identified keystone taxa within each cluster that we propose are central in microbiome composition and function. Finally, the abundance of one network cluster of nearshore organisms exhibited a seasonal shift from heterotrophic to autotrophic metabolisms and correlated with microbial metabolism, possibly indicating an ecological role for these organisms as foundational species in driving biogeochemical reactions within the hyporheic zone. Taken together, our research demonstrates a predominant role for deterministic assembly across highly-connected environments and provides insight into niche dynamics associated with seasonal changes in hyporheic microbiome composition and metabolism.« less

Theory and applications of a deterministic approximation to the coalescent model

PubMed Central

Jewett, Ethan M.; Rosenberg, Noah A.

2014-01-01

Under the coalescent model, the random number nt of lineages ancestral to a sample is nearly deterministic as a function of time when nt is moderate to large in value, and it is well approximated by its expectation E[nt]. In turn, this expectation is well approximated by simple deterministic functions that are easy to compute. Such deterministic functions have been applied to estimate allele age, effective population size, and genetic diversity, and they have been used to study properties of models of infectious disease dynamics. Although a number of simple approximations of E[nt] have been derived and applied to problems of population-genetic inference, the theoretical accuracy of the formulas and the inferences obtained using these approximations is not known, and the range of problems to which they can be applied is not well understood. Here, we demonstrate general procedures by which the approximation nt ≈ E[nt] can be used to reduce the computational complexity of coalescent formulas, and we show that the resulting approximations converge to their true values under simple assumptions. Such approximations provide alternatives to exact formulas that are computationally intractable or numerically unstable when the number of sampled lineages is moderate or large. We also extend an existing class of approximations of E[nt] to the case of multiple populations of time-varying size with migration among them. Our results facilitate the use of the deterministic approximation nt ≈ E[nt] for deriving functionally simple, computationally efficient, and numerically stable approximations of coalescent formulas under complicated demographic scenarios. PMID:24412419

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Renewable energy in electric utility capacity planning: a decomposition approach with application to a Mexican utility

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

Staschus, K.

1985-01-01

In this dissertation, efficient algorithms for electric-utility capacity expansion planning with renewable energy are developed. The algorithms include a deterministic phase that quickly finds a near-optimal expansion plan using derating and a linearized approximation to the time-dependent availability of nondispatchable energy sources. A probabilistic second phase needs comparatively few computer-time consuming probabilistic simulation iterations to modify this solution towards the optimal expansion plan. For the deterministic first phase, two algorithms, based on a Lagrangian Dual decomposition and a Generalized Benders Decomposition, are developed. The probabilistic second phase uses a Generalized Benders Decomposition approach. Extensive computational tests of the algorithms aremore » reported. Among the deterministic algorithms, the one based on Lagrangian Duality proves fastest. The two-phase approach is shown to save up to 80% in computing time as compared to a purely probabilistic algorithm. The algorithms are applied to determine the optimal expansion plan for the Tijuana-Mexicali subsystem of the Mexican electric utility system. A strong recommendation to push conservation programs in the desert city of Mexicali results from this implementation.« less

Time Domain and Frequency Domain Deterministic Channel Modeling for Tunnel/Mining Environments.

PubMed

Zhou, Chenming; Jacksha, Ronald; Yan, Lincan; Reyes, Miguel; Kovalchik, Peter

2017-01-01

Understanding wireless channels in complex mining environments is critical for designing optimized wireless systems operated in these environments. In this paper, we propose two physics-based, deterministic ultra-wideband (UWB) channel models for characterizing wireless channels in mining/tunnel environments - one in the time domain and the other in the frequency domain. For the time domain model, a general Channel Impulse Response (CIR) is derived and the result is expressed in the classic UWB tapped delay line model. The derived time domain channel model takes into account major propagation controlling factors including tunnel or entry dimensions, frequency, polarization, electrical properties of the four tunnel walls, and transmitter and receiver locations. For the frequency domain model, a complex channel transfer function is derived analytically. Based on the proposed physics-based deterministic channel models, channel parameters such as delay spread, multipath component number, and angular spread are analyzed. It is found that, despite the presence of heavy multipath, both channel delay spread and angular spread for tunnel environments are relatively smaller compared to that of typical indoor environments. The results and findings in this paper have application in the design and deployment of wireless systems in underground mining environments.

Time Domain and Frequency Domain Deterministic Channel Modeling for Tunnel/Mining Environments

PubMed Central

Zhou, Chenming; Jacksha, Ronald; Yan, Lincan; Reyes, Miguel; Kovalchik, Peter

2018-01-01

Understanding wireless channels in complex mining environments is critical for designing optimized wireless systems operated in these environments. In this paper, we propose two physics-based, deterministic ultra-wideband (UWB) channel models for characterizing wireless channels in mining/tunnel environments — one in the time domain and the other in the frequency domain. For the time domain model, a general Channel Impulse Response (CIR) is derived and the result is expressed in the classic UWB tapped delay line model. The derived time domain channel model takes into account major propagation controlling factors including tunnel or entry dimensions, frequency, polarization, electrical properties of the four tunnel walls, and transmitter and receiver locations. For the frequency domain model, a complex channel transfer function is derived analytically. Based on the proposed physics-based deterministic channel models, channel parameters such as delay spread, multipath component number, and angular spread are analyzed. It is found that, despite the presence of heavy multipath, both channel delay spread and angular spread for tunnel environments are relatively smaller compared to that of typical indoor environments. The results and findings in this paper have application in the design and deployment of wireless systems in underground mining environments.† PMID:29457801

Complex Analysis and Related Topics. Proceedings of the Conference held in Amsterdam on 27 - 29 January 1993

DTIC Science & Technology

1993-01-29

Bessel functions and Jacobi functions (cf. [2]). References [1] R. Askey & J. Wilson, Some basic hypergeometric orthogonal polynomials that gen- eralize...1; 1] can be treated as a part of general theory of T-systems (see [81 for that theory and [7] for some aspects of the Chebyshev polynomials theory...waves in elastic media. It has been known for some time that these multiplicities sometimes occur for topological reasons and are present generically , see

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

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

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

2011-04-15

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

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Robust planning of dynamic wireless charging infrastructure for battery electric buses

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

Liu, Zhaocai; Song, Ziqi

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

Robust planning of dynamic wireless charging infrastructure for battery electric buses

DOE PAGES

Liu, Zhaocai; Song, Ziqi

2017-10-01

Battery electric buses with zero tailpipe emissions have great potential in improving environmental sustainability and livability of urban areas. However, the problems of high cost and limited range associated with on-board batteries have substantially limited the popularity of battery electric buses. The technology of dynamic wireless power transfer (DWPT), which provides bus operators with the ability to charge buses while in motion, may be able to effectively alleviate the drawbacks of electric buses. In this paper, we address the problem of simultaneously selecting the optimal location of the DWPT facilities and designing the optimal battery sizes of electric buses formore » a DWPT electric bus system. The problem is first constructed as a deterministic model in which the uncertainty of energy consumption and travel time of electric buses is neglected. The methodology of robust optimization (RO) is then adopted to address the uncertainty of energy consumption and travel time. The affinely adjustable robust counterpart (AARC) of the deterministic model is developed, and its equivalent tractable mathematical programming is derived. Both the deterministic model and the robust model are demonstrated with a real-world bus system. The results of our study demonstrate that the proposed deterministic model can effectively determine the allocation of DWPT facilities and the battery sizes of electric buses for a DWPT electric bus system; and the robust model can further provide optimal designs that are robust against the uncertainty of energy consumption and travel time for electric buses.« less

Improving ground-penetrating radar data in sedimentary rocks using deterministic deconvolution

USGS Publications Warehouse

Xia, J.; Franseen, E.K.; Miller, R.D.; Weis, T.V.; Byrnes, A.P.

2003-01-01

Resolution is key to confidently identifying unique geologic features using ground-penetrating radar (GPR) data. Source wavelet "ringing" (related to bandwidth) in a GPR section limits resolution because of wavelet interference, and can smear reflections in time and/or space. The resultant potential for misinterpretation limits the usefulness of GPR. Deconvolution offers the ability to compress the source wavelet and improve temporal resolution. Unlike statistical deconvolution, deterministic deconvolution is mathematically simple and stable while providing the highest possible resolution because it uses the source wavelet unique to the specific radar equipment. Source wavelets generated in, transmitted through and acquired from air allow successful application of deterministic approaches to wavelet suppression. We demonstrate the validity of using a source wavelet acquired in air as the operator for deterministic deconvolution in a field application using "400-MHz" antennas at a quarry site characterized by interbedded carbonates with shale partings. We collected GPR data on a bench adjacent to cleanly exposed quarry faces in which we placed conductive rods to provide conclusive groundtruth for this approach to deconvolution. The best deconvolution results, which are confirmed by the conductive rods for the 400-MHz antenna tests, were observed for wavelets acquired when the transmitter and receiver were separated by 0.3 m. Applying deterministic deconvolution to GPR data collected in sedimentary strata at our study site resulted in an improvement in resolution (50%) and improved spatial location (0.10-0.15 m) of geologic features compared to the same data processed without deterministic deconvolution. The effectiveness of deterministic deconvolution for increased resolution and spatial accuracy of specific geologic features is further demonstrated by comparing results of deconvolved data with nondeconvolved data acquired along a 30-m transect immediately adjacent to a fresh quarry face. The results at this site support using deterministic deconvolution, which incorporates the GPR instrument's unique source wavelet, as a standard part of routine GPR data processing. ?? 2003 Elsevier B.V. All rights reserved.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Coherent orthogonal polynomials

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines the corresponding OP family. •Generalized coherent polynomials are obtained from OP.« less

Rare event computation in deterministic chaotic systems using genealogical particle analysis

NASA Astrophysics Data System (ADS)

Wouters, J.; Bouchet, F.

2016-09-01

In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in deterministic dynamical systems. We demonstrate that genealogical particle analysis algorithms can be successfully applied to a toy model of atmospheric dynamics, the Lorenz ’96 model. We furthermore use the Ornstein-Uhlenbeck system to illustrate a number of implementation issues. We also show how a time-dependent objective function based on the fluctuation path to a high threshold can greatly improve the performance of the estimator compared to a fixed-in-time objective function.

Pedestrian detection in crowded scenes with the histogram of gradients principle

NASA Astrophysics Data System (ADS)

Sidla, O.; Rosner, M.; Lypetskyy, Y.

2006-10-01

This paper describes a close to real-time scale invariant implementation of a pedestrian detector system which is based on the Histogram of Oriented Gradients (HOG) principle. Salient HOG features are first selected from a manually created very large database of samples with an evolutionary optimization procedure that directly trains a polynomial Support Vector Machine (SVM). Real-time operation is achieved by a cascaded 2-step classifier which uses first a very fast linear SVM (with the same features as the polynomial SVM) to reject most of the irrelevant detections and then computes the decision function with a polynomial SVM on the remaining set of candidate detections. Scale invariance is achieved by running the detector of constant size on scaled versions of the original input images and by clustering the results over all resolutions. The pedestrian detection system has been implemented in two versions: i) fully body detection, and ii) upper body only detection. The latter is especially suited for very busy and crowded scenarios. On a state-of-the-art PC it is able to run at a frequency of 8 - 20 frames/sec.

Simple Proof of Jury Test for Complex Polynomials

NASA Astrophysics Data System (ADS)

Choo, Younseok; Kim, Dongmin

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

Probabilistic direct counterfactual quantum communication

NASA Astrophysics Data System (ADS)

Zhang, Sheng

2017-02-01

It is striking that the quantum Zeno effect can be used to launch a direct counterfactual communication between two spatially separated parties, Alice and Bob. So far, existing protocols of this type only provide a deterministic counterfactual communication service. However, this counterfactuality should be payed at a price. Firstly, the transmission time is much longer than a classical transmission costs. Secondly, the chained-cycle structure makes them more sensitive to channel noises. Here, we extend the idea of counterfactual communication, and present a probabilistic-counterfactual quantum communication protocol, which is proved to have advantages over the deterministic ones. Moreover, the presented protocol could evolve to a deterministic one solely by adjusting the parameters of the beam splitters. Project supported by the National Natural Science Foundation of China (Grant No. 61300203).

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Stochastic Multi-Timescale Power System Operations With Variable Wind Generation

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

Wu, Hongyu; Krad, Ibrahim; Florita, Anthony

This paper describes a novel set of stochastic unit commitment and economic dispatch models that consider stochastic loads and variable generation at multiple operational timescales. The stochastic model includes four distinct stages: stochastic day-ahead security-constrained unit commitment (SCUC), stochastic real-time SCUC, stochastic real-time security-constrained economic dispatch (SCED), and deterministic automatic generation control (AGC). These sub-models are integrated together such that they are continually updated with decisions passed from one to another. The progressive hedging algorithm (PHA) is applied to solve the stochastic models to maintain the computational tractability of the proposed models. Comparative case studies with deterministic approaches are conductedmore » in low wind and high wind penetration scenarios to highlight the advantages of the proposed methodology, one with perfect forecasts and the other with current state-of-the-art but imperfect deterministic forecasts. The effectiveness of the proposed method is evaluated with sensitivity tests using both economic and reliability metrics to provide a broader view of its impact.« less

A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy

NASA Astrophysics Data System (ADS)

Liu, Xiangdong; Li, Qingze; Pan, Jianxin

2018-06-01

Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.

Nonclassical point of view of the Brownian motion generation via fractional deterministic model

NASA Astrophysics Data System (ADS)

Gilardi-Velázquez, H. E.; Campos-Cantón, E.

In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.

Non-Deterministic Dynamic Instability of Composite Shells

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2004-01-01

A computationally effective method is described to evaluate the non-deterministic dynamic instability (probabilistic dynamic buckling) of thin composite shells. The method is a judicious combination of available computer codes for finite element, composite mechanics, and probabilistic structural analysis. The solution method is incrementally updated Lagrangian. It is illustrated by applying it to thin composite cylindrical shell subjected to dynamic loads. Both deterministic and probabilistic buckling loads are evaluated to demonstrate the effectiveness of the method. A universal plot is obtained for the specific shell that can be used to approximate buckling loads for different load rates and different probability levels. Results from this plot show that the faster the rate, the higher the buckling load and the shorter the time. The lower the probability, the lower is the buckling load for a specific time. Probabilistic sensitivity results show that the ply thickness, the fiber volume ratio and the fiber longitudinal modulus, dynamic load and loading rate are the dominant uncertainties, in that order.

Exploring the use of random regression models with legendre polynomials to analyze measures of volume of ejaculate in Holstein bulls.

PubMed

Carabaño, M J; Díaz, C; Ugarte, C; Serrano, M

2007-02-01

Artificial insemination centers routinely collect records of quantity and quality of semen of bulls throughout the animals' productive period. The goal of this paper was to explore the use of random regression models with orthogonal polynomials to analyze repeated measures of semen production of Spanish Holstein bulls. A total of 8,773 records of volume of first ejaculate (VFE) collected between 12 and 30 mo of age from 213 Spanish Holstein bulls was analyzed under alternative random regression models. Legendre polynomial functions of increasing order (0 to 6) were fitted to the average trajectory, additive genetic and permanent environmental effects. Age at collection and days in production were used as time variables. Heterogeneous and homogeneous residual variances were alternatively assumed. Analyses were carried out within a Bayesian framework. The logarithm of the marginal density and the cross-validation predictive ability of the data were used as model comparison criteria. Based on both criteria, age at collection as a time variable and heterogeneous residuals models are recommended to analyze changes of VFE over time. Both criteria indicated that fitting random curves for genetic and permanent environmental components as well as for the average trajector improved the quality of models. Furthermore, models with a higher order polynomial for the permanent environmental (5 to 6) than for the genetic components (4 to 5) and the average trajectory (2 to 3) tended to perform best. High-order polynomials were needed to accommodate the highly oscillating nature of the phenotypic values. Heritability and repeatability estimates, disregarding the extremes of the studied period, ranged from 0.15 to 0.35 and from 0.20 to 0.50, respectively, indicating that selection for VFE may be effective at any stage. Small differences among models were observed. Apart from the extremes, estimated correlations between ages decreased steadily from 0.9 and 0.4 for measures 1 mo apart to 0.4 and 0.2 for most distant measures for additive genetic and phenotypic components, respectively. Further investigation to account for environmental factors that may be responsible for the oscillating observations of VFE is needed.

Maximal blood flow acceleration analysis in the early diastolic phase for aortocoronary artery bypass grafts: a new transit-time flow measurement predictor of graft failure following coronary artery bypass grafting.

PubMed

Handa, Takemi; Orihashi, Kazumasa; Nishimori, Hideaki; Yamamoto, Masaki

2016-11-01

Maximal graft flow acceleration (max df/dt) determined using transit-time flowmetry (TTFM) in the diastolic phase was assessed as a potential predictor of graft failure for aortocoronary artery (AC) bypass grafts in coronary artery bypass patients. Max df/dt was retrospectively measured in 114 aortocoronary artery bypass grafts. TTFM data were fitted to a 9-polynomial curve, which was derived from the first-derivative curve, to measure max df/dt (9-polynomial max df/dt). Abnormal TTFM was defined as a mean flow of <15 ml/min, a pulsatility index of >5 or a diastolic filling ratio of <50 %. Postoperative assessments were routinely performed by coronary artery angiography (CAG) at 1 year after surgery. Using TTFM, 68 grafts were normal, 4 of which were failing on CAG, and 46 grafts were abnormal, 21 of which were failing on CAG. 9-polynomial max df/dt was significantly lower in abnormal TTFM/failing by the CAG group compared with abnormal TTFM/patent by the CAG group (1.08 ± 0.89 vs. 2.05 ± 1.51 ml/s(2), respectively; P < 0.01, Mann-Whitney U test, Holm adjustment). TTFM 9-polynomial max df/dt in the early diastolic phase may be a promising predictor of future graft failure for AC bypass grafts, particularly in abnormal TTFM grafts.

Nodal Statistics for the Van Vleck Polynomials

NASA Astrophysics Data System (ADS)

Bourget, Alain

The Van Vleck polynomials naturally arise from the generalized Lamé equation as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N --> ∞.

A Constant-Factor Approximation Algorithm for the Link Building Problem

NASA Astrophysics Data System (ADS)

Olsen, Martin; Viglas, Anastasios; Zvedeniouk, Ilia

In this work we consider the problem of maximizing the PageRank of a given target node in a graph by adding k new links. We consider the case that the new links must point to the given target node (backlinks). Previous work [7] shows that this problem has no fully polynomial time approximation schemes unless P = NP. We present a polynomial time algorithm yielding a PageRank value within a constant factor from the optimal. We also consider the naive algorithm where we choose backlinks from nodes with high PageRank values compared to the outdegree and show that the naive algorithm performs much worse on certain graphs compared to the constant factor approximation scheme.

Bioeconomic of profit maximization of red tilapia (Oreochromis sp.) culture using polynomial growth model

NASA Astrophysics Data System (ADS)

Wijayanto, D.; Kurohman, F.; Nugroho, RA

2018-03-01

The research purpose was to develop a model bioeconomic of profit maximization that can be applied to red tilapia culture. The development of fish growth model used polynomial growth function. Profit maximization process used the first derivative of profit equation to time of culture equal to zero. This research has also developed the equations to estimate the culture time to reach the target size of the fish harvest. The research proved that this research model could be applied in the red tilapia culture. In the case of this study, red tilapia culture can achieve the maximum profit at 584 days and the profit of Rp. 28,605,731 per culture cycle. If used size target of 250 g, the culture of red tilapia need 82 days of culture time.

Legendre modified moments for Euler's constant

NASA Astrophysics Data System (ADS)

Prévost, Marc

2008-10-01

Polynomial moments are often used for the computation of Gauss quadrature to stabilize the numerical calculation of the orthogonal polynomials, see [W. Gautschi, Computational aspects of orthogonal polynomials, in: P. Nevai (Ed.), Orthogonal Polynomials-Theory and Practice, NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, 1990, pp. 181-216 [6]; W. Gautschi, On the sensitivity of orthogonal polynomials to perturbations in the moments, Numer. Math. 48(4) (1986) 369-382 [5]; W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3(3) (1982) 289-317 [4

On multiple orthogonal polynomials for discrete Meixner measures

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

Sorokin, Vladimir N

2010-12-07

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

THEORETICAL p-MODE OSCILLATION FREQUENCIES FOR THE RAPIDLY ROTATING {delta} SCUTI STAR {alpha} OPHIUCHI

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

Deupree, Robert G., E-mail: bdeupree@ap.smu.ca

2011-11-20

A rotating, two-dimensional stellar model is evolved to match the approximate conditions of {alpha} Oph. Both axisymmetric and nonaxisymmetric oscillation frequencies are computed for two-dimensional rotating models which approximate the properties of {alpha} Oph. These computed frequencies are compared to the observed frequencies. Oscillation calculations are made assuming the eigenfunction can be fitted with six Legendre polynomials, but comparison calculations with eight Legendre polynomials show the frequencies agree to within about 0.26% on average. The surface horizontal shape of the eigenfunctions for the two sets of assumed number of Legendre polynomials agrees less well, but all calculations show significant departuresmore » from that of a single Legendre polynomial. It is still possible to determine the large separation, although the small separation is more complicated to estimate. With the addition of the nonaxisymmetric modes with |m| {<=} 4, the frequency space becomes sufficiently dense that it is difficult to comment on the adequacy of the fit of the computed to the observed frequencies. While the nonaxisymmetric frequency mode splitting is no longer uniform, the frequency difference between the frequencies for positive and negative values of the same m remains 2m times the rotation rate.« less

Random regression models using different functions to model milk flow in dairy cows.

PubMed

Laureano, M M M; Bignardi, A B; El Faro, L; Cardoso, V L; Tonhati, H; Albuquerque, L G

2014-09-12

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.

Process-driven inference of biological network structure: feasibility, minimality, and multiplicity

NASA Astrophysics Data System (ADS)

Zeng, Chen

2012-02-01

For a given dynamic process, identifying the putative interaction networks to achieve it is the inference problem. In this talk, we address the computational complexity of inference problem in the context of Boolean networks under dominant inhibition condition. The first is a proof that the feasibility problem (is there a network that explains the dynamics?) can be solved in polynomial-time. Second, while the minimality problem (what is the smallest network that explains the dynamics?) is shown to be NP-hard, a simple polynomial-time heuristic is shown to produce near-minimal solutions, as demonstrated by simulation. Third, the theoretical framework also leads to a fast polynomial-time heuristic to estimate the number of network solutions with reasonable accuracy. We will apply these approaches to two simplified Boolean network models for the cell cycle process of budding yeast (Li 2004) and fission yeast (Davidich 2008). Our results demonstrate that each of these networks contains a giant backbone motif spanning all the network nodes that provides the desired main functionality, while the remaining edges in the network form smaller motifs whose role is to confer stability properties rather than provide function. Moreover, we show that the bioprocesses of these two cell cycle models differ considerably from a typically generated process and are intrinsically cascade-like.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

Statistics of Data Fitting: Flaws and Fixes of Polynomial Analysis of Channeled Spectra

NASA Astrophysics Data System (ADS)

Karstens, William; Smith, David

2013-03-01

Starting from general statistical principles, we have critically examined Baumeister's procedure* for determining the refractive index of thin films from channeled spectra. Briefly, the method assumes that the index and interference fringe order may be approximated by polynomials quadratic and cubic in photon energy, respectively. The coefficients of the polynomials are related by differentiation, which is equivalent to comparing energy differences between fringes. However, we find that when the fringe order is calculated from the published IR index for silicon* and then analyzed with Baumeister's procedure, the results do not reproduce the original index. This problem has been traced to 1. Use of unphysical powers in the polynomials (e.g., time-reversal invariance requires that the index is an even function of photon energy), and 2. Use of insufficient terms of the correct parity. Exclusion of unphysical terms and addition of quartic and quintic terms to the index and order polynomials yields significantly better fits with fewer parameters. This represents a specific example of using statistics to determine if the assumed fitting model adequately captures the physics contained in experimental data. The use of analysis of variance (ANOVA) and the Durbin-Watson statistic to test criteria for the validity of least-squares fitting will be discussed. *D.F. Edwards and E. Ochoa, Appl. Opt. 19, 4130 (1980). Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.

Single product lot-sizing on unrelated parallel machines with non-decreasing processing times

NASA Astrophysics Data System (ADS)

Eremeev, A.; Kovalyov, M.; Kuznetsov, P.

2018-01-01

We consider a problem in which at least a given quantity of a single product has to be partitioned into lots, and lots have to be assigned to unrelated parallel machines for processing. In one version of the problem, the maximum machine completion time should be minimized, in another version of the problem, the sum of machine completion times is to be minimized. Machine-dependent lower and upper bounds on the lot size are given. The product is either assumed to be continuously divisible or discrete. The processing time of each machine is defined by an increasing function of the lot volume, given as an oracle. Setup times and costs are assumed to be negligibly small, and therefore, they are not considered. We derive optimal polynomial time algorithms for several special cases of the problem. An NP-hard case is shown to admit a fully polynomial time approximation scheme. An application of the problem in energy efficient processors scheduling is considered.

Programming with non-heap memory in the real time specification for Java

NASA Technical Reports Server (NTRS)

Bollella, G.; Canham, T.; Carson, V.; Champlin, V.; Dvorak, D.; Giovannoni, B.; Indictor, M.; Meyer, K.; Reinholtz, A.; Murray, K.

2003-01-01

The Real-Time Specification for Java (RTSJ) provides facilities for deterministic, real-time execution in a language that is otherwise subject to variable latencies in memory allocation and garbage collection.

Independence polynomial and matching polynomial of the Koch network

NASA Astrophysics Data System (ADS)

Liao, Yunhua; Xie, Xiaoliang

2015-11-01

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “#P-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

A modified interval symmetric single step procedure ISS-5D for simultaneous inclusion of polynomial zeros

NASA Astrophysics Data System (ADS)

Sham, Atiyah W. M.; Monsi, Mansor; Hassan, Nasruddin; Suleiman, Mohamed

2013-04-01

The aim of this paper is to present a new modified interval symmetric single-step procedure ISS-5D which is the extension from the previous procedure, ISS1. The ISS-5D method will produce successively smaller intervals that are guaranteed to still contain the zeros. The efficiency of this method is measured on the CPU times and the number of iteration. The procedure is run on five test polynomials and the results obtained are shown in this paper.

Necessary and sufficient conditions for the complete controllability and observability of systems in series using the coprime factorization of a rational matrix

NASA Technical Reports Server (NTRS)

Callier, F. M.; Nahum, C. D.

1975-01-01

The series connection of two linear time-invariant systems that have minimal state space system descriptions is considered. From these descriptions, strict-system-equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of the subsystems as a ratio of two right or left coprime polynomial matrices. They give rise to a simple polynomial matrix system description of the tandem connection. Theorem 1 states that for the complete controllability and observability of the state space system description of the series connection, it is necessary and sufficient that certain 'denominator' and 'numerator' groups are coprime. Consequences for feedback systems are drawn in Corollary 1. The role of pole-zero cancellations is explained by Lemma 3 and Corollaires 2 and 3.

Convex optimisation approach to constrained fuel optimal control of spacecraft in close relative motion

NASA Astrophysics Data System (ADS)

Massioni, Paolo; Massari, Mauro

2018-05-01

This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

Architecture for time or transform domain decoding of reed-solomon codes

NASA Technical Reports Server (NTRS)

Hsu, In-Shek (Inventor); Truong, Trieu-Kie (Inventor); Deutsch, Leslie J. (Inventor); Shao, Howard M. (Inventor)

1989-01-01

Two pipeline (255,233) RS decoders, one a time domain decoder and the other a transform domain decoder, use the same first part to develop an errata locator polynomial .tau.(x), and an errata evaluator polynominal A(x). Both the time domain decoder and transform domain decoder have a modified GCD that uses an input multiplexer and an output demultiplexer to reduce the number of GCD cells required. The time domain decoder uses a Chien search and polynomial evaluator on the GCD outputs .tau.(x) and A(x), for the final decoding steps, while the transform domain decoder uses a transform error pattern algorithm operating on .tau.(x) and the initial syndrome computation S(x), followed by an inverse transform algorithm in sequence for the final decoding steps prior to adding the received RS coded message to produce a decoded output message.

Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2008-10-01

We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

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

Vignat, C.; Lamberti, P. W.

2009-10-15

Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

Finite-size effects and switching times for Moran process with mutation.

PubMed

DeVille, Lee; Galiardi, Meghan

2017-04-01

We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population. We also show that the stochastic system has asymmetries in the form of a skew for parameter values where the deterministic limit is symmetric.

Exact and approximate stochastic simulation of intracellular calcium dynamics.

PubMed

Wieder, Nicolas; Fink, Rainer H A; Wegner, Frederic von

2011-01-01

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms.

Automated Flight Routing Using Stochastic Dynamic Programming

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Modeling disease transmission near eradication: An equation free approach

NASA Astrophysics Data System (ADS)

Williams, Matthew O.; Proctor, Joshua L.; Kutz, J. Nathan

2015-01-01

Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic "coarse" model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigns.

Hadamard Factorization of Stable Polynomials

NASA Astrophysics Data System (ADS)

Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar

2011-11-01

The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

Characterization of normality of chaotic systems including prediction and detection of anomalies

NASA Astrophysics Data System (ADS)

Engler, Joseph John

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

NASA Astrophysics Data System (ADS)

Gupta, Atma Ram; Kumar, Ashwani

2017-12-01

Distribution system network today is facing the challenge of meeting increased load demands from the industrial, commercial and residential sectors. The pattern of load is highly dependent on consumer behavior and temporal factors such as season of the year, day of the week or time of the day. For deterministic radial distribution load flow studies load is taken as constant. But, load varies continually with a high degree of uncertainty. So, there is a need to model probable realistic load. Monte-Carlo Simulation is used to model the probable realistic load by generating random values of active and reactive power load from the mean and standard deviation of the load and for solving a Deterministic Radial Load Flow with these values. The probabilistic solution is reconstructed from deterministic data obtained for each simulation. The main contribution of the work is: Finding impact of probable realistic ZIP load modeling on balanced radial distribution load flow. Finding impact of probable realistic ZIP load modeling on unbalanced radial distribution load flow. Compare the voltage profile and losses with probable realistic ZIP load modeling for balanced and unbalanced radial distribution load flow.

Down to the roughness scale assessment of piston-ring/liner contacts

NASA Astrophysics Data System (ADS)

Checo, H. M.; Jaramillo, A.; Ausas, R. F.; Jai, M.; Buscaglia, G. C.

2017-02-01

The effects of surface roughness in hydrodynamic bearings been accounted for through several approaches, the most widely used being averaging or stochastic techniques. With these the surface is not treated “as it is”, but by means of an assumed probability distribution for the roughness. The so called direct, deterministic or measured-surface simulation) solve the lubrication problem with realistic surfaces down to the roughness scale. This leads to expensive computational problems. Most researchers have tackled this problem considering non-moving surfaces and neglecting the ring dynamics to reduce the computational burden. What is proposed here is to solve the fully-deterministic simulation both in space and in time, so that the actual movement of the surfaces and the rings dynamics are taken into account. This simulation is much more complex than previous ones, as it is intrinsically transient. The feasibility of these fully-deterministic simulations is illustrated two cases: fully deterministic simulation of liner surfaces with diverse finishings (honed and coated bores) with constant piston velocity and load on the ring and also in real engine conditions.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

On Certain Wronskians of Multiple Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Zhang, Lun; Filipuk, Galina

2014-11-01

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

NASA Technical Reports Server (NTRS)

Busby, Judy; Sondak, Doug; Staubach, Brent; Davis, Roger

1998-01-01

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads using a steady computational approach. The LDS model is obtained from an unsteady inviscid calculation. The LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. Both two-dimensional and three-dimensional applications are examined. The inviscid LDS model produces good results for the two-dimensional case and requires less than 10% of the CPU time of the unsteady viscous run. For the three-dimensional case, the LDS model does a good job of reproducing the time-averaged viscous temperature migration and separation as well as heat load on the outer air seal at a CPU cost that is 25% of that of an unsteady viscous computation.

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Differential geometric treewidth estimation in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Wang, Chi; Jonckheere, Edmond; Brun, Todd

2016-10-01

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.

Symbolic discrete event system specification

NASA Technical Reports Server (NTRS)

Zeigler, Bernard P.; Chi, Sungdo

1992-01-01

Extending discrete event modeling formalisms to facilitate greater symbol manipulation capabilities is important to further their use in intelligent control and design of high autonomy systems. An extension to the DEVS formalism that facilitates symbolic expression of event times by extending the time base from the real numbers to the field of linear polynomials over the reals is defined. A simulation algorithm is developed to generate the branching trajectories resulting from the underlying nondeterminism. To efficiently manage symbolic constraints, a consistency checking algorithm for linear polynomial constraints based on feasibility checking algorithms borrowed from linear programming has been developed. The extended formalism offers a convenient means to conduct multiple, simultaneous explorations of model behaviors. Examples of application are given with concentration on fault model analysis.

The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

NASA Astrophysics Data System (ADS)

Li, Chunxia; Li, Shi-Hao

2018-06-01

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

A random walk on water (Henry Darcy Medal Lecture)

NASA Astrophysics Data System (ADS)

Koutsoyiannis, D.

2009-04-01

Randomness and uncertainty had been well appreciated in hydrology and water resources engineering in their initial steps as scientific disciplines. However, this changed through the years and, following other geosciences, hydrology adopted a naïve view of randomness in natural processes. Such a view separates natural phenomena into two mutually exclusive types, random or stochastic, and deterministic. When a classification of a specific process into one of these two types fails, then a separation of the process into two different, usually additive, parts is typically devised, each of which may be further subdivided into subparts (e.g., deterministic subparts such as periodic and aperiodic or trends). This dichotomous logic is typically combined with a manichean perception, in which the deterministic part supposedly represents cause-effect relationships and thus is physics and science (the "good"), whereas randomness has little relationship with science and no relationship with understanding (the "evil"). Probability theory and statistics, which traditionally provided the tools for dealing with randomness and uncertainty, have been regarded by some as the "necessary evil" but not as an essential part of hydrology and geophysics. Some took a step further to banish them from hydrology, replacing them with deterministic sensitivity analysis and fuzzy-logic representations. Others attempted to demonstrate that irregular fluctuations observed in natural processes are au fond manifestations of underlying chaotic deterministic dynamics with low dimensionality, thus attempting to render probabilistic descriptions unnecessary. Some of the above recent developments are simply flawed because they make erroneous use of probability and statistics (which, remarkably, provide the tools for such analyses), whereas the entire underlying logic is just a false dichotomy. To see this, it suffices to recall that Pierre Simon Laplace, perhaps the most famous proponent of determinism in the history of philosophy of science (cf. Laplace's demon), is, at the same time, one of the founders of probability theory, which he regarded as "nothing but common sense reduced to calculation". This harmonizes with James Clerk Maxwell's view that "the true logic for this world is the calculus of Probabilities" and was more recently and epigrammatically formulated in the title of Edwin Thompson Jaynes's book "Probability Theory: The Logic of Science" (2003). Abandoning dichotomous logic, either on ontological or epistemic grounds, we can identify randomness or stochasticity with unpredictability. Admitting that (a) uncertainty is an intrinsic property of nature; (b) causality implies dependence of natural processes in time and thus suggests predictability; but, (c) even the tiniest uncertainty (e.g., in initial conditions) may result in unpredictability after a certain time horizon, we may shape a stochastic representation of natural processes that is consistent with Karl Popper's indeterministic world view. In this representation, probability quantifies uncertainty according to the Kolmogorov system, in which probability is a normalized measure, i.e., a function that maps sets (areas where the initial conditions or the parameter values lie) to real numbers (in the interval [0, 1]). In such a representation, predictability (suggested by deterministic laws) and unpredictability (randomness) coexist, are not separable or additive components, and it is a matter of specifying the time horizon of prediction to decide which of the two dominates. An elementary numerical example has been devised to illustrate the above ideas and demonstrate that they offer a pragmatic and useful guide for practice, rather than just pertaining to philosophical discussions. A chaotic model, with fully and a priori known deterministic dynamics and deterministic inputs (without any random agent), is assumed to represent the hydrological balance in an area partly covered by vegetation. Experimentation with this toy model demonstrates, inter alia, that: (1) for short time horizons the deterministic dynamics is able to give good predictions; but (2) these predictions become extremely inaccurate and useless for long time horizons; (3) for such horizons a naïve statistical prediction (average of past data) which fully neglects the deterministic dynamics is more skilful; and (4) if this statistical prediction, in addition to past data, is combined with the probability theory (the principle of maximum entropy, in particular), it can provide a more informative prediction. Also, the toy model shows that the trajectories of the system state (and derivative properties thereof) do not resemble a regular (e.g., periodic) deterministic process nor a purely random process, but exhibit patterns indicating anti-persistence and persistence (where the latter statistically complies with a Hurst-Kolmogorov behaviour). If the process is averaged over long time scales, the anti-persistent behaviour improves predictability, whereas the persistent behaviour substantially deteriorates it. A stochastic representation of this deterministic system, which incorporates dynamics, is not only possible, but also powerful as it provides good predictions for both short and long horizons and helps to decide on when the deterministic dynamics should be considered or neglected. Obviously, a natural system is extremely more complex than this simple toy model and hence unpredictability is naturally even more prominent in the former. In addition, in a complex natural system, we can never know the exact dynamics and we must infer it from past data, which implies additional uncertainty and an additional role of stochastics in the process of formulating the system equations and estimating the involved parameters. Data also offer the only solid grounds to test any hypothesis about the dynamics, and failure of performing such testing against evidence from data renders the hypothesised dynamics worthless. If this perception of natural phenomena is adequately plausible, then it may help in studying interesting fundamental questions regarding the current state and the trends of hydrological and water resources research and their promising future paths. For instance: (i) Will it ever be possible to achieve a fully "physically based" modelling of hydrological systems that will not depend on data or stochastic representations? (ii) To what extent can hydrological uncertainty be reduced and what are the effective means for such reduction? (iii) Are current stochastic methods in hydrology consistent with observed natural behaviours? What paths should we explore for their advancement? (iv) Can deterministic methods provide solid scientific grounds for water resources engineering and management? In particular, can there be risk-free hydraulic engineering and water management? (v) Is the current (particularly important) interface between hydrology and climate satisfactory?. In particular, should hydrology rely on climate models that are not properly validated (i.e., for periods and scales not used in calibration)? In effect, is the evolution of climate and its impacts on water resources deterministically predictable?

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Topology of Large-Scale Structures of Galaxies in two Dimensions—Systematic Effects

NASA Astrophysics Data System (ADS)

Appleby, Stephen; Park, Changbom; Hong, Sungwook E.; Kim, Juhan

2017-02-01

We study the two-dimensional topology of galactic distribution when projected onto two-dimensional spherical shells. Using the latest Horizon Run 4 simulation data, we construct the genus of the two-dimensional field and consider how this statistic is affected by late-time nonlinear effects—principally gravitational collapse and redshift space distortion (RSD). We also consider systematic and numerical artifacts, such as shot noise, galaxy bias, and finite pixel effects. We model the systematics using a Hermite polynomial expansion and perform a comprehensive analysis of known effects on the two-dimensional genus, with a view toward using the statistic for cosmological parameter estimation. We find that the finite pixel effect is dominated by an amplitude drop and can be made less than 1% by adopting pixels smaller than 1/3 of the angular smoothing length. Nonlinear gravitational evolution introduces time-dependent coefficients of the zeroth, first, and second Hermite polynomials, but the genus amplitude changes by less than 1% between z = 1 and z = 0 for smoothing scales {R}{{G}}> 9 {Mpc}/{{h}}. Non-zero terms are measured up to third order in the Hermite polynomial expansion when studying RSD. Differences in the shapes of the genus curves in real and redshift space are small when we adopt thick redshift shells, but the amplitude change remains a significant ˜ { O }(10 % ) effect. The combined effects of galaxy biasing and shot noise produce systematic effects up to the second Hermite polynomial. It is shown that, when sampling, the use of galaxy mass cuts significantly reduces the effect of shot noise relative to random sampling.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Determinants with orthogonal polynomial entries

NASA Astrophysics Data System (ADS)

Ismail, Mourad E. H.

2005-06-01

We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

Efficiently approximating the Pareto frontier: Hydropower dam placement in the Amazon basin

USGS Publications Warehouse

Wu, Xiaojian; Gomes-Selman, Jonathan; Shi, Qinru; Xue, Yexiang; Garcia-Villacorta, Roosevelt; Anderson, Elizabeth; Sethi, Suresh; Steinschneider, Scott; Flecker, Alexander; Gomes, Carla P.

2018-01-01

Real–world problems are often not fully characterized by a single optimal solution, as they frequently involve multiple competing objectives; it is therefore important to identify the so-called Pareto frontier, which captures solution trade-offs. We propose a fully polynomial-time approximation scheme based on Dynamic Programming (DP) for computing a polynomially succinct curve that approximates the Pareto frontier to within an arbitrarily small > 0 on treestructured networks. Given a set of objectives, our approximation scheme runs in time polynomial in the size of the instance and 1/. We also propose a Mixed Integer Programming (MIP) scheme to approximate the Pareto frontier. The DP and MIP Pareto frontier approaches have complementary strengths and are surprisingly effective. We provide empirical results showing that our methods outperform other approaches in efficiency and accuracy. Our work is motivated by a problem in computational sustainability concerning the proliferation of hydropower dams throughout the Amazon basin. Our goal is to support decision-makers in evaluating impacted ecosystem services on the full scale of the Amazon basin. Our work is general and can be applied to approximate the Pareto frontier of a variety of multiobjective problems on tree-structured networks.

Deterministic Wave Predictions from the WaMoS II

DTIC Science & Technology

2014-10-23

Monitoring System WaMoS II as input to a wave pre- diction system . The utility of wave prediction is primarily ves- sel motion prediction. Specific...successful prediction. The envisioned prediction system may provide graphical output in the form of a decision support system (Fig. 1). Predictions are...quality and accuracy of WaMoS as input to a deterministic wave prediction system . In the context of this paper, the Time Now Forecast H e a v e Hindcast

Comparison of space radiation calculations for deterministic and Monte Carlo transport codes

NASA Astrophysics Data System (ADS)

Lin, Zi-Wei; Adams, James; Barghouty, Abdulnasser; Randeniya, Sharmalee; Tripathi, Ram; Watts, John; Yepes, Pablo

For space radiation protection of astronauts or electronic equipments, it is necessary to develop and use accurate radiation transport codes. Radiation transport codes include deterministic codes, such as HZETRN from NASA and UPROP from the Naval Research Laboratory, and Monte Carlo codes such as FLUKA, the Geant4 toolkit and HETC-HEDS. The deterministic codes and Monte Carlo codes complement each other in that deterministic codes are very fast while Monte Carlo codes are more elaborate. Therefore it is important to investigate how well the results of deterministic codes compare with those of Monte Carlo transport codes and where they differ. In this study we evaluate these different codes in their space radiation applications by comparing their output results in the same given space radiation environments, shielding geometry and material. Typical space radiation environments such as the 1977 solar minimum galactic cosmic ray environment are used as the well-defined input, and simple geometries made of aluminum, water and/or polyethylene are used to represent the shielding material. We then compare various outputs of these codes, such as the dose-depth curves and the flux spectra of different fragments and other secondary particles. These comparisons enable us to learn more about the main differences between these space radiation transport codes. At the same time, they help us to learn the qualitative and quantitative features that these transport codes have in common.

Northern Hemisphere glaciation and the evolution of Plio-Pleistocene climate noise

NASA Astrophysics Data System (ADS)

Meyers, Stephen R.; Hinnov, Linda A.

2010-08-01

Deterministic orbital controls on climate variability are commonly inferred to dominate across timescales of 104-106 years, although some studies have suggested that stochastic processes may be of equal or greater importance. Here we explicitly quantify changes in deterministic orbital processes (forcing and/or pacing) versus stochastic climate processes during the Plio-Pleistocene, via time-frequency analysis of two prominent foraminifera oxygen isotopic stacks. Our results indicate that development of the Northern Hemisphere ice sheet is paralleled by an overall amplification of both deterministic and stochastic climate energy, but their relative dominance is variable. The progression from a more stochastic early Pliocene to a strongly deterministic late Pleistocene is primarily accommodated during two transitory phases of Northern Hemisphere ice sheet growth. This long-term trend is punctuated by “stochastic events,” which we interpret as evidence for abrupt reorganization of the climate system at the initiation and termination of the mid-Pleistocene transition and at the onset of Northern Hemisphere glaciation. In addition to highlighting a complex interplay between deterministic and stochastic climate change during the Plio-Pleistocene, our results support an early onset for Northern Hemisphere glaciation (between 3.5 and 3.7 Ma) and reveal some new characteristics of the orbital signal response, such as the puzzling emergence of 100 ka and 400 ka cyclic climate variability during theoretical eccentricity nodes.

From sequences to polynomials and back, via operator orderings

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

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Extending Romanovski polynomials in quantum mechanics

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

Quesne, C.

2013-12-15

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties ofmore » second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.« less

Polynomial solutions of the Monge-Ampère equation

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

Aminov, Yu A

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

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

Hayes, T.; Smith, K.S.; Severino, F.

A critical capability of the new RHIC low level rf (LLRF) system is the ability to synchronize signals across multiple locations. The 'Update Link' provides this functionality. The 'Update Link' is a deterministic serial data link based on the Xilinx RocketIO protocol that is broadcast over fiber optic cable at 1 gigabit per second (Gbps). The link provides timing events and data packets as well as time stamp information for synchronizing diagnostic data from multiple sources. The new RHIC LLRF was designed to be a flexible, modular system. The system is constructed of numerous independent RF Controller chassis. To providemore » synchronization among all of these chassis, the Update Link system was designed. The Update Link system provides a low latency, deterministic data path to broadcast information to all receivers in the system. The Update Link system is based on a central hub, the Update Link Master (ULM), which generates the data stream that is distributed via fiber optic links. Downstream chassis have non-deterministic connections back to the ULM that allow any chassis to provide data that is broadcast globally.« less

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

A note on the zeros of Freud-Sobolev orthogonal polynomials

NASA Astrophysics Data System (ADS)

Moreno-Balcazar, Juan J.

2007-10-01

We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

MIMICKING COUNTERFACTUAL OUTCOMES TO ESTIMATE CAUSAL EFFECTS.

PubMed

Lok, Judith J

2017-04-01

In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates, and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Structural nested models have been applied in this setting. Structural nested models are based on counterfactuals: the outcome a person would have had had treatment been withheld after a certain time. Previous work on continuous-time structural nested models assumes that counterfactuals depend deterministically on observed data, while conjecturing that this assumption can be relaxed. This article proves that one can mimic counterfactuals by constructing random variables, solutions to a differential equation, that have the same distribution as the counterfactuals, even given past observed data. These "mimicking" variables can be used to estimate the parameters of structural nested models without assuming the treatment effect to be deterministic.

A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

NASA Technical Reports Server (NTRS)

Truong, T. K.

1994-01-01

This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.

Bin Packing, Number Balancing, and Rescaling Linear Programs

NASA Astrophysics Data System (ADS)

Hoberg, Rebecca

This thesis deals with several important algorithmic questions using techniques from diverse areas including discrepancy theory, machine learning and lattice theory. In Chapter 2, we construct an improved approximation algorithm for a classical NP-complete problem, the bin packing problem. In this problem, the goal is to pack items of sizes si ∈ [0,1] into as few bins as possible, where a set of items fits into a bin provided the sum of the item sizes is at most one. We give a polynomial-time rounding scheme for a standard linear programming relaxation of the problem, yielding a packing that uses at most OPT + O(log OPT) bins. This makes progress towards one of the "10 open problems in approximation algorithms" stated in the book of Shmoys and Williamson. In fact, based on related combinatorial lower bounds, Rothvoss conjectures that theta(logOPT) may be a tight bound on the additive integrality gap of this LP relaxation. In Chapter 3, we give a new polynomial-time algorithm for linear programming. Our algorithm is based on the multiplicative weights update (MWU) method, which is a general framework that is currently of great interest in theoretical computer science. An algorithm for linear programming based on MWU was known previously, but was not polynomial time--we remedy this by alternating between a MWU phase and a rescaling phase. The rescaling methods we introduce improve upon previous methods by reducing the number of iterations needed until one can rescale, and they can be used for any algorithm with a similar rescaling structure. Finally, we note that the MWU phase of the algorithm has a simple interpretation as gradient descent of a particular potential function, and we show we can speed up this phase by walking in a direction that decreases both the potential function and its gradient. In Chapter 4, we show that an approximate oracle for Minkowski's Theorem gives an approximate oracle for the number balancing problem, and conversely. Number balancing is the problem of minimizing | 〈a,x〉 | over x ∈ {-1,0,1}n \\ { 0}, given a ∈ [0,1]n. While an application of the pigeonhole principle shows that there always exists x with | 〈a,x〉| ≤ O(√ n/2n), the best known algorithm only guarantees |〈a,x〉| ≤ 2-ntheta(log n). We show that an oracle for Minkowski's Theorem with approximation factor rho would give an algorithm for NBP that guarantees | 〈a,x〉 | ≤ 2-ntheta(1/rho). In particular, this would beat the bound of Karmarkar and Karp provided rho ≤ O(logn/loglogn). In the other direction, we prove that any polynomial time algorithm for NBP that guarantees a solution of difference at most 2√n/2 n would give a polynomial approximation for Minkowski as well as a polynomial factor approximation algorithm for the Shortest Vector Problem.

Bicubic uniform B-spline wavefront fitting technology applied in computer-generated holograms

NASA Astrophysics Data System (ADS)

Cao, Hui; Sun, Jun-qiang; Chen, Guo-jie

2006-02-01

This paper presented a bicubic uniform B-spline wavefront fitting technology to figure out the analytical expression for object wavefront used in Computer-Generated Holograms (CGHs). In many cases, to decrease the difficulty of optical processing, off-axis CGHs rather than complex aspherical surface elements are used in modern advanced military optical systems. In order to design and fabricate off-axis CGH, we have to fit out the analytical expression for object wavefront. Zernike Polynomial is competent for fitting wavefront of centrosymmetric optical systems, but not for axisymmetrical optical systems. Although adopting high-degree polynomials fitting method would achieve higher fitting precision in all fitting nodes, the greatest shortcoming of this method is that any departure from the fitting nodes would result in great fitting error, which is so-called pulsation phenomenon. Furthermore, high-degree polynomials fitting method would increase the calculation time in coding computer-generated hologram and solving basic equation. Basing on the basis function of cubic uniform B-spline and the character mesh of bicubic uniform B-spline wavefront, bicubic uniform B-spline wavefront are described as the product of a series of matrices. Employing standard MATLAB routines, four kinds of different analytical expressions for object wavefront are fitted out by bicubic uniform B-spline as well as high-degree polynomials. Calculation results indicate that, compared with high-degree polynomials, bicubic uniform B-spline is a more competitive method to fit out the analytical expression for object wavefront used in off-axis CGH, for its higher fitting precision and C2 continuity.

AKLSQF - LEAST SQUARES CURVE FITTING

NASA Technical Reports Server (NTRS)

Kantak, A. V.

1994-01-01

The Least Squares Curve Fitting program, AKLSQF, computes the polynomial which will least square fit uniformly spaced data easily and efficiently. The program allows the user to specify the tolerable least squares error in the fitting or allows the user to specify the polynomial degree. In both cases AKLSQF returns the polynomial and the actual least squares fit error incurred in the operation. The data may be supplied to the routine either by direct keyboard entry or via a file. AKLSQF produces the least squares polynomial in two steps. First, the data points are least squares fitted using the orthogonal factorial polynomials. The result is then reduced to a regular polynomial using Sterling numbers of the first kind. If an error tolerance is specified, the program starts with a polynomial of degree 1 and computes the least squares fit error. The degree of the polynomial used for fitting is then increased successively until the error criterion specified by the user is met. At every step the polynomial as well as the least squares fitting error is printed to the screen. In general, the program can produce a curve fitting up to a 100 degree polynomial. All computations in the program are carried out under Double Precision format for real numbers and under long integer format for integers to provide the maximum accuracy possible. AKLSQF was written for an IBM PC X/AT or compatible using Microsoft's Quick Basic compiler. It has been implemented under DOS 3.2.1 using 23K of RAM. AKLSQF was developed in 1989.

Fast and accurate fitting and filtering of noisy exponentials in Legendre space.

PubMed

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

PubMed

Papadopoulos, Anthony

2009-01-01

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.

Deterministic generation of multiparticle entanglement by quantum Zeno dynamics.

PubMed

Barontini, Giovanni; Hohmann, Leander; Haas, Florian; Estève, Jérôme; Reichel, Jakob

2015-09-18

Multiparticle entangled quantum states, a key resource in quantum-enhanced metrology and computing, are usually generated by coherent operations exclusively. However, unusual forms of quantum dynamics can be obtained when environment coupling is used as part of the state generation. In this work, we used quantum Zeno dynamics (QZD), based on nondestructive measurement with an optical microcavity, to deterministically generate different multiparticle entangled states in an ensemble of 36 qubit atoms in less than 5 microseconds. We characterized the resulting states by performing quantum tomography, yielding a time-resolved account of the entanglement generation. In addition, we studied the dependence of quantum states on measurement strength and quantified the depth of entanglement. Our results show that QZD is a versatile tool for fast and deterministic entanglement generation in quantum engineering applications. Copyright © 2015, American Association for the Advancement of Science.

Deterministic error correction for nonlocal spatial-polarization hyperentanglement

PubMed Central

Li, Tao; Wang, Guan-Yu; Deng, Fu-Guo; Long, Gui-Lu

2016-01-01

Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication. PMID:26861681

Deterministic error correction for nonlocal spatial-polarization hyperentanglement.

PubMed

Li, Tao; Wang, Guan-Yu; Deng, Fu-Guo; Long, Gui-Lu

2016-02-10

Hyperentanglement is an effective quantum source for quantum communication network due to its high capacity, low loss rate, and its unusual character in teleportation of quantum particle fully. Here we present a deterministic error-correction scheme for nonlocal spatial-polarization hyperentangled photon pairs over collective-noise channels. In our scheme, the spatial-polarization hyperentanglement is first encoded into a spatial-defined time-bin entanglement with identical polarization before it is transmitted over collective-noise channels, which leads to the error rejection of the spatial entanglement during the transmission. The polarization noise affecting the polarization entanglement can be corrected with a proper one-step decoding procedure. The two parties in quantum communication can, in principle, obtain a nonlocal maximally entangled spatial-polarization hyperentanglement in a deterministic way, which makes our protocol more convenient than others in long-distance quantum communication.

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

DOE PAGES

Teichert, Gregory H.; Gunda, N. S. Harsha; Rudraraju, Shiva; ...

2016-12-18

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energymore » data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.« less

Short communication: Genetic variation of saturated fatty acids in Holsteins in the Walloon region of Belgium.

PubMed

Arnould, V M-R; Hammami, H; Soyeurt, H; Gengler, N

2010-09-01

Random regression test-day models using Legendre polynomials are commonly used for the estimation of genetic parameters and genetic evaluation for test-day milk production traits. However, some researchers have reported that these models present some undesirable properties such as the overestimation of variances at the edges of lactation. Describing genetic variation of saturated fatty acids expressed in milk fat might require the testing of different models. Therefore, 3 different functions were used and compared to take into account the lactation curve: (1) Legendre polynomials with the same order as currently applied for genetic model for production traits; 2) linear splines with 10 knots; and 3) linear splines with the same 10 knots reduced to 3 parameters. The criteria used were Akaike's information and Bayesian information criteria, percentage square biases, and log-likelihood function. These criteria indentified Legendre polynomials and linear splines with 10 knots reduced to 3 parameters models as the most useful. Reducing more complex models using eigenvalues seemed appealing because the resulting models are less time demanding and can reduce convergence difficulties, because convergence properties also seemed to be improved. Finally, the results showed that the reduced spline model was very similar to the Legendre polynomials model. Copyright (c) 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

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

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendationsmore » on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.« less

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

Soil pH mediates the balance between stochastic and deterministic assembly of bacteria

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

Tripathi, Binu M.; Stegen, James C.; Kim, Mincheol

Little is known about the factors affecting the relative influence of stochastic and deterministic processes that governs the assembly of microbial communities in successional soils. Here, we conducted a meta-analysis of bacterial communities using six different successional soils data sets, scattered across different regions, with different pH conditions in early and late successional soils. We found that soil pH was the best predictor of bacterial community assembly and the relative importance of stochastic and deterministic processes along successional soils. Extreme acidic or alkaline pH conditions lead to assembly of phylogenetically more clustered bacterial communities through deterministic processes, whereas pH conditionsmore » close to neutral lead to phylogenetically less clustered bacterial communities with more stochasticity. We suggest that the influence of pH, rather than successional age, is the main driving force in producing trends in phylogenetic assembly of bacteria, and that pH also influences the relative balance of stochastic and deterministic processes along successional soils. Given that pH had a much stronger association with community assembly than did successional age, we evaluated whether the inferred influence of pH was maintained when studying globally-distributed samples collected without regard for successional age. This dataset confirmed the strong influence of pH, suggesting that the influence of soil pH on community assembly processes occurs globally. Extreme pH conditions likely exert more stringent limits on survival and fitness, imposing strong selective pressures through ecological and evolutionary time. Taken together, these findings suggest that the degree to which stochastic vs. deterministic processes shape soil bacterial community assembly is a consequence of soil pH rather than successional age.« less

The meta-Gaussian Bayesian Processor of forecasts and associated preliminary experiments

NASA Astrophysics Data System (ADS)

Chen, Fajing; Jiao, Meiyan; Chen, Jing

2013-04-01

Public weather services are trending toward providing users with probabilistic weather forecasts, in place of traditional deterministic forecasts. Probabilistic forecasting techniques are continually being improved to optimize available forecasting information. The Bayesian Processor of Forecast (BPF), a new statistical method for probabilistic forecast, can transform a deterministic forecast into a probabilistic forecast according to the historical statistical relationship between observations and forecasts generated by that forecasting system. This technique accounts for the typical forecasting performance of a deterministic forecasting system in quantifying the forecast uncertainty. The meta-Gaussian likelihood model is suitable for a variety of stochastic dependence structures with monotone likelihood ratios. The meta-Gaussian BPF adopting this kind of likelihood model can therefore be applied across many fields, including meteorology and hydrology. The Bayes theorem with two continuous random variables and the normal-linear BPF are briefly introduced. The meta-Gaussian BPF for a continuous predictand using a single predictor is then presented and discussed. The performance of the meta-Gaussian BPF is tested in a preliminary experiment. Control forecasts of daily surface temperature at 0000 UTC at Changsha and Wuhan stations are used as the deterministic forecast data. These control forecasts are taken from ensemble predictions with a 96-h lead time generated by the National Meteorological Center of the China Meteorological Administration, the European Centre for Medium-Range Weather Forecasts, and the US National Centers for Environmental Prediction during January 2008. The results of the experiment show that the meta-Gaussian BPF can transform a deterministic control forecast of surface temperature from any one of the three ensemble predictions into a useful probabilistic forecast of surface temperature. These probabilistic forecasts quantify the uncertainty of the control forecast; accordingly, the performance of the probabilistic forecasts differs based on the source of the underlying deterministic control forecasts.

PolyWaTT: A polynomial water travel time estimator based on Derivative Dynamic Time Warping and Perceptually Important Points

NASA Astrophysics Data System (ADS)

Claure, Yuri Navarro; Matsubara, Edson Takashi; Padovani, Carlos; Prati, Ronaldo Cristiano

2018-03-01

Traditional methods for estimating timing parameters in hydrological science require a rigorous study of the relations of flow resistance, slope, flow regime, watershed size, water velocity, and other local variables. These studies are mostly based on empirical observations, where the timing parameter is estimated using empirically derived formulas. The application of these studies to other locations is not always direct. The locations in which equations are used should have comparable characteristics to the locations from which such equations have been derived. To overcome this barrier, in this work, we developed a data-driven approach to estimate timing parameters such as travel time. Our proposal estimates timing parameters using historical data of the location without the need of adapting or using empirical formulas from other locations. The proposal only uses one variable measured at two different locations on the same river (for instance, two river-level measurements, one upstream and the other downstream on the same river). The recorded data from each location generates two time series. Our method aligns these two time series using derivative dynamic time warping (DDTW) and perceptually important points (PIP). Using data from timing parameters, a polynomial function generalizes the data by inducing a polynomial water travel time estimator, called PolyWaTT. To evaluate the potential of our proposal, we applied PolyWaTT to three different watersheds: a floodplain ecosystem located in the part of Brazil known as Pantanal, the world's largest tropical wetland area; and the Missouri River and the Pearl River, in United States of America. We compared our proposal with empirical formulas and a data-driven state-of-the-art method. The experimental results demonstrate that PolyWaTT showed a lower mean absolute error than all other methods tested in this study, and for longer distances the mean absolute error achieved by PolyWaTT is three times smaller than empirical formulas.

Zernike ultrasonic tomography for fluid velocity imaging based on pipeline intrusive time-of-flight measurements.

PubMed

Besic, Nikola; Vasile, Gabriel; Anghel, Andrei; Petrut, Teodor-Ion; Ioana, Cornel; Stankovic, Srdjan; Girard, Alexandre; d'Urso, Guy

2014-11-01

In this paper, we propose a novel ultrasonic tomography method for pipeline flow field imaging, based on the Zernike polynomial series. Having intrusive multipath time-offlight ultrasonic measurements (difference in flight time and speed of ultrasound) at the input, we provide at the output tomograms of the fluid velocity components (axial, radial, and orthoradial velocity). Principally, by representing these velocities as Zernike polynomial series, we reduce the tomography problem to an ill-posed problem of finding the coefficients of the series, relying on the acquired ultrasonic measurements. Thereupon, this problem is treated by applying and comparing Tikhonov regularization and quadratically constrained ℓ1 minimization. To enhance the comparative analysis, we additionally introduce sparsity, by employing SVD-based filtering in selecting Zernike polynomials which are to be included in the series. The first approach-Tikhonov regularization without filtering, is used because it is the most suitable method. The performances are quantitatively tested by considering a residual norm and by estimating the flow using the axial velocity tomogram. Finally, the obtained results show the relative residual norm and the error in flow estimation, respectively, ~0.3% and ~1.6% for the less turbulent flow and ~0.5% and ~1.8% for the turbulent flow. Additionally, a qualitative validation is performed by proximate matching of the derived tomograms with a flow physical model.

On the degree conjecture for separability of multipartite quantum states

NASA Astrophysics Data System (ADS)

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-01

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matrices match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.

Using forbidden ordinal patterns to detect determinism in irregularly sampled time series.

PubMed

Kulp, C W; Chobot, J M; Niskala, B J; Needhammer, C J

2016-02-01

It is known that when symbolizing a time series into ordinal patterns using the Bandt-Pompe (BP) methodology, there will be ordinal patterns called forbidden patterns that do not occur in a deterministic series. The existence of forbidden patterns can be used to identify deterministic dynamics. In this paper, the ability to use forbidden patterns to detect determinism in irregularly sampled time series is tested on data generated from a continuous model system. The study is done in three parts. First, the effects of sampling time on the number of forbidden patterns are studied on regularly sampled time series. The next two parts focus on two types of irregular-sampling, missing data and timing jitter. It is shown that forbidden patterns can be used to detect determinism in irregularly sampled time series for low degrees of sampling irregularity (as defined in the paper). In addition, comments are made about the appropriateness of using the BP methodology to symbolize irregularly sampled time series.

Rational solutions to the KPI equation and multi rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-04-01

We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.

Alternative predictors in chaotic time series

NASA Astrophysics Data System (ADS)

Alves, P. R. L.; Duarte, L. G. S.; da Mota, L. A. C. P.

2017-06-01

In the scheme of reconstruction, non-polynomial predictors improve the forecast from chaotic time series. The algebraic manipulation in the Maple environment is the basis for obtaining of accurate predictors. Beyond the different times of prediction, the optional arguments of the computational routines optimize the running and the analysis of global mappings.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

A stochastic electricity market clearing formulation with consistent pricing properties

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

Zavala, Victor M.; Kim, Kibaek; Anitescu, Mihai

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives. We extend and analyze a previously proposed stochastic clearing formulation in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price bounded price distortions, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities equal a quantile of their real-time counterparts. The undesired effects of price distortions suggest that stochasticmore » settings provide significant benefits over deterministic ones that go beyond social surplus improvements. Finally, we propose additional metrics to evaluate these benefits.« less

A stochastic electricity market clearing formulation with consistent pricing properties

DOE PAGES

Zavala, Victor M.; Kim, Kibaek; Anitescu, Mihai; ...

2017-03-16

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives. We extend and analyze a previously proposed stochastic clearing formulation in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price bounded price distortions, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities equal a quantile of their real-time counterparts. The undesired effects of price distortions suggest that stochasticmore » settings provide significant benefits over deterministic ones that go beyond social surplus improvements. Finally, we propose additional metrics to evaluate these benefits.« less

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem.

PubMed

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A; Hazen, Terry C; Tiedje, James M; Arkin, Adam P

2014-03-04

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession.

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Degenerate r-Stirling Numbers and r-Bell Polynomials

NASA Astrophysics Data System (ADS)

Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

2018-01-01

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

From Chebyshev to Bernstein: A Tour of Polynomials Small and Large

ERIC Educational Resources Information Center

Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin

2006-01-01

Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.

Umbral orthogonal polynomials

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

Lopez-Sendino, J. E.; del Olmo, M. A.

2010-12-23

We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

Fully polynomial-time approximation scheme for a special case of a quadratic Euclidean 2-clustering problem

NASA Astrophysics Data System (ADS)

Kel'manov, A. V.; Khandeev, V. I.

2016-02-01

The strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters of given sizes (cardinalities) minimizing the sum (over both clusters) of the intracluster sums of squared distances from the elements of the clusters to their centers is considered. It is assumed that the center of one of the sought clusters is specified at the desired (arbitrary) point of space (without loss of generality, at the origin), while the center of the other one is unknown and determined as the mean value over all elements of this cluster. It is shown that unless P = NP, there is no fully polynomial-time approximation scheme for this problem, and such a scheme is substantiated in the case of a fixed space dimension.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

Polynomial-Time Approximation Algorithm for the Problem of Cardinality-Weighted Variance-Based 2-Clustering with a Given Center

NASA Astrophysics Data System (ADS)

Kel'manov, A. V.; Motkova, A. V.

2018-01-01

A strongly NP-hard problem of partitioning a finite set of points of Euclidean space into two clusters is considered. The solution criterion is the minimum of the sum (over both clusters) of weighted sums of squared distances from the elements of each cluster to its geometric center. The weights of the sums are equal to the cardinalities of the desired clusters. The center of one cluster is given as input, while the center of the other is unknown and is determined as the point of space equal to the mean of the cluster elements. A version of the problem is analyzed in which the cardinalities of the clusters are given as input. A polynomial-time 2-approximation algorithm for solving the problem is constructed.

Quantum resonant activation.

PubMed

Magazzù, Luca; Hänggi, Peter; Spagnolo, Bernardo; Valenti, Davide

2017-04-01

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multipeaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency ν^{*} which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.

Quantum resonant activation

NASA Astrophysics Data System (ADS)

Magazzó, Luca; Hänggi, Peter; Spagnolo, Bernardo; Valenti, Davide

2017-04-01

Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probability density function (pdf) displays a complex, multipeaked behavior, which depends crucially on the details of initial phase, frequency, and strength of the driving. As an interesting feature we find that the mean first passage time enters the resonant activation regime at a critical frequency ν* which depends very weakly on the strength of the driving. Moreover, we provide the relation between the first passage time pdf and the statistics of residence times.

Design and Use of a Learning Object for Finding Complex Polynomial Roots

ERIC Educational Resources Information Center

Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime

2013-01-01

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

ERIC Educational Resources Information Center

Miller, David A.; Moseley, James

2012-01-01

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

NASA Astrophysics Data System (ADS)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

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

Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl{sub -1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from the q{yields}-1 limit of the dual q-Hahn polynomials. The Hopf algebra sl{sub -1}(2) has four generators including an involution, it is also a q{yields}-1 limit of the quantum algebra sl{sub q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of themore » -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl{sub -1}(2) algebras, so that the Clebsch-Gordan coefficients of sl{sub -1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.« less

Failed rib region prediction in a human body model during crash events with precrash braking.

PubMed

Guleyupoglu, B; Koya, B; Barnard, R; Gayzik, F S

2018-02-28

The objective of this study is 2-fold. We used a validated human body finite element model to study the predicted chest injury (focusing on rib fracture as a function of element strain) based on varying levels of simulated precrash braking. Furthermore, we compare deterministic and probabilistic methods of rib injury prediction in the computational model. The Global Human Body Models Consortium (GHBMC) M50-O model was gravity settled in the driver position of a generic interior equipped with an advanced 3-point belt and airbag. Twelve cases were investigated with permutations for failure, precrash braking system, and crash severity. The severities used were median (17 kph), severe (34 kph), and New Car Assessment Program (NCAP; 56.4 kph). Cases with failure enabled removed rib cortical bone elements once 1.8% effective plastic strain was exceeded. Alternatively, a probabilistic framework found in the literature was used to predict rib failure. Both the probabilistic and deterministic methods take into consideration location (anterior, lateral, and posterior). The deterministic method is based on a rubric that defines failed rib regions dependent on a threshold for contiguous failed elements. The probabilistic method depends on age-based strain and failure functions. Kinematics between both methods were similar (peak max deviation: ΔX head = 17 mm; ΔZ head = 4 mm; ΔX thorax = 5 mm; ΔZ thorax = 1 mm). Seat belt forces at the time of probabilistic failed region initiation were lower than those at deterministic failed region initiation. The probabilistic method for rib fracture predicted more failed regions in the rib (an analog for fracture) than the deterministic method in all but 1 case where they were equal. The failed region patterns between models are similar; however, there are differences that arise due to stress reduced from element elimination that cause probabilistic failed regions to continue to rise after no deterministic failed region would be predicted. Both the probabilistic and deterministic methods indicate similar trends with regards to the effect of precrash braking; however, there are tradeoffs. The deterministic failed region method is more spatially sensitive to failure and is more sensitive to belt loads. The probabilistic failed region method allows for increased capability in postprocessing with respect to age. The probabilistic failed region method predicted more failed regions than the deterministic failed region method due to force distribution differences.

Interbasis expansions in the Zernike system

NASA Astrophysics Data System (ADS)

Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo; Yakhno, Alexander

2017-10-01

The differential equation with free boundary conditions on the unit disk that was proposed by Frits Zernike in 1934 to find Jacobi polynomial solutions (indicated as I) serves to define a classical system and a quantum system which have been found to be superintegrable. We have determined two new orthogonal polynomial solutions (indicated as II and III) that are separable and involve Legendre and Gegenbauer polynomials. Here we report on their three interbasis expansion coefficients: between the I-II and I-III bases, they are given by F32(⋯|1 ) polynomials that are also special su(2) Clebsch-Gordan coefficients and Hahn polynomials. Between the II-III bases, we find an expansion expressed by F43(⋯|1 ) 's and Racah polynomials that are related to the Wigner 6j coefficients.

Shielding Calculations on Waste Packages - The Limits and Possibilities of different Calculation Methods by the example of homogeneous and inhomogeneous Waste Packages

NASA Astrophysics Data System (ADS)

Adams, Mike; Smalian, Silva

2017-09-01

For nuclear waste packages the expected dose rates and nuclide inventory are beforehand calculated. Depending on the package of the nuclear waste deterministic programs like MicroShield® provide a range of results for each type of packaging. Stochastic programs like "Monte-Carlo N-Particle Transport Code System" (MCNP®) on the other hand provide reliable results for complex geometries. However this type of program requires a fully trained operator and calculations are time consuming. The problem here is to choose an appropriate program for a specific geometry. Therefore we compared the results of deterministic programs like MicroShield® and stochastic programs like MCNP®. These comparisons enable us to make a statement about the applicability of the various programs for chosen types of containers. As a conclusion we found that for thin-walled geometries deterministic programs like MicroShield® are well suited to calculate the dose rate. For cylindrical containers with inner shielding however, deterministic programs hit their limits. Furthermore we investigate the effect of an inhomogeneous material and activity distribution on the results. The calculations are still ongoing. Results will be presented in the final abstract.

Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

NASA Astrophysics Data System (ADS)

Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

2009-12-01

We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.

PubMed

Haglund, J; Haiman, M; Loehr, N

2005-02-22

Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

Detection of "noisy" chaos in a time series

NASA Technical Reports Server (NTRS)

Chon, K. H.; Kanters, J. K.; Cohen, R. J.; Holstein-Rathlou, N. H.

1997-01-01

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

An Analysis of Coherent Digital Receivers in the Presence of Colored Noise Interference.

DTIC Science & Technology

1985-06-01

115 6.4 Pe for Det-erministic Jamnmers, JSR = 0.01, E0.3---------------------------------------------116 6.5 Pe for Deterministic Jamnmers, JSR = 0.1...k k where h p(t) and hhi(t) are the particular and homogeneous solutions, respectively, to a differential equation derived from the Fredholm I...yields 2 2D(s2)c (s) = N(s ) (3.4)c Multiplication by s corresponds to differentiation with respect to t in the time domain. So, Eq. (3.4) becomes D(p 2)K

The threshold of a stochastic delayed SIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2016-11-01

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

Deterministic and storable single-photon source based on a quantum memory.

PubMed

Chen, Shuai; Chen, Yu-Ao; Strassel, Thorsten; Yuan, Zhen-Sheng; Zhao, Bo; Schmiedmayer, Jörg; Pan, Jian-Wei

2006-10-27

A single-photon source is realized with a cold atomic ensemble (87Rb atoms). A single excitation, written in an atomic quantum memory by Raman scattering of a laser pulse, is retrieved deterministically as a single photon at a predetermined time. It is shown that the production rate of single photons can be enhanced considerably by a feedback circuit while the single-photon quality is conserved. Such a single-photon source is well suited for future large-scale realization of quantum communication and linear optical quantum computation.

Production scheduling and rescheduling with genetic algorithms.

PubMed

Bierwirth, C; Mattfeld, D C

1999-01-01

A general model for job shop scheduling is described which applies to static, dynamic and non-deterministic production environments. Next, a Genetic Algorithm is presented which solves the job shop scheduling problem. This algorithm is tested in a dynamic environment under different workload situations. Thereby, a highly efficient decoding procedure is proposed which strongly improves the quality of schedules. Finally, this technique is tested for scheduling and rescheduling in a non-deterministic environment. It is shown by experiment that conventional methods of production control are clearly outperformed at reasonable run-time costs.

Spatial scaling patterns and functional redundancies in a changing boreal lake landscape

USGS Publications Warehouse

Angeler, David G.; Allen, Craig R.; Uden, Daniel R.; Johnson, Richard K.

2015-01-01

Global transformations extend beyond local habitats; therefore, larger-scale approaches are needed to assess community-level responses and resilience to unfolding environmental changes. Using longterm data (1996–2011), we evaluated spatial patterns and functional redundancies in the littoral invertebrate communities of 85 Swedish lakes, with the objective of assessing their potential resilience to environmental change at regional scales (that is, spatial resilience). Multivariate spatial modeling was used to differentiate groups of invertebrate species exhibiting spatial patterns in composition and abundance (that is, deterministic species) from those lacking spatial patterns (that is, stochastic species). We then determined the functional feeding attributes of the deterministic and stochastic invertebrate species, to infer resilience. Between one and three distinct spatial patterns in invertebrate composition and abundance were identified in approximately one-third of the species; the remainder were stochastic. We observed substantial differences in metrics between deterministic and stochastic species. Functional richness and diversity decreased over time in the deterministic group, suggesting a loss of resilience in regional invertebrate communities. However, taxon richness and redundancy increased monotonically in the stochastic group, indicating the capacity of regional invertebrate communities to adapt to change. Our results suggest that a refined picture of spatial resilience emerges if patterns of both the deterministic and stochastic species are accounted for. Spatially extensive monitoring may help increase our mechanistic understanding of community-level responses and resilience to regional environmental change, insights that are critical for developing management and conservation agendas in this current period of rapid environmental transformation.

Conversion from Engineering Units to Telemetry Counts on Dryden Flight Simulators

NASA Technical Reports Server (NTRS)

Fantini, Jay A.

1998-01-01

Dryden real-time flight simulators encompass the simulation of pulse code modulation (PCM) telemetry signals. This paper presents a new method whereby the calibration polynomial (from first to sixth order), representing the conversion from counts to engineering units (EU), is numerically inverted in real time. The result is less than one-count error for valid EU inputs. The Newton-Raphson method is used to numerically invert the polynomial. A reverse linear interpolation between the EU limits is used to obtain an initial value for the desired telemetry count. The method presented here is not new. What is new is how classical numerical techniques are optimized to take advantage of modem computer power to perform the desired calculations in real time. This technique makes the method simple to understand and implement. There are no interpolation tables to store in memory as in traditional methods. The NASA F-15 simulation converts and transmits over 1000 parameters at 80 times/sec. This paper presents algorithm development, FORTRAN code, and performance results.

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Probabilistic track coverage in cooperative sensor networks.

PubMed

Ferrari, Silvia; Zhang, Guoxian; Wettergren, Thomas A

2010-12-01

The quality of service of a network performing cooperative track detection is represented by the probability of obtaining multiple elementary detections over time along a target track. Recently, two different lines of research, namely, distributed-search theory and geometric transversals, have been used in the literature for deriving the probability of track detection as a function of random and deterministic sensors' positions, respectively. In this paper, we prove that these two approaches are equivalent under the same problem formulation. Also, we present a new performance function that is derived by extending the geometric-transversal approach to the case of random sensors' positions using Poisson flats. As a result, a unified approach for addressing track detection in both deterministic and probabilistic sensor networks is obtained. The new performance function is validated through numerical simulations and is shown to bring about considerable computational savings for both deterministic and probabilistic sensor networks.

Deterministic blade row interactions in a centrifugal compressor stage

NASA Technical Reports Server (NTRS)

Kirtley, K. R.; Beach, T. A.

1991-01-01

The three-dimensional viscous flow in a low speed centrifugal compressor stage is simulated using an average passage Navier-Stokes analysis. The impeller discharge flow is of the jet/wake type with low momentum fluid in the shroud-pressure side corner coincident with the tip leakage vortex. This nonuniformity introduces periodic unsteadiness in the vane frame of reference. The effect of such deterministic unsteadiness on the time-mean is included in the analysis through the average passage stress, which allows the analysis of blade row interactions. The magnitude of the divergence of the deterministic unsteady stress is of the order of the divergence of the Reynolds stress over most of the span, from the impeller trailing edge to the vane throat. Although the potential effects on the blade trailing edge from the diffuser vane are small, strong secondary flows generated by the impeller degrade the performance of the diffuser vanes.

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1992-01-01

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Conformal Galilei algebras, symmetric polynomials and singular vectors

NASA Astrophysics Data System (ADS)

Křižka, Libor; Somberg, Petr

2018-01-01

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga_ℓ (d,C) with d=1 for any integer value ℓ \\in N. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.

Identities associated with Milne-Thomson type polynomials and special numbers.

PubMed

Simsek, Yilmaz; Cakic, Nenad

2018-01-01

The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

Integrating stochastic time-dependent travel speed in solution methods for the dynamic dial-a-ride problem.

PubMed

Schilde, M; Doerner, K F; Hartl, R F

2014-10-01

In urban areas, logistic transportation operations often run into problems because travel speeds change, depending on the current traffic situation. If not accounted for, time-dependent and stochastic travel speeds frequently lead to missed time windows and thus poorer service. Especially in the case of passenger transportation, it often leads to excessive passenger ride times as well. Therefore, time-dependent and stochastic influences on travel speeds are relevant for finding feasible and reliable solutions. This study considers the effect of exploiting statistical information available about historical accidents, using stochastic solution approaches for the dynamic dial-a-ride problem (dynamic DARP). The authors propose two pairs of metaheuristic solution approaches, each consisting of a deterministic method (average time-dependent travel speeds for planning) and its corresponding stochastic version (exploiting stochastic information while planning). The results, using test instances with up to 762 requests based on a real-world road network, show that in certain conditions, exploiting stochastic information about travel speeds leads to significant improvements over deterministic approaches.

Adequacy assessment of composite generation and transmission systems incorporating wind energy conversion systems

NASA Astrophysics Data System (ADS)

Gao, Yi

The development and utilization of wind energy for satisfying electrical demand has received considerable attention in recent years due to its tremendous environmental, social and economic benefits, together with public support and government incentives. Electric power generation from wind energy behaves quite differently from that of conventional sources. The fundamentally different operating characteristics of wind energy facilities therefore affect power system reliability in a different manner than those of conventional systems. The reliability impact of such a highly variable energy source is an important aspect that must be assessed when the wind power penetration is significant. The focus of the research described in this thesis is on the utilization of state sampling Monte Carlo simulation in wind integrated bulk electric system reliability analysis and the application of these concepts in system planning and decision making. Load forecast uncertainty is an important factor in long range planning and system development. This thesis describes two approximate approaches developed to reduce the number of steps in a load duration curve which includes load forecast uncertainty, and to provide reasonably accurate generating and bulk system reliability index predictions. The developed approaches are illustrated by application to two composite test systems. A method of generating correlated random numbers with uniform distributions and a specified correlation coefficient in the state sampling method is proposed and used to conduct adequacy assessment in generating systems and in bulk electric systems containing correlated wind farms in this thesis. The studies described show that it is possible to use the state sampling Monte Carlo simulation technique to quantitatively assess the reliability implications associated with adding wind power to a composite generation and transmission system including the effects of multiple correlated wind sites. This is an important development as it permits correlated wind farms to be incorporated in large practical system studies without requiring excessive increases in computer solution time. The procedures described in this thesis for creating monthly and seasonal wind farm models should prove useful in situations where time period models are required to incorporate scheduled maintenance of generation and transmission facilities. There is growing interest in combining deterministic considerations with probabilistic assessment in order to evaluate the quantitative system risk and conduct bulk power system planning. A relatively new approach that incorporates deterministic and probabilistic considerations in a single risk assessment framework has been designated as the joint deterministic-probabilistic approach. The research work described in this thesis illustrates that the joint deterministic-probabilistic approach can be effectively used to integrate wind power in bulk electric system planning. The studies described in this thesis show that the application of the joint deterministic-probabilistic method provides more stringent results for a system with wind power than the traditional deterministic N-1 method because the joint deterministic-probabilistic technique is driven by the deterministic N-1 criterion with an added probabilistic perspective which recognizes the power output characteristics of a wind turbine generator.

Geometry Dynamics of α-Helices in Different Class I Major Histocompatibility Complexes

PubMed Central

Karch, Rudolf; Schreiner, Wolfgang

2015-01-01

MHC α-helices form the antigen-binding cleft and are of particular interest for immunological reactions. To monitor these helices in molecular dynamics simulations, we applied a parsimonious fragment-fitting method to trace the axes of the α-helices. Each resulting axis was fitted by polynomials in a least-squares sense and the curvature integral was computed. To find the appropriate polynomial degree, the method was tested on two artificially modelled helices, one performing a bending movement and another a hinge movement. We found that second-order polynomials retrieve predefined parameters of helical motion with minimal relative error. From MD simulations we selected those parts of α-helices that were stable and also close to the TCR/MHC interface. We monitored the curvature integral, generated a ruled surface between the two MHC α-helices, and computed interhelical area and surface torsion, as they changed over time. We found that MHC α-helices undergo rapid but small changes in conformation. The curvature integral of helices proved to be a sensitive measure, which was closely related to changes in shape over time as confirmed by RMSD analysis. We speculate that small changes in the conformation of individual MHC α-helices are part of the intrinsic dynamics induced by engagement with the TCR. PMID:26649324

The Approximability of Partial Vertex Covers in Trees.

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

Mkrtchyan, Vahan; Parekh, Ojas D.; Segev, Danny

Motivated by applications in risk management of computational systems, we focus our attention on a special case of the partial vertex cover problem, where the underlying graph is assumed to be a tree. Here, we consider four possible versions of this setting, depending on whether vertices and edges are weighted or not. Two of these versions, where edges are assumed to be unweighted, are known to be polynomial-time solvable (Gandhi, Khuller, and Srinivasan, 2004). However, the computational complexity of this problem with weighted edges, and possibly with weighted vertices, has not been determined yet. The main contribution of this papermore » is to resolve these questions, by fully characterizing which variants of partial vertex cover remain intractable in trees, and which can be efficiently solved. In particular, we propose a pseudo-polynomial DP-based algorithm for the most general case of having weights on both edges and vertices, which is proven to be NPhard. This algorithm provides a polynomial-time solution method when weights are limited to edges, and combined with additional scaling ideas, leads to an FPTAS for the general case. A secondary contribution of this work is to propose a novel way of using centroid decompositions in trees, which could be useful in other settings as well.« less

Approximating smooth functions using algebraic-trigonometric polynomials

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

Sharapudinov, Idris I

2011-01-14

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3

Parameter reduction in nonlinear state-space identification of hysteresis

NASA Astrophysics Data System (ADS)

Fakhrizadeh Esfahani, Alireza; Dreesen, Philippe; Tiels, Koen; Noël, Jean-Philippe; Schoukens, Johan

2018-05-01

Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50%, while maintaining a comparable output error level.

Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

NASA Astrophysics Data System (ADS)

Kędra, Mariola

2014-02-01

Is the underlying dynamics of river flow random or deterministic? If it is deterministic, is it deterministic chaotic? This issue is still controversial. The application of several independent methods, techniques and tools for studying daily river flow data gives consistent, reliable and clear-cut results to the question. The outcomes point out that the investigated discharge dynamics is not random but deterministic. Moreover, the results completely confirm the nonlinear deterministic chaotic nature of the studied process. The research was conducted on daily discharge from two selected gauging stations of the mountain river in southern Poland, the Raba River.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

Algorithms for optimizing cross-overs in DNA shuffling.

PubMed

He, Lu; Friedman, Alan M; Bailey-Kellogg, Chris

2012-03-21

DNA shuffling generates combinatorial libraries of chimeric genes by stochastically recombining parent genes. The resulting libraries are subjected to large-scale genetic selection or screening to identify those chimeras with favorable properties (e.g., enhanced stability or enzymatic activity). While DNA shuffling has been applied quite successfully, it is limited by its homology-dependent, stochastic nature. Consequently, it is used only with parents of sufficient overall sequence identity, and provides no control over the resulting chimeric library. This paper presents efficient methods to extend the scope of DNA shuffling to handle significantly more diverse parents and to generate more predictable, optimized libraries. Our CODNS (cross-over optimization for DNA shuffling) approach employs polynomial-time dynamic programming algorithms to select codons for the parental amino acids, allowing for zero or a fixed number of conservative substitutions. We first present efficient algorithms to optimize the local sequence identity or the nearest-neighbor approximation of the change in free energy upon annealing, objectives that were previously optimized by computationally-expensive integer programming methods. We then present efficient algorithms for more powerful objectives that seek to localize and enhance the frequency of recombination by producing "runs" of common nucleotides either overall or according to the sequence diversity of the resulting chimeras. We demonstrate the effectiveness of CODNS in choosing codons and allocating substitutions to promote recombination between parents targeted in earlier studies: two GAR transformylases (41% amino acid sequence identity), two very distantly related DNA polymerases, Pol X and β (15%), and beta-lactamases of varying identity (26-47%). Our methods provide the protein engineer with a new approach to DNA shuffling that supports substantially more diverse parents, is more deterministic, and generates more predictable and more diverse chimeric libraries.

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

Brickell, E.F.; Davis, J.A.; Simmons, G.J.

A study of the algorithm and the underlying mathematical concepts of A Polynomial Time Algorithm for Breaking Merkle-Hellman Cryptosystems, by Adi Shamir, is presented. Ways of protecting the Merkle-Hellman knapsack from cryptanalysis are given with derivations. (GHT)

Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1992-01-01

Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

A polynomial primal-dual Dikin-type algorithm for linear programming

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

Jansen, B.; Roos, R.; Terlaky, T.

1994-12-31

We present a new primal-dual affine scaling method for linear programming. The search direction is obtained by using Dikin`s original idea: minimize the objective function (which is the duality gap in a primal-dual algorithm) over a suitable ellipsoid. The search direction has no obvious relationship with the directions proposed in the literature so far. It guarantees a significant decrease in the duality gap in each iteration, and at the same time drives the iterates to the central path. The method admits a polynomial complexity bound that is better than the one for Monteiro et al.`s original primal-dual affine scaling method.

Digital SAR processing using a fast polynomial transform

NASA Technical Reports Server (NTRS)

Butman, S.; Lipes, R.; Rubin, A.; Truong, T. K.

1981-01-01

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network.

Classical verification of quantum circuits containing few basis changes

NASA Astrophysics Data System (ADS)

Demarie, Tommaso F.; Ouyang, Yingkai; Fitzsimons, Joseph F.

2018-04-01

We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier hierarchy, the lowest level for which there is an established quantum advantage. We show that when the circuit has an outcome with probability at least the inverse of some polynomial in the circuit size, the outcome can be checked in polynomial time with bounded error by a completely classical verifier. This verification procedure is based on random sampling of computational paths and is only possible given knowledge of the likely outcome.

Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

NASA Astrophysics Data System (ADS)

Arzani, Francesco; Treps, Nicolas; Ferrini, Giulia

2017-05-01

In quantum computation with continuous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the laboratory. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.

Universal Racah matrices and adjoint knot polynomials: Arborescent knots

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2016-04-01

By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

Imaging characteristics of Zernike and annular polynomial aberrations.

PubMed

Mahajan, Virendra N; Díaz, José Antonio

2013-04-01

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

Improving Deterministic Reserve Requirements for Security Constrained Unit Commitment and Scheduling Problems in Power Systems

NASA Astrophysics Data System (ADS)

Wang, Fengyu

Traditional deterministic reserve requirements rely on ad-hoc, rule of thumb methods to determine adequate reserve in order to ensure a reliable unit commitment. Since congestion and uncertainties exist in the system, both the quantity and the location of reserves are essential to ensure system reliability and market efficiency. The modeling of operating reserves in the existing deterministic reserve requirements acquire the operating reserves on a zonal basis and do not fully capture the impact of congestion. The purpose of a reserve zone is to ensure that operating reserves are spread across the network. Operating reserves are shared inside each reserve zone, but intra-zonal congestion may block the deliverability of operating reserves within a zone. Thus, improving reserve policies such as reserve zones may improve the location and deliverability of reserve. As more non-dispatchable renewable resources are integrated into the grid, it will become increasingly difficult to predict the transfer capabilities and the network congestion. At the same time, renewable resources require operators to acquire more operating reserves. With existing deterministic reserve requirements unable to ensure optimal reserve locations, the importance of reserve location and reserve deliverability will increase. While stochastic programming can be used to determine reserve by explicitly modelling uncertainties, there are still scalability as well as pricing issues. Therefore, new methods to improve existing deterministic reserve requirements are desired. One key barrier of improving existing deterministic reserve requirements is its potential market impacts. A metric, quality of service, is proposed in this thesis to evaluate the price signal and market impacts of proposed hourly reserve zones. Three main goals of this thesis are: 1) to develop a theoretical and mathematical model to better locate reserve while maintaining the deterministic unit commitment and economic dispatch structure, especially with the consideration of renewables, 2) to develop a market settlement scheme of proposed dynamic reserve policies such that the market efficiency is improved, 3) to evaluate the market impacts and price signal of the proposed dynamic reserve policies.

Formal language constrained path problems

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

Barrett, C.; Jacob, R.; Marathe, M.

1997-07-08

In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvablemore » efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.« less

A combinatorial model for the Macdonald polynomials.

PubMed

Haglund, J

2004-11-16

We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdonald polynomial H(mu)[Z; q, t]. We further introduce a general family of polynomials F(T)[Z; q, S], where T is an arbitrary set of squares in the first quadrant of the xy plane, and S is an arbitrary subset of T. The coefficients of the F(T)[Z; q, S] are in N[q], and C(mu)[Z; q, t] is a sum of certain F(T)[Z; q, S] times nonnegative powers of t. We prove F(T)[Z; q, S] is symmetric in the z(i) and satisfies other properties consistent with the conjecture. We also show how the coefficient of a monomial in F(T)[Z; q, S] can be expressed recursively. maple calculations indicate the F(T)[Z; q, S] are Schur-positive, and we present a combinatorial conjecture for their Schur coefficients when the set T is a partition with at most three columns.

Prediction of zeolite-cement-sand unconfined compressive strength using polynomial neural network

NASA Astrophysics Data System (ADS)

MolaAbasi, H.; Shooshpasha, I.

2016-04-01

The improvement of local soils with cement and zeolite can provide great benefits, including strengthening slopes in slope stability problems, stabilizing problematic soils and preventing soil liquefaction. Recently, dosage methodologies are being developed for improved soils based on a rational criterion as it exists in concrete technology. There are numerous earlier studies showing the possibility of relating Unconfined Compressive Strength (UCS) and Cemented sand (CS) parameters (voids/cement ratio) as a power function fits. Taking into account the fact that the existing equations are incapable of estimating UCS for zeolite cemented sand mixture (ZCS) well, artificial intelligence methods are used for forecasting them. Polynomial-type neural network is applied to estimate the UCS from more simply determined index properties such as zeolite and cement content, porosity as well as curing time. In order to assess the merits of the proposed approach, a total number of 216 unconfined compressive tests have been done. A comparison is carried out between the experimentally measured UCS with the predictions in order to evaluate the performance of the current method. The results demonstrate that generalized polynomial-type neural network has a great ability for prediction of the UCS. At the end sensitivity analysis of the polynomial model is applied to study the influence of input parameters on model output. The sensitivity analysis reveals that cement and zeolite content have significant influence on predicting UCS.

Uncertainty Quantification in CO 2 Sequestration Using Surrogate Models from Polynomial Chaos Expansion

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

Zhang, Yan; Sahinidis, Nikolaos V.

2013-03-06

In this paper, surrogate models are iteratively built using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using amore » classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the values of the uncertain parameters into the closed-form polynomial functions. Based on the results of MC simulation, the uncertainties of injecting CO{sub 2} underground are quantified for a saline aquifer. Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO{sub 2} injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.« less

Stochasticity, succession, and environmental perturbations in a fluidic ecosystem

PubMed Central

Zhou, Jizhong; Deng, Ye; Zhang, Ping; Xue, Kai; Liang, Yuting; Van Nostrand, Joy D.; Yang, Yunfeng; He, Zhili; Wu, Liyou; Stahl, David A.; Hazen, Terry C.; Tiedje, James M.; Arkin, Adam P.

2014-01-01

Unraveling the drivers of community structure and succession in response to environmental change is a central goal in ecology. Although the mechanisms shaping community structure have been intensively examined, those controlling ecological succession remain elusive. To understand the relative importance of stochastic and deterministic processes in mediating microbial community succession, a unique framework composed of four different cases was developed for fluidic and nonfluidic ecosystems. The framework was then tested for one fluidic ecosystem: a groundwater system perturbed by adding emulsified vegetable oil (EVO) for uranium immobilization. Our results revealed that groundwater microbial community diverged substantially away from the initial community after EVO amendment and eventually converged to a new community state, which was closely clustered with its initial state. However, their composition and structure were significantly different from each other. Null model analysis indicated that both deterministic and stochastic processes played important roles in controlling the assembly and succession of the groundwater microbial community, but their relative importance was time dependent. Additionally, consistent with the proposed conceptual framework but contradictory to conventional wisdom, the community succession responding to EVO amendment was primarily controlled by stochastic rather than deterministic processes. During the middle phase of the succession, the roles of stochastic processes in controlling community composition increased substantially, ranging from 81.3% to 92.0%. Finally, there are limited successional studies available to support different cases in the conceptual framework, but further well-replicated explicit time-series experiments are needed to understand the relative importance of deterministic and stochastic processes in controlling community succession. PMID:24550501

Causal properties of nonlinear gravitational waves in modified gravity

NASA Astrophysics Data System (ADS)

Suvorov, Arthur George; Melatos, Andrew

2017-09-01

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.

Single-machine group scheduling problems with deteriorating and learning effect

NASA Astrophysics Data System (ADS)

Xingong, Zhang; Yong, Wang; Shikun, Bai

2016-07-01

The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as 'group technology' in the literature. In this paper, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.

Radiometer Calibrations: Saving Time by Automating the Gathering and Analysis Procedures

NASA Technical Reports Server (NTRS)

Sadino, Jeffrey L.

2005-01-01

Mr. Abtahi custom-designs radiometers for Mr. Hook's research group. Inherently, when the radiometers report the temperature of arbitrary surfaces, the results are affected by errors in accuracy. This problem can be reduced if the errors can be accounted for in a polynomial. This is achieved by pointing the radiometer at a constant-temperature surface. We have been using a Hartford Scientific WaterBath. The measurements from the radiometer are collected at many different temperatures and compared to the measurements made by a Hartford Chubb thermometer with a four-decimal point resolution. The data is analyzed and fit to a fifth-order polynomial. This formula is then uploaded into the radiometer software, enabling accurate data gathering. Traditionally, Mr. Abtahi has done this by hand, spending several hours of his time setting the temperature, waiting for stabilization, taking measurements, and then repeating for other temperatures. My program, written in the Python language, has enabled the data gathering and analysis process to be handed off to a less-senior member of the team. Simply by entering several initial settings, the program will simultaneously control all three instruments and organize the data suitable for computer analyses, thus giving the desired fifth-order polynomial. This will save time, allow for a more complete calibration data set, and allow for base calibrations to be developed. The program is expandable to simultaneously take any type of measurement from up to nine distinct instruments.

On the degree conjecture for separability of multipartite quantum states

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

Hassan, Ali Saif M.; Joag, Pramod S.

2008-01-15

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein et al. [Phys. Rev. A 73, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matricesmore » match. We prove the strong form of the conjecture for pure multipartite quantum states using the modified tensor product of graphs defined by Hassan and Joag [J. Phys. A 40, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm, we mean that the execution time of this algorithm increases as a polynomial in m, where m is the number of parts of the quantum system. We give a counterexample to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.« less

BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees.

PubMed

Fleischauer, Markus; Böcker, Sebastian

2018-01-01

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

Applications of polynomial optimization in financial risk investment

NASA Astrophysics Data System (ADS)

Zeng, Meilan; Fu, Hongwei

2017-09-01

Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

A Stochastic Mixed Finite Element Heterogeneous Multiscale Method for Flow in Porous Media

DTIC Science & Technology

2010-08-01

applicable for flow in porous media has drawn significant interest in the last few years. Several techniques like generalized polynomial chaos expansions (gPC...represents the stochastic solution as a polynomial approxima- tion. This interpolant is constructed via independent function calls to the de- terministic...of orthogonal polynomials [34,38] or sparse grid approximations [39–41]. It is well known that the global polynomial interpolation cannot resolve lo

A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

DTIC Science & Technology

1978-03-01

Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS

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

P. T. P. HUTAURUK, D. G. IRELAND, G. ROSNER

2009-04-01

Angular distributions of differential cross sections from the latest CLAS data sets,6 for the reaction γ + p→K+ + Λ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. 1 where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We thenmore » compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.« less

Tutte polynomial in functional magnetic resonance imaging

NASA Astrophysics Data System (ADS)

García-Castillón, Marlly V.

2015-09-01

Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

PubMed Central

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. PMID:24603904

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

On a Family of Multivariate Modified Humbert Polynomials

PubMed Central

Aktaş, Rabia; Erkuş-Duman, Esra

2013-01-01

This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411

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

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Stochastic spectral projection of electrochemical thermal model for lithium-ion cell state estimation

NASA Astrophysics Data System (ADS)

Tagade, Piyush; Hariharan, Krishnan S.; Kolake, Subramanya Mayya; Song, Taewon; Oh, Dukjin

2017-03-01

A novel approach for integrating a pseudo-two dimensional electrochemical thermal (P2D-ECT) model and data assimilation algorithm is presented for lithium-ion cell state estimation. This approach refrains from making any simplifications in the P2D-ECT model while making it amenable for online state estimation. Though deterministic, uncertainty in the initial states induces stochasticity in the P2D-ECT model. This stochasticity is resolved by spectrally projecting the stochastic P2D-ECT model on a set of orthogonal multivariate Hermite polynomials. Volume averaging in the stochastic dimensions is proposed for efficient numerical solution of the resultant model. A state estimation framework is developed using a transformation of the orthogonal basis to assimilate the measurables with this system of equations. Effectiveness of the proposed method is first demonstrated by assimilating the cell voltage and temperature data generated using a synthetic test bed. This validated method is used with the experimentally observed cell voltage and temperature data for state estimation at different operating conditions and drive cycle protocols. The results show increased prediction accuracy when the data is assimilated every 30s. High accuracy of the estimated states is exploited to infer temperature dependent behavior of the lithium-ion cell.

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method

NASA Astrophysics Data System (ADS)

Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei

2017-12-01

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 0.9998, 0.9915, 0.9895, and 0.9940 respectively). The proposed spline interpolation method exhibits better linear correlation and smaller error in the results of the quantitative analysis of Cu compared with polynomial fitting, Lorentz fitting and model-free methods, The simulation and quantitative experimental results show that the spline interpolation method can effectively detect and correct the continuous background.

Impact of Periodic Unsteadiness on Performance and Heat Load in Axial Flow Turbomachines

NASA Technical Reports Server (NTRS)

Sharma, Om P.; Stetson, Gary M.; Daniels, William A,; Greitzer, Edward M.; Blair, Michael F.; Dring, Robert P.

1997-01-01

Results of an analytical and experimental investigation, directed at the understanding of the impact of periodic unsteadiness on the time-averaged flows in axial flow turbomachines, are presented. Analysis of available experimental data, from a large-scale rotating rig (LSRR) (low speed rig), shows that in the time-averaged axisymmetric equations the magnitude of the terms representing the effect of periodic unsteadiness (deterministic stresses) are as large or larger than those due to random unsteadiness (turbulence). Numerical experiments, conducted to highlight physical mechanisms associated with the migration of combustor generated hot-streaks in turbine rotors, indicated that the effect can be simulated by accounting for deterministic stress like terms in the time-averaged mass and energy conservation equations. The experimental portion of this program shows that the aerodynamic loss for the second stator in a 1-1/2 stage turbine are influenced by the axial spacing between the second stator leading edge and the rotor trailing edge. However, the axial spacing has little impact on the heat transfer coefficient. These performance changes are believed to be associated with the change in deterministic stress at the inlet to the second stator. Data were also acquired to quantify the impact of indexing the first stator relative to the second stator. For the range of parameters examined, this effect was found to be of the same order as the effect of axial spacing.

Hybrid Forecasting of Daily River Discharges Considering Autoregressive Heteroscedasticity

NASA Astrophysics Data System (ADS)

Szolgayová, Elena Peksová; Danačová, Michaela; Komorniková, Magda; Szolgay, Ján

2017-06-01

It is widely acknowledged that in the hydrological and meteorological communities, there is a continuing need to improve the quality of quantitative rainfall and river flow forecasts. A hybrid (combined deterministic-stochastic) modelling approach is proposed here that combines the advantages offered by modelling the system dynamics with a deterministic model and a deterministic forecasting error series with a data-driven model in parallel. Since the processes to be modelled are generally nonlinear and the model error series may exhibit nonstationarity and heteroscedasticity, GARCH-type nonlinear time series models are considered here. The fitting, forecasting and simulation performance of such models have to be explored on a case-by-case basis. The goal of this paper is to test and develop an appropriate methodology for model fitting and forecasting applicable for daily river discharge forecast error data from the GARCH family of time series models. We concentrated on verifying whether the use of a GARCH-type model is suitable for modelling and forecasting a hydrological model error time series on the Hron and Morava Rivers in Slovakia. For this purpose we verified the presence of heteroscedasticity in the simulation error series of the KLN multilinear flow routing model; then we fitted the GARCH-type models to the data and compared their fit with that of an ARMA - type model. We produced one-stepahead forecasts from the fitted models and again provided comparisons of the model's performance.

Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines

DOE PAGES

Finney, Charles E.; Kaul, Brian C.; Daw, C. Stuart; ...

2015-02-18

Here we review developments in the understanding of cycle to cycle variability in internal combustion engines, with a focus on spark-ignited and premixed combustion conditions. Much of the research on cyclic variability has focused on stochastic aspects, that is, features that can be modeled as inherently random with no short term predictability. In some cases, models of this type appear to work very well at describing experimental observations, but the lack of predictability limits control options. Also, even when the statistical properties of the stochastic variations are known, it can be very difficult to discern their underlying physical causes andmore » thus mitigate them. Some recent studies have demonstrated that under some conditions, cyclic combustion variations can have a relatively high degree of low dimensional deterministic structure, which implies some degree of predictability and potential for real time control. These deterministic effects are typically more pronounced near critical stability limits (e.g. near tipping points associated with ignition or flame propagation) such during highly dilute fueling or near the onset of homogeneous charge compression ignition. We review recent progress in experimental and analytical characterization of cyclic variability where low dimensional, deterministic effects have been observed. We describe some theories about the sources of these dynamical features and discuss prospects for interactive control and improved engine designs. In conclusion, taken as a whole, the research summarized here implies that the deterministic component of cyclic variability will become a pivotal issue (and potential opportunity) as engine manufacturers strive to meet aggressive emissions and fuel economy regulations in the coming decades.« less

The stochastic energy-Casimir method

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis; Ganaba, Nader; Holm, Darryl D.

2018-04-01

In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for stability in probability of stochastic dynamical systems with symmetries. We illustrate this theory with classical examples of coadjoint motion, including the rigid body, the heavy top, and the compressible Euler equation in two dimensions. The main result is that stable deterministic equilibria remain stable in probability up to a certain stopping time that depends on the amplitude of the noise for finite-dimensional systems and on the amplitude of the spatial derivative of the noise for infinite-dimensional systems. xml:lang="fr"

A high repetition deterministic single ion source

NASA Astrophysics Data System (ADS)

Sahin, C.; Geppert, P.; Müllers, A.; Ott, H.

2017-12-01

We report on a deterministic single ion source with high repetition rate and high fidelity. The source employs a magneto-optical trap, where ultracold rubidium atoms are photoionized. The electrons herald the creation of a corresponding ion, whose timing information is used to manipulate its trajectory in flight. We demonstrate an ion rate of up to 4× {10}4 {{{s}}}-1 and achieve a fidelity for single ion operation of 98%. The technique can be used for all atomic species, which can be laser-cooled, and opens up new applications in ion microscopy, ion implantation and surface spectroscopy.

How synapses can enhance sensibility of a neural network

NASA Astrophysics Data System (ADS)

Protachevicz, P. R.; Borges, F. S.; Iarosz, K. C.; Caldas, I. L.; Baptista, M. S.; Viana, R. L.; Lameu, E. L.; Macau, E. E. N.; Batista, A. M.

2018-02-01

In this work, we study the dynamic range in a neural network modelled by cellular automaton. We consider deterministic and non-deterministic rules to simulate electrical and chemical synapses. Chemical synapses have an intrinsic time-delay and are susceptible to parameter variations guided by learning Hebbian rules of behaviour. The learning rules are related to neuroplasticity that describes change to the neural connections in the brain. Our results show that chemical synapses can abruptly enhance sensibility of the neural network, a manifestation that can become even more predominant if learning rules of evolution are applied to the chemical synapses.

Deterministic Migration-Based Separation of White Blood Cells.

PubMed

Kim, Byeongyeon; Choi, Young Joon; Seo, Hyekyung; Shin, Eui-Cheol; Choi, Sungyoung

2016-10-01

Functional and phenotypic analyses of peripheral white blood cells provide useful clinical information. However, separation of white blood cells from peripheral blood requires a time-consuming, inconvenient process and thus analyses of separated white blood cells are limited in clinical settings. To overcome this limitation, a microfluidic separation platform is developed to enable deterministic migration of white blood cells, directing the cells into designated positions according to a ridge pattern. The platform uses slant ridge structures on the channel top to induce the deterministic migration, which allows efficient and high-throughput separation of white blood cells from unprocessed whole blood. The extent of the deterministic migration under various rheological conditions is explored, enabling highly efficient migration of white blood cells in whole blood and achieving high-throughput separation of the cells (processing 1 mL of whole blood less than 7 min). In the separated cell population, the composition of lymphocyte subpopulations is well preserved, and T cells secrete cytokines without any functional impairment. On the basis of the results, this microfluidic platform is a promising tool for the rapid enrichment of white blood cells, and it is useful for functional and phenotypic analyses of peripheral white blood cells. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Comparison between deterministic and statistical wavelet estimation methods through predictive deconvolution: Seismic to well tie example from the North Sea

NASA Astrophysics Data System (ADS)

de Macedo, Isadora A. S.; da Silva, Carolina B.; de Figueiredo, J. J. S.; Omoboya, Bode

2017-01-01

Wavelet estimation as well as seismic-to-well tie procedures are at the core of every seismic interpretation workflow. In this paper we perform a comparative study of wavelet estimation methods for seismic-to-well tie. Two approaches to wavelet estimation are discussed: a deterministic estimation, based on both seismic and well log data, and a statistical estimation, based on predictive deconvolution and the classical assumptions of the convolutional model, which provides a minimum-phase wavelet. Our algorithms, for both wavelet estimation methods introduce a semi-automatic approach to determine the optimum parameters of deterministic wavelet estimation and statistical wavelet estimation and, further, to estimate the optimum seismic wavelets by searching for the highest correlation coefficient between the recorded trace and the synthetic trace, when the time-depth relationship is accurate. Tests with numerical data show some qualitative conclusions, which are probably useful for seismic inversion and interpretation of field data, by comparing deterministic wavelet estimation and statistical wavelet estimation in detail, especially for field data example. The feasibility of this approach is verified on real seismic and well data from Viking Graben field, North Sea, Norway. Our results also show the influence of the washout zones on well log data on the quality of the well to seismic tie.

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

NASA Astrophysics Data System (ADS)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Parallel Stochastic discrete event simulation of calcium dynamics in neuron.

PubMed

Ishlam Patoary, Mohammad Nazrul; Tropper, Carl; McDougal, Robert A; Zhongwei, Lin; Lytton, William W

2017-09-26

The intra-cellular calcium signaling pathways of a neuron depends on both biochemical reactions and diffusions. Some quasi-isolated compartments (e.g. spines) are so small and calcium concentrations are so low that one extra molecule diffusing in by chance can make a nontrivial difference in its concentration (percentage-wise). These rare events can affect dynamics discretely in such way that they cannot be evaluated by a deterministic simulation. Stochastic models of such a system provide a more detailed understanding of these systems than existing deterministic models because they capture their behavior at a molecular level. Our research focuses on the development of a high performance parallel discrete event simulation environment, Neuron Time Warp (NTW), which is intended for use in the parallel simulation of stochastic reaction-diffusion systems such as intra-calcium signaling. NTW is integrated with NEURON, a simulator which is widely used within the neuroscience community. We simulate two models, a calcium buffer and a calcium wave model. The calcium buffer model is employed in order to verify the correctness and performance of NTW by comparing it to a serial deterministic simulation in NEURON. We also derived a discrete event calcium wave model from a deterministic model using the stochastic IP3R structure.

Real-time flood forecasting

USGS Publications Warehouse

Lai, C.; Tsay, T.-K.; Chien, C.-H.; Wu, I.-L.

2009-01-01

Researchers at the Hydroinformatic Research and Development Team (HIRDT) of the National Taiwan University undertook a project to create a real time flood forecasting model, with an aim to predict the current in the Tamsui River Basin. The model was designed based on deterministic approach with mathematic modeling of complex phenomenon, and specific parameter values operated to produce a discrete result. The project also devised a rainfall-stage model that relates the rate of rainfall upland directly to the change of the state of river, and is further related to another typhoon-rainfall model. The geographic information system (GIS) data, based on precise contour model of the terrain, estimate the regions that were perilous to flooding. The HIRDT, in response to the project's progress, also devoted their application of a deterministic model to unsteady flow of thermodynamics to help predict river authorities issue timely warnings and take other emergency measures.

Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

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

Shao, Sihong, E-mail: sihong@math.pku.edu.cn; Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-11-01

Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution ofmore » a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.« less

Forbidden patterns in financial time series

NASA Astrophysics Data System (ADS)

Zanin, Massimiliano

2008-03-01

The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, such as Lyapunov exponent or Kolmogorov entropy, thus allowing to separate deterministic (usually chaotic) from random series; however, it requires fewer values of the series to be calculated, and it is suitable for using with small datasets. In this paper, the appearance of forbidden patterns is studied in different economical indicators such as stock indices (Dow Jones Industrial Average and Nasdaq Composite), NYSE stocks (IBM and Boeing), and others (ten year Bond interest rate), to find evidence of deterministic behavior in their evolutions. Moreover, the rate of appearance of the forbidden patterns is calculated, and some considerations about the underlying dynamics are suggested.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Analysis on the misalignment errors between Hartmann-Shack sensor and 45-element deformable mirror

NASA Astrophysics Data System (ADS)

Liu, Lihui; Zhang, Yi; Tao, Jianjun; Cao, Fen; Long, Yin; Tian, Pingchuan; Chen, Shangwu

2017-02-01

Aiming at 45-element adaptive optics system, the model of 45-element deformable mirror is truly built by COMSOL Multiphysics, and every actuator's influence function is acquired by finite element method. The process of this system correcting optical aberration is simulated by making use of procedure, and aiming for Strehl ratio of corrected diffraction facula, in the condition of existing different translation and rotation error between Hartmann-Shack sensor and deformable mirror, the system's correction ability for 3-20 Zernike polynomial wave aberration is analyzed. The computed result shows: the system's correction ability for 3-9 Zernike polynomial wave aberration is higher than that of 10-20 Zernike polynomial wave aberration. The correction ability for 3-20 Zernike polynomial wave aberration does not change with misalignment error changing. With rotation error between Hartmann-Shack sensor and deformable mirror increasing, the correction ability for 3-20 Zernike polynomial wave aberration gradually goes down, and with translation error increasing, the correction ability for 3-9 Zernike polynomial wave aberration gradually goes down, but the correction ability for 10-20 Zernike polynomial wave aberration behave up-and-down depression.

Stability analysis of fuzzy parametric uncertain systems.

PubMed

Bhiwani, R J; Patre, B M

2011-10-01

In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2004-08-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

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

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

On the Analytical and Numerical Properties of the Truncated Laplace Transform I

DTIC Science & Technology

2014-09-05

contains generalizations and conclusions. 2 2 Preliminaries 2.1 The Legendre Polynomials In this subsection we summarize some of the properties of the the...standard Legendre Polynomi - als, and restate these properties for shifted and normalized forms of the Legendre Polynomials . We define the Shifted... Legendre Polynomial of degree k = 0, 1, ..., which we will be denoting by P ∗k , by the formula P ∗k (x) = Pk(2x− 1), (5) where Pk is the Legendre

Effects of Air Drag and Lunar Third-Body Perturbations on Motion Near a Reference KAM Torus

DTIC Science & Technology

2011-03-01

body m 1) mass of satellite; 2) order of associated Legendre polynomial n 1) mean motion; 2) degree of associated Legendre polynomial n3 mean motion...physical momentum pi ith physical momentum Pmn associated Legendre polynomial of order m and degree n q̇ physical coordinate derivatives vector, [q̇1...are constants specifying the shape of the gravitational field; and Pmn are associated Legendre polynomials . When m = n = 0, the geopotential function

Luigi Gatteschi's work on asymptotics of special functions and their zeros

NASA Astrophysics Data System (ADS)

Gautschi, Walter; Giordano, Carla

2008-12-01

A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

Maximizing Submodular Functions under Matroid Constraints by Evolutionary Algorithms.

PubMed

Friedrich, Tobias; Neumann, Frank

2015-01-01

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a simple single objective evolutionary algorithm called (1 + 1) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints, we show that the GSEMO achieves a (1 - 1/e)-approximation in expected polynomial time. For the case of monotone functions where the constraints are given by the intersection of K ≥ 2 matroids, we show that the (1 + 1) EA achieves a (1/k + δ)-approximation in expected polynomial time for any constant δ > 0. Turning to nonmonotone symmetric submodular functions with k ≥ 1 matroid intersection constraints, we show that the GSEMO achieves a 1/((k + 2)(1 + ε))-approximation in expected time O(n(k + 6)log(n)/ε.

Solving the Swath Segment Selection Problem

NASA Technical Reports Server (NTRS)

Knight, Russell; Smith, Benjamin

2006-01-01

Several artificial-intelligence search techniques have been tested as means of solving the swath segment selection problem (SSSP) -- a real-world problem that is not only of interest in its own right, but is also useful as a test bed for search techniques in general. In simplest terms, the SSSP is the problem of scheduling the observation times of an airborne or spaceborne synthetic-aperture radar (SAR) system to effect the maximum coverage of a specified area (denoted the target), given a schedule of downlinks (opportunities for radio transmission of SAR scan data to a ground station), given the limit on the quantity of SAR scan data that can be stored in an onboard memory between downlink opportunities, and given the limit on the achievable downlink data rate. The SSSP is NP complete (short for "nondeterministic polynomial time complete" -- characteristic of a class of intractable problems that can be solved only by use of computers capable of making guesses and then checking the guesses in polynomial time).

Polynomial fuzzy observer designs: a sum-of-squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

2012-10-01

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

Multi-dimensional photonic states from a quantum dot

NASA Astrophysics Data System (ADS)

Lee, J. P.; Bennett, A. J.; Stevenson, R. M.; Ellis, D. J. P.; Farrer, I.; Ritchie, D. A.; Shields, A. J.

2018-04-01

Quantum states superposed across multiple particles or degrees of freedom offer an advantage in the development of quantum technologies. Creating these states deterministically and with high efficiency is an ongoing challenge. A promising approach is the repeated excitation of multi-level quantum emitters, which have been shown to naturally generate light with quantum statistics. Here we describe how to create one class of higher dimensional quantum state, a so called W-state, which is superposed across multiple time bins. We do this by repeated Raman scattering of photons from a charged quantum dot in a pillar microcavity. We show this method can be scaled to larger dimensions with no reduction in coherence or single-photon character. We explain how to extend this work to enable the deterministic creation of arbitrary time-bin encoded qudits.

Deterministic Secure Quantum Communication and Authentication Protocol based on Extended GHZ-W State and Quantum One-time Pad

NASA Astrophysics Data System (ADS)

Li, Na; Li, Jian; Li, Lei-Lei; Wang, Zheng; Wang, Tao

2016-08-01

A deterministic secure quantum communication and authentication protocol based on extended GHZ-W state and quantum one-time pad is proposed. In the protocol, state | φ -> is used as the carrier. One photon of | φ -> state is sent to Alice, and Alice obtains a random key by measuring photons with bases determined by ID. The information of bases is secret to others except Alice and Bob. Extended GHZ-W states are used as decoy photons, the positions of which in information sequence are encoded with identity string ID of the legal user, and the eavesdropping detection rate reaches 81%. The eavesdropping detection based on extended GHZ-W state combines with authentication and the secret ID ensures the security of the protocol.

Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

PubMed

Richardson, Megan; Lambers, James V

2016-01-01

This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Frequency domain system identification methods - Matrix fraction description approach

NASA Technical Reports Server (NTRS)

Horta, Luca G.; Juang, Jer-Nan

1993-01-01

This paper presents the use of matrix fraction descriptions for least-squares curve fitting of the frequency spectra to compute two matrix polynomials. The matrix polynomials are intermediate step to obtain a linearized representation of the experimental transfer function. Two approaches are presented: first, the matrix polynomials are identified using an estimated transfer function; second, the matrix polynomials are identified directly from the cross/auto spectra of the input and output signals. A set of Markov parameters are computed from the polynomials and subsequently realization theory is used to recover a minimum order state space model. Unevenly spaced frequency response functions may be used. Results from a simple numerical example and an experiment are discussed to highlight some of the important aspect of the algorithm.

By any other name: when will preschoolers produce several labels for a referent?

PubMed

Deák, G O; Yen, L; Pettit, J

2001-10-01

Two experiments investigated why preschool children sometimes produce multiple words for a referent (i.e. polynomy), but other times seem to allow only one word. In Experiment 1, 40 three- and four-year-olds completed a modification of Deák & Maratsos' (1998) naming task. Although social demands to produce multiple words were reduced, children produced, on average, more than two words per object. Number of words produced was predicted by receptive vocabulary. Lexical insight (i.e. knowing that a word refers to function or appearance) and metalexical beliefs (i.e. that a hypothetical referent has one label, or more than one) were not preconditions of polynomy. Polynomy was independent of bias to map novel words to unfamiliar referents. In Experiment 2, 40 three- and four-year-olds learned new words for nameable objects. Children showed a correction effect, yet produced more than two words per object. Children do not have a generalized one-word-per-object bias, even during word learning. Other explanations (e.g. contextual restriction of lexical access) are discussed.

Nano-transfersomes as a novel carrier for transdermal delivery.

PubMed

Chaudhary, Hema; Kohli, Kanchan; Kumar, Vikash

2013-09-15

The aim of this study was to design and optimize a nano-transfersomes of Diclofenac diethylamine (DDEA) and Curcumin (CRM). A 3(3) factorial design (Box-Behnken) was used to derive a polynomial equation (second order) to construct 2-D (contour) and 3-D (Response Surface) plots for prediction of responses. The ratio of lipid to surfactant (X1), weight of lipid to surfactant (X2) and sonication time (X3) (independent variables) and dependent variables [entrapment efficiency of DDEA (Y1), entrapment efficiency of CRM (Y2), effect on particle size (Y3), flux of DDEA (Y4), and flux of CRM (Y5)] were studied. The 2-D and 3-D plots were drawn and a statistical validity of the polynomials was established to find the compositions of optimized formulation. The design established the role of the derived polynomial equation, 2-D and 3-D plots in predicting the values of dependent variables for the preparation and optimization of nano-transfersomes for transdermal drug release. Copyright © 2013 Elsevier B.V. All rights reserved.

A New Navigation Satellite Clock Bias Prediction Method Based on Modified Clock-bias Quadratic Polynomial Model

NASA Astrophysics Data System (ADS)

Wang, Y. P.; Lu, Z. P.; Sun, D. S.; Wang, N.

2016-01-01

In order to better express the characteristics of satellite clock bias (SCB) and improve SCB prediction precision, this paper proposed a new SCB prediction model which can take physical characteristics of space-borne atomic clock, the cyclic variation, and random part of SCB into consideration. First, the new model employs a quadratic polynomial model with periodic items to fit and extract the trend term and cyclic term of SCB; then based on the characteristics of fitting residuals, a time series ARIMA ~(Auto-Regressive Integrated Moving Average) model is used to model the residuals; eventually, the results from the two models are combined to obtain final SCB prediction values. At last, this paper uses precise SCB data from IGS (International GNSS Service) to conduct prediction tests, and the results show that the proposed model is effective and has better prediction performance compared with the quadratic polynomial model, grey model, and ARIMA model. In addition, the new method can also overcome the insufficiency of the ARIMA model in model recognition and order determination.

Comparison Between Polynomial, Euler Beta-Function and Expo-Rational B-Spline Bases

NASA Astrophysics Data System (ADS)

Kristoffersen, Arnt R.; Dechevsky, Lubomir T.; Laksa˚, Arne; Bang, Børre

2011-12-01

Euler Beta-function B-splines (BFBS) are the practically most important instance of generalized expo-rational B-splines (GERBS) which are not true expo-rational B-splines (ERBS). BFBS do not enjoy the full range of the superproperties of ERBS but, while ERBS are special functions computable by a very rapidly converging yet approximate numerical quadrature algorithms, BFBS are explicitly computable piecewise polynomial (for integer multiplicities), similar to classical Schoenberg B-splines. In the present communication we define, compute and visualize for the first time all possible BFBS of degree up to 3 which provide Hermite interpolation in three consecutive knots of multiplicity up to 3, i.e., the function is being interpolated together with its derivatives of order up to 2. We compare the BFBS obtained for different degrees and multiplicities among themselves and versus the classical Schoenberg polynomial B-splines and the true ERBS for the considered knots. The results of the graphical comparison are discussed from analytical point of view. For the numerical computation and visualization of the new B-splines we have used Maple 12.

Automated image segmentation-assisted flattening of atomic force microscopy images.

PubMed

Wang, Yuliang; Lu, Tongda; Li, Xiaolai; Wang, Huimin

2018-01-01

Atomic force microscopy (AFM) images normally exhibit various artifacts. As a result, image flattening is required prior to image analysis. To obtain optimized flattening results, foreground features are generally manually excluded using rectangular masks in image flattening, which is time consuming and inaccurate. In this study, a two-step scheme was proposed to achieve optimized image flattening in an automated manner. In the first step, the convex and concave features in the foreground were automatically segmented with accurate boundary detection. The extracted foreground features were taken as exclusion masks. In the second step, data points in the background were fitted as polynomial curves/surfaces, which were then subtracted from raw images to get the flattened images. Moreover, sliding-window-based polynomial fitting was proposed to process images with complex background trends. The working principle of the two-step image flattening scheme were presented, followed by the investigation of the influence of a sliding-window size and polynomial fitting direction on the flattened images. Additionally, the role of image flattening on the morphological characterization and segmentation of AFM images were verified with the proposed method.

Minimum Sobolev norm interpolation of scattered derivative data

NASA Astrophysics Data System (ADS)

Chandrasekaran, S.; Gorman, C. H.; Mhaskar, H. N.

2018-07-01

We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data of the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree ≤n given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable, efficient, and of high-order.

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2008-01-01

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

Digital SAR processing using a fast polynomial transform

NASA Technical Reports Server (NTRS)

Truong, T. K.; Lipes, R. G.; Butman, S. A.; Reed, I. S.; Rubin, A. L.

1984-01-01

A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network. Previously announced in STAR as N82-11295

Heat transfer of phase-change materials in two-dimensional cylindrical coordinates

NASA Technical Reports Server (NTRS)

Labdon, M. B.; Guceri, S. I.

1981-01-01

Two-dimensional phase-change problem is numerically solved in cylindrical coordinates (r and z) by utilizing two Taylor series expansions for the temperature distributions in the neighborhood of the interface location. These two expansions form two polynomials in r and z directions. For the regions sufficiently away from the interface the temperature field equations are numerically solved in the usual way and the results are coupled with the polynomials. The main advantages of this efficient approach include ability to accept arbitrarily time dependent boundary conditions of all types and arbitrarily specified initial temperature distributions. A modified approach using a single Taylor series expansion in two variables is also suggested.

Linear decomposition approach for a class of nonconvex programming problems.

PubMed

Shen, Peiping; Wang, Chunfeng

2017-01-01

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

Generalized indical forces on deforming rectangular wings in supersonic flight

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Fuller, Franklyn B; Sluder, Loma

1955-01-01

A method is presented for determining the time-dependent flow over a rectangular wing moving with a supersonic forward speed and undergoing small vertical distortions expressible as polynomials involving spanwise and chordwise distances. The solution for the velocity potential is presented in a form analogous to that for steady supersonic flow having the familiar "reflected area" concept discovered by Evvard. Particular attention is paid to indicial-type motions and results are expressed in terms of generalized indicial forces. Numerical results for Mach numbers equal to 1.1 and 1.2 are given for polynomials of the first and fifth degree in the chordwise and spanwise directions, respectively, on a wing having an aspect ratio of 4.

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

Hunt, H.B. III; Rosenkrantz, D.J.; Stearns, R.E.

We study both the complexity and approximability of various graph and combinatorial problems specified using two dimensional narrow periodic specifications (see [CM93, HW92, KMW67, KO91, Or84b, Wa93]). The following two general kinds of results are presented. (1) We prove that a number of natural graph and combinatorial problems are NEXPTIME- or EXPSPACE-complete when instances are so specified; (2) In contrast, we prove that the optimization versions of several of these NEXPTIME-, EXPSPACE-complete problems have polynomial time approximation algorithms with constant performance guarantees. Moreover, some of these problems even have polynomial time approximation schemes. We also sketch how our NEXPTIME-hardness resultsmore » can be used to prove analogous NEXPTIME-hardness results for problems specified using other kinds of succinct specification languages. Our results provide the first natural problems for which there is a proven exponential (and possibly doubly exponential) gap between the complexities of finding exact and approximate solutions.« less

A Legendre tau-spectral method for solving time-fractional heat equation with nonlocal conditions.

PubMed

Bhrawy, A H; Alghamdi, M A

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem.

A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions

PubMed Central

Bhrawy, A. H.; Alghamdi, M. A.

2014-01-01

We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507

TreeCmp: Comparison of Trees in Polynomial Time

PubMed Central

Bogdanowicz, Damian; Giaro, Krzysztof; Wróbel, Borys

2012-01-01

When a phylogenetic reconstruction does not result in one tree but in several, tree metrics permit finding out how far the reconstructed trees are from one another. They also permit to assess the accuracy of a reconstruction if a true tree is known. TreeCmp implements eight metrics that can be calculated in polynomial time for arbitrary (not only bifurcating) trees: four for unrooted (Matching Split metric, which we have recently proposed, Robinson-Foulds, Path Difference, Quartet) and four for rooted trees (Matching Cluster, Robinson-Foulds cluster, Nodal Splitted and Triple). TreeCmp is the first implementation of Matching Split/Cluster metrics and the first efficient and convenient implementation of Nodal Splitted. It allows to compare relatively large trees. We provide an example of the application of TreeCmp to compare the accuracy of ten approaches to phylogenetic reconstruction with trees up to 5000 external nodes, using a measure of accuracy based on normalized similarity between trees.

Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.

PubMed

Petrinović, Davor; Brezović, Marko

2011-04-01

We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device. © 2011 IEEE

Establishing a direct connection between detrended fluctuation analysis and Fourier analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken

2015-10-01

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), S (f ) ˜f-β , a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent α , which satisfies the scaling relation α =(β +1 )/2 ; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by m +1 , where m is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve the scale distortion by introducing the corrected time scale in the DFA corresponding to the inverse of the frequency scale in the PSD. In addition, our analytical approach makes it possible to characterize variants of the DFA using different types of detrending. As an application, properties of the detrending moving average algorithm are discussed.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

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

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817