WorldWideScience

Sample records for deterministic polynomial time

  1. Distinguishing deterministic and noise components in ELM time series

    International Nuclear Information System (INIS)

    Zvejnieks, G.; Kuzovkov, V.N

    2004-01-01

    Full text: One of the main problems in the preliminary data analysis is distinguishing the deterministic and noise components in the experimental signals. For example, in plasma physics the question arises analyzing edge localized modes (ELMs): is observed ELM behavior governed by a complicate deterministic chaos or just by random processes. We have developed methodology based on financial engineering principles, which allows us to distinguish deterministic and noise components. We extended the linear auto regression method (AR) by including the non-linearity (NAR method). As a starting point we have chosen the nonlinearity in the polynomial form, however, the NAR method can be extended to any other type of non-linear functions. The best polynomial model describing the experimental ELM time series was selected using Bayesian Information Criterion (BIC). With this method we have analyzed type I ELM behavior in a subset of ASDEX Upgrade shots. Obtained results indicate that a linear AR model can describe the ELM behavior. In turn, it means that type I ELM behavior is of a relaxation or random type

  2. Pseudo-deterministic Algorithms

    OpenAIRE

    Goldwasser , Shafi

    2012-01-01

    International audience; In this talk we describe a new type of probabilistic algorithm which we call Bellagio Algorithms: a randomized algorithm which is guaranteed to run in expected polynomial time, and to produce a correct and unique solution with high probability. These algorithms are pseudo-deterministic: they can not be distinguished from deterministic algorithms in polynomial time by a probabilistic polynomial time observer with black box access to the algorithm. We show a necessary an...

  3. Exponential time paradigms through the polynomial time lens

    NARCIS (Netherlands)

    Drucker, A.; Nederlof, J.; Santhanam, R.; Sankowski, P.; Zaroliagis, C.

    2016-01-01

    We propose a general approach to modelling algorithmic paradigms for the exact solution of NP-hard problems. Our approach is based on polynomial time reductions to succinct versions of problems solvable in polynomial time. We use this viewpoint to explore and compare the power of paradigms such as

  4. Deterministic Chaos in Radon Time Variation

    International Nuclear Information System (INIS)

    Planinic, J.; Vukovic, B.; Radolic, V.; Faj, Z.; Stanic, D.

    2003-01-01

    Radon concentrations were continuously measured outdoors, in living room and basement in 10-minute intervals for a month. The radon time series were analyzed by comparing algorithms to extract phase-space dynamical information. The application of fractal methods enabled to explore the chaotic nature of radon in the atmosphere. The computed fractal dimensions, such as Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent (λ ) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0< H<0.5) indicated anti-persistent behavior (non random changes) of the time series, but the positive values of the λ pointed out the grate sensitivity on initial conditions and appearing deterministic chaos by radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere. (author)

  5. Radon time variations and deterministic chaos

    Energy Technology Data Exchange (ETDEWEB)

    Planinic, J. E-mail: planinic@pedos.hr; Vukovic, B.; Radolic, V

    2004-07-01

    Radon concentrations were continuously measured outdoors, in the living room and in the basement at 10 min intervals for a month. Radon time series were analyzed by comparing algorithms to extract phase space dynamical information. The application of fractal methods enabled exploration of the chaotic nature of radon in atmosphere. The computed fractal dimensions, such as the Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent ({lambda}) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0time series, but the positive values of {lambda} pointed out the grate sensitivity on initial conditions and the deterministic chaos that appeared due to radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere.

  6. Radon time variations and deterministic chaos

    International Nuclear Information System (INIS)

    Planinic, J.; Vukovic, B.; Radolic, V.

    2004-01-01

    Radon concentrations were continuously measured outdoors, in the living room and in the basement at 10 min intervals for a month. Radon time series were analyzed by comparing algorithms to extract phase space dynamical information. The application of fractal methods enabled exploration of the chaotic nature of radon in atmosphere. The computed fractal dimensions, such as the Hurst exponent (H) from the rescaled range analysis, Lyapunov exponent (λ) and attractor dimension, provided estimates of the degree of chaotic behavior. The obtained low values of the Hurst exponent (0< H<0.5) indicated anti-persistent behavior (non-random changes) of the time series, but the positive values of λ pointed out the grate sensitivity on initial conditions and the deterministic chaos that appeared due to radon time variations. The calculated fractal dimensions of attractors indicated more influencing (meteorological) parameters on radon in the atmosphere

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

  9. Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

    OpenAIRE

    N. Stojanovic; N. Stamenkovic; I. Krstic

    2016-01-01

    A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approx...

  10. Interpretation of stream programs: characterizing type 2 polynomial time complexity

    OpenAIRE

    Férée , Hugo; Hainry , Emmanuel; Hoyrup , Mathieu; Péchoux , Romain

    2010-01-01

    International audience; We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These charac- terizations provide a new insight on the complexity of stream programs. Finally, we adapt these results to functions over th...

  11. Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

    Directory of Open Access Journals (Sweden)

    N. Stojanovic

    2016-09-01

    Full Text Available A new approximation to design continuoustime and discrete-time low-pass filters, presented in this paper, based on the product of Gegenbauer polynomials, provides the ability of more flexible adjustment of passband and stopband responses. The design is achieved taking into account a prescribed specification, leading to a better trade-off among the magnitude and group delay responses. Many well-known continuous-time and discrete-time transitional filter based on the classical polynomial approximations(Chebyshev, Legendre, Butterworth are shown to be a special cases of proposed approximation method.

  12. Optimum short-time polynomial regression for signal analysis

    Indian Academy of Sciences (India)

    A Sreenivasa Murthy

    the Proceedings of European Signal Processing Conference. (EUSIPCO) 2008. ... In a seminal paper, Savitzky and Golay [4] showed that short-time polynomial modeling is ...... We next consider a linearly frequency-modulated chirp with an exponentially .... 1 http://www.physionet.org/physiotools/matlab/ECGwaveGen/.

  13. Statistical methods of parameter estimation for deterministically chaotic time series

    Science.gov (United States)

    Pisarenko, V. F.; Sornette, D.

    2004-03-01

    We discuss the possibility of applying some standard statistical methods (the least-square method, the maximum likelihood method, and the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional dynamic system (the logistic map) containing an observational noise. A “segmentation fitting” maximum likelihood (ML) method is suggested to estimate the structural parameter of the logistic map along with the initial value x1 considered as an additional unknown parameter. The segmentation fitting method, called “piece-wise” ML, is similar in spirit but simpler and has smaller bias than the “multiple shooting” previously proposed. Comparisons with different previously proposed techniques on simulated numerical examples give favorable results (at least, for the investigated combinations of sample size N and noise level). Besides, unlike some suggested techniques, our method does not require the a priori knowledge of the noise variance. We also clarify the nature of the inherent difficulties in the statistical analysis of deterministically chaotic time series and the status of previously proposed Bayesian approaches. We note the trade off between the need of using a large number of data points in the ML analysis to decrease the bias (to guarantee consistency of the estimation) and the unstable nature of dynamical trajectories with exponentially fast loss of memory of the initial condition. The method of statistical moments for the estimation of the parameter of the logistic map is discussed. This method seems to be the unique method whose consistency for deterministically chaotic time series is proved so far theoretically (not only numerically).

  14. Predicting physical time series using dynamic ridge polynomial neural networks.

    Directory of Open Access Journals (Sweden)

    Dhiya Al-Jumeily

    Full Text Available 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.

  15. Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines

    Science.gov (United States)

    Traversa, Fabio L.; Di Ventra, Massimiliano

    2017-02-01

    We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.

  16. Finite-Time Stability and Controller Design of Continuous-Time Polynomial Fuzzy Systems

    Directory of Open Access Journals (Sweden)

    Xiaoxing Chen

    2017-01-01

    Full Text Available Finite-time stability and stabilization problem is first investigated for continuous-time polynomial fuzzy systems. The concept of finite-time stability and stabilization is given for polynomial fuzzy systems based on the idea of classical references. A sum-of-squares- (SOS- based approach is used to obtain the finite-time stability and stabilization conditions, which include some classical results as special cases. The proposed conditions can be solved with the help of powerful Matlab toolbox SOSTOOLS and a semidefinite-program (SDP solver. Finally, two numerical examples and one practical example are employed to illustrate the validity and effectiveness of the provided conditions.

  17. Recognition of deterministic ETOL languages in logarithmic space

    DEFF Research Database (Denmark)

    Jones, Neil D.; Skyum, Sven

    1977-01-01

    It is shown that if G is a deterministic ETOL system, there is a nondeterministic log space algorithm to determine membership in L(G). Consequently, every deterministic ETOL language is recognizable in polynomial time. As a corollary, all context-free languages of finite index, and all Indian...

  18. Beeping a Deterministic Time-Optimal Leader Election

    OpenAIRE

    Dufoulon , Fabien; Burman , Janna; Beauquier , Joffroy

    2018-01-01

    The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints o...

  19. Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems with Time Delay under Imperfect Premise Matching

    OpenAIRE

    Li, Xiaomiao; Lam, Hak Keung; Song, Ge; Liu, Fucai

    2017-01-01

    This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based ({PFMB}) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares (SOS)-based stability ana...

  20. A real time sorting algorithm to time sort any deterministic time disordered data stream

    Science.gov (United States)

    Saini, J.; Mandal, S.; Chakrabarti, A.; Chattopadhyay, S.

    2017-12-01

    In new generation high intensity high energy physics experiments, millions of free streaming high rate data sources are to be readout. Free streaming data with associated time-stamp can only be controlled by thresholds as there is no trigger information available for the readout. Therefore, these readouts are prone to collect large amount of noise and unwanted data. For this reason, these experiments can have output data rate of several orders of magnitude higher than the useful signal data rate. It is therefore necessary to perform online processing of the data to extract useful information from the full data set. Without trigger information, pre-processing on the free streaming data can only be done with time based correlation among the data set. Multiple data sources have different path delays and bandwidth utilizations and therefore the unsorted merged data requires significant computational efforts for real time manifestation of sorting before analysis. Present work reports a new high speed scalable data stream sorting algorithm with its architectural design, verified through Field programmable Gate Array (FPGA) based hardware simulation. Realistic time based simulated data likely to be collected in an high energy physics experiment have been used to study the performance of the algorithm. The proposed algorithm uses parallel read-write blocks with added memory management and zero suppression features to make it efficient for high rate data-streams. This algorithm is best suited for online data streams with deterministic time disorder/unsorting on FPGA like hardware.

  1. Study on deterministic response time design for a class of nuclear Instrumentation and Control systems

    International Nuclear Information System (INIS)

    Chen, Chang-Kuo; Hou, Yi-You; Luo, Cheng-Long

    2012-01-01

    Highlights: ► An efficient design procedure for deterministic response time design of nuclear I and C system. ► We model the concurrent operations based on sequence diagrams and Petri nets. ► The model can achieve the deterministic behavior by using symbolic time representation. ► An illustrative example of the bistable processor logic is given. - Abstract: This study is concerned with a deterministic response time design for computer-based systems in the nuclear industry. In current approach, Petri nets are used to model the requirement of a system specified with sequence diagrams. Also, the linear logic is proposed to characterize the state of changes in the Petri net model accurately by using symbolic time representation for the purpose of acquiring deterministic behavior. An illustrative example of the bistable processor logic is provided to demonstrate the practicability of the proposed approach.

  2. Deterministic one-way simulation of two-way, real-time cellular automata and its related problems

    Energy Technology Data Exchange (ETDEWEB)

    Umeo, H; Morita, K; Sugata, K

    1982-06-13

    The authors show that for any deterministic two-way, real-time cellular automaton, m, there exists a deterministic one-way cellular automation which can simulate m in twice real-time. Moreover the authors present a new type of deterministic one-way cellular automata, called circular cellular automata, which are computationally equivalent to deterministic two-way cellular automata. 7 references.

  3. Time-dependent deterministic transport on parallel architectures using PARTISN

    International Nuclear Information System (INIS)

    Alcouffe, R.E.; Baker, R.S.

    1998-01-01

    In addition to the ability to solve the static transport equation, the authors have also incorporated time dependence into the parallel S N code PARTISN. Using a semi-implicit scheme, PARTISN is capable of performing time-dependent calculations for both fissioning and pure source driven problems. They have applied this to various types of problems such as shielding and prompt fission experiments. This paper describes the form of the time-dependent equations implemented, their solution strategies in PARTISN including iteration acceleration, and the strategies used for time-step control. Results are presented for a iron-water shielding calculation and a criticality excursion in a uranium solution configuration

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

    Science.gov (United States)

    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…

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

    Science.gov (United States)

    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.

  6. Exponential Time Complexity of the Permanent and the Tutte Polynomial

    DEFF Research Database (Denmark)

    Dell, Holger; Husfeldt, Thore; Marx, Dániel

    2014-01-01

    bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH; namely, that the satisfying assignments cannot be counted......We show conditional lower bounds for well-studied #P-hard problems: The number of satisfying assignments of a 2-CNF formula with n variables cannot be computed in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. The permanent of an n× n...

  7. A polynomial time algorithm for checking regularity of totally normed process algebra

    NARCIS (Netherlands)

    Yang, F.; Huang, H.

    2015-01-01

    A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is O(n 3 +mn) O(n3+mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for

  8. Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

    Directory of Open Access Journals (Sweden)

    Marlowe Thomas J.

    1998-01-01

    Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants. We illustrate this approach using threshhold graphs, and show that any computation of reliability using Gilbert's formula will be polynomial-time if and only if the number of invariants considered is polynomial; we then show families of graphs with polynomial-time, and non-polynomial reliability computation, and show that these encompass most previously known results. We then codify our approach to indicate how it can be used for other classes of graphs, and suggest several classes to which the technique can be applied.

  9. A polynomial time biclustering algorithm for finding approximate expression patterns in gene expression time series

    Directory of Open Access Journals (Sweden)

    Madeira Sara C

    2009-06-01

    Full Text Available Abstract Background The ability to monitor the change in expression patterns over time, and to observe the emergence of coherent temporal responses using gene expression time series, obtained from microarray experiments, is critical to advance our understanding of complex biological processes. In this context, biclustering algorithms have been recognized as an important tool for the discovery of local expression patterns, which are crucial to unravel potential regulatory mechanisms. Although most formulations of the biclustering problem are NP-hard, when working with time series expression data the interesting biclusters can be restricted to those with contiguous columns. This restriction leads to a tractable problem and enables the design of efficient biclustering algorithms able to identify all maximal contiguous column coherent biclusters. Methods In this work, we propose e-CCC-Biclustering, a biclustering algorithm that finds and reports all maximal contiguous column coherent biclusters with approximate expression patterns in time polynomial in the size of the time series gene expression matrix. This polynomial time complexity is achieved by manipulating a discretized version of the original matrix using efficient string processing techniques. We also propose extensions to deal with missing values, discover anticorrelated and scaled expression patterns, and different ways to compute the errors allowed in the expression patterns. We propose a scoring criterion combining the statistical significance of expression patterns with a similarity measure between overlapping biclusters. Results We present results in real data showing the effectiveness of e-CCC-Biclustering and its relevance in the discovery of regulatory modules describing the transcriptomic expression patterns occurring in Saccharomyces cerevisiae in response to heat stress. In particular, the results show the advantage of considering approximate patterns when compared to state of

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

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

    Directory of Open Access Journals (Sweden)

    Waddah Waheeb

    Full Text Available 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.

  13. A deterministic, gigabit serial timing, synchronization and data link for the RHIC LLRF

    International Nuclear Information System (INIS)

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

    2011-01-01

    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 provide 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.

  14. Approximating the Value of a Concurrent Reachability Game in the Polynomial Time Hierarchy

    DEFF Research Database (Denmark)

    Frederiksen, Søren Kristoffer Stiil; Miltersen, Peter Bro

    2013-01-01

    We show that the value of a finite-state concurrent reachability game can be approximated to arbitrary precision in TFNP[NP], that is, in the polynomial time hierarchy. Previously, no better bound than PSPACE was known for this problem. The proof is based on formulating a variant of the state red...... reduction algorithm for Markov chains using arbitrary precision floating point arithmetic and giving a rigorous error analysis of the algorithm.......We show that the value of a finite-state concurrent reachability game can be approximated to arbitrary precision in TFNP[NP], that is, in the polynomial time hierarchy. Previously, no better bound than PSPACE was known for this problem. The proof is based on formulating a variant of the state...

  15. A Note on "A polynomial-time algorithm for global value numbering"

    OpenAIRE

    Nabeezath, Saleena; Paleri, Vineeth

    2013-01-01

    Global Value Numbering(GVN) is a popular method for detecting redundant computations. A polynomial time algorithm for GVN is presented by Gulwani and Necula(2006). Here we present two limitations of this GVN algorithm due to which detection of certain kinds of redundancies can not be done using this algorithm. The first one is concerning the use of this algorithm in detecting some instances of the classical global common subexpressions, and the second is concerning its use in the detection of...

  16. A novel stabilization condition for T-S polynomial fuzzy system with time-delay:A sum-of-squares approach

    OpenAIRE

    Tsai, Shun Hung; Chen, Yu-An; Chen, Yu-Wen; Lo, Ji-Chang; Lam, Hak-Keung

    2017-01-01

    A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with time-delay ...

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

    Science.gov (United States)

    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.

  18. Learning Read-constant Polynomials of Constant Degree modulo Composites

    DEFF Research Database (Denmark)

    Chattopadhyay, Arkadev; Gavaldá, Richard; Hansen, Kristoffer Arnsfelt

    2011-01-01

    Boolean functions that have constant degree polynomial representation over a fixed finite ring form a natural and strict subclass of the complexity class \\textACC0ACC0. They are also precisely the functions computable efficiently by programs over fixed and finite nilpotent groups. This class...... is not known to be learnable in any reasonable learning model. In this paper, we provide a deterministic polynomial time algorithm for learning Boolean functions represented by polynomials of constant degree over arbitrary finite rings from membership queries, with the additional constraint that each variable...

  19. Factoring polynomials over arbitrary finite fields

    NARCIS (Netherlands)

    Lange, T.; Winterhof, A.

    2000-01-01

    We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of

  20. A polynomial time algorithm for solving the maximum flow problem in directed networks

    International Nuclear Information System (INIS)

    Tlas, M.

    2015-01-01

    An efficient polynomial time algorithm for solving maximum flow problems has been proposed in this paper. The algorithm is basically based on the binary representation of capacities; it solves the maximum flow problem as a sequence of O(m) shortest path problems on residual networks with nodes and m arcs. It runs in O(m"2r) time, where is the smallest integer greater than or equal to log B , and B is the largest arc capacity of the network. A numerical example has been illustrated using this proposed algorithm.(author)

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

    Science.gov (United States)

    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.

  2. Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

    Energy Technology Data Exchange (ETDEWEB)

    Shao, Sihong, E-mail: sihong@math.pku.edu.cn [LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)

    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 of 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.

  3. Pruning-Based, Energy-Optimal, Deterministic I/O Device Scheduling for Hard Real-Time Systems

    Science.gov (United States)

    2005-02-01

    However, DPM via I/O device scheduling for hard real - time systems has received relatively little attention. In this paper,we present an offline I/O...polynomial time. We present experimental results to show that EDS and MDO reduce the energy consumption of I/O devices significantly for hard real - time systems .

  4. Sum-of-squares based observer design for polynomial systems with a known fixed time delay

    Czech Academy of Sciences Publication Activity Database

    Rehák, Branislav

    2015-01-01

    Roč. 51, č. 5 (2015), s. 858-873 ISSN 0023-5954 R&D Projects: GA ČR GA13-02149S Institutional support: RVO:67985556 Keywords : sum-of-squares polynomial * observer * polynomial system Subject RIV: BC - Control Systems Theory Impact factor: 0.628, year: 2015 http://www.kybernetika.cz/content/2015/5/856

  5. Deterministic Graphical Games Revisited

    DEFF Research Database (Denmark)

    Andersson, Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro

    2008-01-01

    We revisit the deterministic graphical games of Washburn. A deterministic graphical game can be described as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity of solving deterministic graphical...... games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game. The existence of a linear time comparison-based algorithm remains an open problem....

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

    Science.gov (United States)

    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.

  7. Time-Dependent Global Sensitivity Analysis for Long-Term Degeneracy Model Using Polynomial Chaos

    Directory of Open Access Journals (Sweden)

    Jianbin Guo

    2014-07-01

    Full Text Available Global sensitivity is used to quantify the influence of uncertain model inputs on the output variability of static models in general. However, very few approaches can be applied for the sensitivity analysis of long-term degeneracy models, as far as time-dependent reliability is concerned. The reason is that the static sensitivity may not reflect the completed sensitivity during the entire life circle. This paper presents time-dependent global sensitivity analysis for long-term degeneracy models based on polynomial chaos expansion (PCE. Sobol’ indices are employed as the time-dependent global sensitivity since they provide accurate information on the selected uncertain inputs. In order to compute Sobol’ indices more efficiently, this paper proposes a moving least squares (MLS method to obtain the time-dependent PCE coefficients with acceptable simulation effort. Then Sobol’ indices can be calculated analytically as a postprocessing of the time-dependent PCE coefficients with almost no additional cost. A test case is used to show how to conduct the proposed method, then this approach is applied to an engineering case, and the time-dependent global sensitivity is obtained for the long-term degeneracy mechanism model.

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

    Science.gov (United States)

    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

  9. Deterministic decomposition and seasonal ARIMA time series models applied to airport noise forecasting

    Science.gov (United States)

    Guarnaccia, Claudio; Quartieri, Joseph; Tepedino, Carmine

    2017-06-01

    One of the most hazardous physical polluting agents, considering their effects on human health, is acoustical noise. Airports are a strong source of acoustical noise, due to the airplanes turbines, to the aero-dynamical noise of transits, to the acceleration or the breaking during the take-off and landing phases of aircrafts, to the road traffic around the airport, etc.. The monitoring and the prediction of the acoustical level emitted by airports can be very useful to assess the impact on human health and activities. In the airports noise scenario, thanks to flights scheduling, the predominant sources may have a periodic behaviour. Thus, a Time Series Analysis approach can be adopted, considering that a general trend and a seasonal behaviour can be highlighted and used to build a predictive model. In this paper, two different approaches are adopted, thus two predictive models are constructed and tested. The first model is based on deterministic decomposition and is built composing the trend, that is the long term behaviour, the seasonality, that is the periodic component, and the random variations. The second model is based on seasonal autoregressive moving average, and it belongs to the stochastic class of models. The two different models are fitted on an acoustical level dataset collected close to the Nice (France) international airport. Results will be encouraging and will show good prediction performances of both the adopted strategies. A residual analysis is performed, in order to quantify the forecasting error features.

  10. A data analysis method for identifying deterministic components of stable and unstable time-delayed systems with colored noise

    Energy Technology Data Exchange (ETDEWEB)

    Patanarapeelert, K. [Faculty of Science, Department of Mathematics, Mahidol University, Rama VI Road, Bangkok 10400 (Thailand); Frank, T.D. [Institute for Theoretical Physics, University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster (Germany)]. E-mail: tdfrank@uni-muenster.de; Friedrich, R. [Institute for Theoretical Physics, University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster (Germany); Beek, P.J. [Faculty of Human Movement Sciences and Institute for Fundamental and Clinical Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT Amsterdam (Netherlands); Tang, I.M. [Faculty of Science, Department of Physics, Mahidol University, Rama VI Road, Bangkok 10400 (Thailand)

    2006-12-18

    A method is proposed to identify deterministic components of stable and unstable time-delayed systems subjected to noise sources with finite correlation times (colored noise). Both neutral and retarded delay systems are considered. For vanishing correlation times it is shown how to determine their noise amplitudes by minimizing appropriately defined Kullback measures. The method is illustrated by applying it to simulated data from stochastic time-delayed systems representing delay-induced bifurcations, postural sway and ship rolling.

  11. Orthogonal polynomials

    CERN Document Server

    Freud, Géza

    1971-01-01

    Orthogonal Polynomials contains an up-to-date survey of the general theory of orthogonal polynomials. It deals with the problem of polynomials and reveals that the sequence of these polynomials forms an orthogonal system with respect to a non-negative m-distribution defined on the real numerical axis. Comprised of five chapters, the book begins with the fundamental properties of orthogonal polynomials. After discussing the momentum problem, it then explains the quadrature procedure, the convergence theory, and G. Szegő's theory. This book is useful for those who intend to use it as referenc

  12. Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

    Science.gov (United States)

    Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

    2018-02-13

    Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

  13. Separation of Stochastic and Deterministic Information from Seismological Time Series with Nonlinear Dynamics and Maximum Entropy Methods

    International Nuclear Information System (INIS)

    Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias

    2007-01-01

    We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information

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

    Science.gov (United States)

    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.

  15. Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

    Directory of Open Access Journals (Sweden)

    Mahmoud Paripour

    2014-08-01

    Full Text Available In this paper, the Bernstein polynomials are used to approximatethe solutions of linear integral equations with multiple time lags (IEMTL through expansion methods (collocation method, partition method, Galerkin method. The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is carried out

  16. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

    Science.gov (United States)

    Cotter, C J; Gottwald, G A; Holm, D D

    2017-09-01

    In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

  17. Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

    Science.gov (United States)

    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.

  18. Pattern recognition techniques and neo-deterministic seismic hazard: Time dependent scenarios for North-Eastern Italy

    International Nuclear Information System (INIS)

    Peresan, A.; Vaccari, F.; Panza, G.F.; Zuccolo, E.; Gorshkov, A.

    2009-05-01

    An integrated neo-deterministic approach to seismic hazard assessment has been developed that combines different pattern recognition techniques, designed for the space-time identification of strong earthquakes, with algorithms for the realistic modeling of seismic ground motion. The integrated approach allows for a time dependent definition of the seismic input, through the routine updating of earthquake predictions. The scenarios of expected ground motion, associated with the alarmed areas, are defined by means of full waveform modeling. A set of neo-deterministic scenarios of ground motion is defined at regional and local scale, thus providing a prioritization tool for timely prevention and mitigation actions. Constraints about the space and time of occurrence of the impending strong earthquakes are provided by three formally defined and globally tested algorithms, which have been developed according to a pattern recognition scheme. Two algorithms, namely CN and M8, are routinely used for intermediate-term middle-range earthquake predictions, while a third algorithm allows for the identification of the areas prone to large events. These independent procedures have been combined to better constrain the alarmed area. The pattern recognition of earthquake-prone areas does not belong to the family of earthquake prediction algorithms since it does not provide any information about the time of occurrence of the expected earthquakes. Nevertheless, it can be considered as the term-less zero-approximation, which restrains the alerted areas (e.g. defined by CN or M8) to the more precise location of large events. Italy is the only region of moderate seismic activity where the two different prediction algorithms CN and M8S (i.e. a spatially stabilized variant of M8) are applied simultaneously and a real-time test of predictions, for earthquakes with magnitude larger than 5.4, is ongoing since 2003. The application of the CN to the Adriatic region (s.l.), which is relevant

  19. An Adaptive Channel Estimation Algorithm Using Time-Frequency Polynomial Model for OFDM with Fading Multipath Channels

    Directory of Open Access Journals (Sweden)

    Liu KJ Ray

    2002-01-01

    Full Text Available Orthogonal frequency division multiplexing (OFDM is an effective technique for the future 3G communications because of its great immunity to impulse noise and intersymbol interference. The channel estimation is a crucial aspect in the design of OFDM systems. In this work, we propose a channel estimation algorithm based on a time-frequency polynomial model of the fading multipath channels. The algorithm exploits the correlation of the channel responses in both time and frequency domains and hence reduce more noise than the methods using only time or frequency polynomial model. The estimator is also more robust compared to the existing methods based on Fourier transform. The simulation shows that it has more than improvement in terms of mean-squared estimation error under some practical channel conditions. The algorithm needs little prior knowledge about the delay and fading properties of the channel. The algorithm can be implemented recursively and can adjust itself to follow the variation of the channel statistics.

  20. Univariate Lp and ɭ p Averaging, 0 < p < 1, in Polynomial Time by Utilization of Statistical Structure

    Directory of Open Access Journals (Sweden)

    John E. Lavery

    2012-10-01

    Full Text Available We present evidence that one can calculate generically combinatorially expensive Lp and lp averages, 0 < p < 1, in polynomial time by restricting the data to come from a wide class of statistical distributions. Our approach differs from the approaches in the previous literature, which are based on a priori sparsity requirements or on accepting a local minimum as a replacement for a global minimum. The functionals by which Lp averages are calculated are not convex but are radially monotonic and the functionals by which lp averages are calculated are nearly so, which are the keys to solvability in polynomial time. Analytical results for symmetric, radially monotonic univariate distributions are presented. An algorithm for univariate lp averaging is presented. Computational results for a Gaussian distribution, a class of symmetric heavy-tailed distributions and a class of asymmetric heavy-tailed distributions are presented. Many phenomena in human-based areas are increasingly known to be represented by data that have large numbers of outliers and belong to very heavy-tailed distributions. When tails of distributions are so heavy that even medians (L1 and l1 averages do not exist, one needs to consider using lp minimization principles with 0 < p < 1.

  1. Time-division polynomial pre-distorter for linearisation of 1.5 T MRI power amplifier

    Directory of Open Access Journals (Sweden)

    Ming Hui

    2017-06-01

    Full Text Available A time-division polynomial (TDP model is proposed for modelling and linearising a 1.5 T magnetic resonance imaging (MRI power amplifier (PA with strong non-linearity in high input signal dynamic range. In order to demonstrate the merit of this non-linear model, a 64 dBm 1.5 T MRI PA (63.89 MHz and two different Sinc-pulse signals are used in modelling and linearisation measurements. The TDP is compared with the conventional non-memory polynomial (NMP and no digital pre-distortion for the 1.5 T MRI PA, which is driven by test signal with 2 ms time length and 2% duty cycle. The proposed TDP leads to up to 9 dB improvement in the normalised mean square error compared with the NMP in two different test signals. More importantly, TDP illustrates significantly better reduction in amplitude modulation/amplitude modulation (AM/AM and amplitude modulation/phase modulation (AM/PM conversion compared with the NMP.

  2. An Innovative Real-time Environment for Unified Deterministic and Stochastic Groundwater Modeling

    Science.gov (United States)

    Li, S.; Liu, Q.

    2003-12-01

    Despite an exponential growth of computational capability over the last two decades-one that has allowed computational science and engineering to become a unique, powerful tool for scientific discovery-the extreme cost of groundwater modeling continues to limit its use. This occurs primarily because the modeling paradigm that has been employed for decades limits our ability to take full advantage of recent developments in computer, communication, graphic, and visualization technologies. In this presentation we introduce an innovative and sophisticated computational environment for groundwater modeling that promises to eliminate the current bottleneck and greatly expand the utility of computational tools for scientific discovery related to groundwater. Based on a set of efficient and robust computational algorithms, the new software system, called Interactive Groundwater (IGW), allows simulating complex flow and transport in aquifers subject to both systematic and "randomly" varying stresses and geological and chemical heterogeneity. Adopting a new paradigm, IGW eliminates a major bottleneck inherent in the traditional fragmented modeling technologies and enables real-time modeling, real-time visualization, real-time analysis, and real-time presentation. IGW functions as a "numerical laboratory" in which a researcher can freely explore in real-time: creating visually an aquifer of desired configurations, interactively imposing desired stresses, and then immediately investigating and visualizing the geology and the processes of flow and contaminant transport and transformation. A modeler can pause to edit at any time and interact on-line with any aspects (e.g., conceptual and numerical representation, boundary conditions, model solvers, and ways of visualization and analysis) of the integrated modeling process; he/she can initiate or stop, whenever needed, particle tracking, plume modeling, subscale modeling, cross-sectional modeling, stochastic modeling, monitoring

  3. Dynamics of soluble and inert pollutant concentrations in linear and deterministic systems with time varying parameters

    International Nuclear Information System (INIS)

    Meltzer, M.

    1977-04-01

    The tracer theory in steady and non-steady systems is presented. The unsteady system was applied in the study of the concentration dynamics of the National Water Carrier in Israel. A method that uses Bromine 82 for the investigation of the transfer time distribution and of the dynamics of inert matter concentration in the system is desribed. (B.G.)

  4. Characterisation of dispersion mechanisms in an urban catchment using a deterministic spatially distributed direct hydrograph travel time model

    Science.gov (United States)

    Rossel, F.; Gironas, J. A.

    2012-12-01

    The link between stream network structure and hydrologic response for natural basins has been extensively studied. It is well known that stream network organization and flow dynamics in the reaches combine to shape the hydrologic response of natural basins. Geomorphologic dispersion and hydrodynamic dispersion along with hillslope processes control to a large extent the overall variance of the hydrograph, particularly under the assumption of constant celerity throughout the basin. In addition, a third mechanism referred as to kinematic dispersion becomes relevant when considering spatial variations of celerity. On contrary, the link between the drainage network structure and overall urban terrain, and the hydrologic response in urban catchments has been much less studied. In particular, the characterization of the different dispersion mechanisms within urban areas remains to be better understood. In such areas artificial elements are expected to contribute to the total dispersion due to the variety of geometries and the spatial distribution of imperviousness. This work quantifies the different dispersion mechanisms in an urban catchment, focusing on their relevance and the spatial scales involved. For this purpose we use the Urban Morpho-climatic Instantaneous Unit Hydrograph model, a deterministic spatially distributed direct hydrograph travel time model, which computes travel times in hillslope, pipe, street and channel cells using formulations derived from kinematic wave theory. The model was applied to the Aubeniere catchment, located in Nantes, France. Unlike stochastic models, this deterministic model allows the quantification of dispersion mechanism at the local scale (i.e. the grid-cell). We found that kinematic dispersion is more relevant for small storm events, whereas geomorphologic dispersion becomes more significant for larger storms, as the mean celerity within the catchment increases. In addition, the total dispersion relates to the drainage area in

  5. Deterministic computation of functional integrals

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.

    1995-09-01

    A new method of numerical integration in functional spaces is described. This method is based on the rigorous definition of a functional integral in complete separable metric space and on the use of approximation formulas which we constructed for this kind of integral. The method is applicable to solution of some partial differential equations and to calculation of various characteristics in quantum physics. No preliminary discretization of space and time is required in this method, as well as no simplifying assumptions like semi-classical, mean field approximations, collective excitations, introduction of ''short-time'' propagators, etc are necessary in our approach. The constructed approximation formulas satisfy the condition of being exact on a given class of functionals, namely polynomial functionals of a given degree. The employment of these formulas replaces the evaluation of a functional integral by computation of the ''ordinary'' (Riemannian) integral of a low dimension, thus allowing to use the more preferable deterministic algorithms (normally - Gaussian quadratures) in computations rather than traditional stochastic (Monte Carlo) methods which are commonly used for solution of the problem under consideration. The results of application of the method to computation of the Green function of the Schroedinger equation in imaginary time as well as the study of some models of Euclidean quantum mechanics are presented. The comparison with results of other authors shows that our method gives significant (by an order of magnitude) economy of computer time and memory versus other known methods while providing the results with the same or better accuracy. The funcitonal measure of the Gaussian type is considered and some of its particular cases, namely conditional Wiener measure in quantum statistical mechanics and functional measure in a Schwartz distribution space in two-dimensional quantum field theory are studied in detail. Numerical examples demonstrating the

  6. Irreversible data compression concepts with polynomial fitting in time-order of particle trajectory for visualization of huge particle system

    International Nuclear Information System (INIS)

    Ohtani, H; Ito, A M; Hagita, K; Kato, T; Saitoh, T; Takeda, T

    2013-01-01

    We propose in this paper a data compression scheme for large-scale particle simulations, which has favorable prospects for scientific visualization of particle systems. Our data compression concepts deal with the data of particle orbits obtained by simulation directly and have the following features: (i) Through control over the compression scheme, the difference between the simulation variables and the reconstructed values for the visualization from the compressed data becomes smaller than a given constant. (ii) The particles in the simulation are regarded as independent particles and the time-series data for each particle is compressed with an independent time-step for the particle. (iii) A particle trajectory is approximated by a polynomial function based on the characteristic motion of the particle. It is reconstructed as a continuous curve through interpolation from the values of the function for intermediate values of the sample data. We name this concept ''TOKI (Time-Order Kinetic Irreversible compression)''. In this paper, we present an example of an implementation of a data-compression scheme with the above features. Several application results are shown for plasma and galaxy formation simulation data

  7. Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'

    International Nuclear Information System (INIS)

    Cregg, P J; Svedlindh, P

    2007-01-01

    A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)

  8. An orthogonal-polynomial approach to first-hitting times of birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    In a recent paper in this journal, Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor’s classical results on first-hitting times of a birth–death process on the nonnegative integers by establishing a representation for the Laplace transform E[exp(sTij)] of the

  9. An orthogonal-polynomial approach to first-hitting times of birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    In a recent paper [J. Theor. Probab. 25 (2012) 950-980] Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's classical results on first-hitting times of a birth-death process on the nonnegative integers by establishing a representation for the Laplace transform

  10. Polynomial-time computability of the edge-reliability of graphs using Gilbert's formula

    Directory of Open Access Journals (Sweden)

    Thomas J. Marlowe

    1998-01-01

    Full Text Available Reliability is an important consideration in analyzing computer and other communication networks, but current techniques are extremely limited in the classes of graphs which can be analyzed efficiently. While Gilbert's formula establishes a theoretically elegant recursive relationship between the edge reliability of a graph and the reliability of its subgraphs, naive evaluation requires consideration of all sequences of deletions of individual vertices, and for many graphs has time complexity essentially Θ (N!. We discuss a general approach which significantly reduces complexity, encoding subgraph isomorphism in a finer partition by invariants, and recursing through the set of invariants.

  11. A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State

    OpenAIRE

    Antoniadis, Antonios; Huang, Chien-Chung; Ott, Sebastian

    2014-01-01

    We study classical deadline-based preemptive scheduling of tasks in a computing environment equipped with both dynamic speed scaling and sleep state capabilities: Each task is specified by a release time, a deadline and a processing volume, and has to be scheduled on a single, speed-scalable processor that is supplied with a sleep state. In the sleep state, the processor consumes no energy, but a constant wake-up cost is required to transition back to the active state. In contrast to speed sc...

  12. JAUS to EtherCAT Bridge: Toward Real-Time and Deterministic Joint Architecture for Unmanned Systems

    Directory of Open Access Journals (Sweden)

    Jie Sheng

    2014-01-01

    Full Text Available The Joint Architecture for Unmanned Systems (JAUS is a communication standard that allows for interoperability between Unmanned Vehicles (UVs. Current research indicates that JAUS-compliant systems do not meet real-time performance guidelines necessary for internal systems in UVs. However, there is a lack of quantitative data illustrating the performance shortcomings of JAUS or clear explanations on what causes these performance issues or comparisons with existing internal communication systems. In this research, we first develop a basic C++ implementation of JAUS and evaluate its performance with quantitative data and compare the results with published performance data of Controller Area Network (CAN to determine the feasibility of the JAUS standard. Our results indicate that the main reason of JAUS’s poor performance lies in the latency inherent in the hierarchical structure of JAUS and the overhead of User Datagram Protocol (UDP messages, which has been used with JAUS and is slower than the high-speed CAN. Additionally, UDP has no scheduling mechanism, which makes it virtually impossible to guarantee messages meeting their deadlines. Considering the slow and nondeterministic JAUS communication from subsystems to components, which is JAUS Level 3 compliance, we then propose a solution by bringing Ethernet for Control Automation Technology (EtherCAT to add speed, deterministic feature, and security. The JAUS-EtherCAT mapping, which we called a JEBridge, is implemented into nodes and components. Both quantitative and qualitative results are provided to show that JEBridge and JAUS Level 3 compliance can bring not only interoperability but also reasonable performance to UVs.

  13. Transit timing observations from Kepler. V. Transit timing variation candidates in the first sixteen months from polynomial models

    DEFF Research Database (Denmark)

    Ford, E.B.; Ragozzine, D.; Holman, M.J.

    2012-01-01

    Transit timing variations provide a powerful tool for confirming and characterizing transiting planets, as well as detecting non-transiting planets. We report the results of an updated transit timing variation (TTV) analysis for 1481 planet candidates based on transit times measured during...... that several of these planet candidates could be confirmed and perhaps characterized with more detailed TTV analyses using publicly available Kepler observations. For many others, Kepler has observed a long-term TTV trend, but an extended Kepler mission will be required to characterize the system via TTVs. We...

  14. The influence of deterministic and stochastic waiting time for triggering mortality and colonization events on the coexistence of cooperators and defectors in an evolutionary game model

    Directory of Open Access Journals (Sweden)

    YouHua Chen

    2014-06-01

    Full Text Available In the present report, the coexistence of Prisoners' Dilemma game players (cooperators and defectors were explored in an individual-based framework with the consideration of the impacts of deterministic and stochastic waiting time (WT for triggering mortality and/or colonization events. For the type of deterministic waiting time, the time step for triggering a mortality and/or colonization event is fixed. For the type of stochastic waiting time, whether a mortality and/or colonization event should be triggered for each time step of a simulation is randomly determined by a given acceptance probability (the event takes place when a variate drawn from a uniform distribution [0,1] is smaller than the acceptance probability. The two strategies of modeling waiting time are considered simultaneously and applied to both quantities (mortality: WTm, colonization: WTc. As such, when WT (WTm and/or WTc is an integral >=1, it indicated a deterministically triggering strategy. In contrast, when 1>WT>0, it indicated a stochastically triggering strategy and the WT value itself is used as the acceptance probability. The parameter space between the waiting time for mortality (WTm-[0.1,40] and colonization (WTc-[0.1,40] was traversed to explore the coexistence and non-coexistence regions. The role of defense award was evaluated. My results showed that, one non-coexistence region is identified consistently, located at the area where 1>=WTm>=0.3 and 40>=WTc>=0.1. As a consequence, it was found that the coexistence of cooperators and defectors in the community is largely dependent on the waiting time of mortality events, regardless of the defense or cooperation rewards. When the mortality events happen in terms of stochastic waiting time (1>=WTm>=0.3, extinction of either cooperators or defectors or both could be very likely, leading to the emergence of non-coexistence scenarios. However, when the mortality events occur in forms of relatively long deterministic

  15. A two warehouse deterministic inventory model for deteriorating items with a linear trend in time dependent demand over finite time horizon by Elitist Real-Coded Genetic Algorithm

    Directory of Open Access Journals (Sweden)

    A.K. Bhunia

    2013-04-01

    Full Text Available This paper deals with a deterministic inventory model developed for deteriorating items having two separate storage facilities (owned and rented warehouses due to limited capacity of the existing storage (owned warehouse with linear time dependent demand (increasing over a fixed finite time horizon. The model is formulated with infinite replenishment and the successive replenishment cycle lengths are in arithmetic progression. Partially backlogged shortages are allowed. The stocks of rented warehouse (RW are transported to the owned warehouse (OW in continuous release pattern. For this purpose, the model is formulated as a constrained non-linear mixed integer programming problem. For solving the problem, an advanced genetic algorithm (GA has been developed. This advanced GA is based on ranking selection, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. Our objective is to determine the optimal replenishment number, lot-size of two-warehouses (OW and RW by maximizing the profit function. The model is illustrated with four numerical examples and sensitivity analyses of the optimal solution are performed with respect to different parameters.

  16. TRANSIT TIMING OBSERVATIONS FROM KEPLER. V. TRANSIT TIMING VARIATION CANDIDATES IN THE FIRST SIXTEEN MONTHS FROM POLYNOMIAL MODELS

    Energy Technology Data Exchange (ETDEWEB)

    Ford, Eric B. [Astronomy Department, University of Florida, 211 Bryant Space Sciences Center, Gainesville, FL 32111 (United States); Ragozzine, Darin; Holman, Matthew J. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Rowe, Jason F.; Barclay, Thomas; Borucki, William J.; Bryson, Stephen T.; Caldwell, Douglas A.; Kinemuchi, Karen; Koch, David G.; Lissauer, Jack J.; Still, Martin; Tenenbaum, Peter [NASA Ames Research Center, Moffett Field, CA 94035 (United States); Steffen, Jason H. [Fermilab Center for Particle Astrophysics, P.O. Box 500, MS 127, Batavia, IL 60510 (United States); Batalha, Natalie M. [Department of Physics and Astronomy, San Jose State University, San Jose, CA 95192 (United States); Fabrycky, Daniel C. [UCO/Lick Observatory, University of California, Santa Cruz, CA 95064 (United States); Gautier, Thomas N. [Jet Propulsion Laboratory/California Institute of Technology, Pasadena, CA 91109 (United States); Ibrahim, Khadeejah A.; Uddin, Kamal [Orbital Sciences Corporation/NASA Ames Research Center, Moffett Field, CA 94035 (United States); Kjeldsen, Hans, E-mail: eford@astro.ufl.edu [Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C (Denmark); and others

    2012-09-10

    Transit timing variations provide a powerful tool for confirming and characterizing transiting planets, as well as detecting non-transiting planets. We report the results of an updated transit timing variation (TTV) analysis for 1481 planet candidates based on transit times measured during the first sixteen months of Kepler observations. We present 39 strong TTV candidates based on long-term trends (2.8% of suitable data sets). We present another 136 weaker TTV candidates (9.8% of suitable data sets) based on the excess scatter of TTV measurements about a linear ephemeris. We anticipate that several of these planet candidates could be confirmed and perhaps characterized with more detailed TTV analyses using publicly available Kepler observations. For many others, Kepler has observed a long-term TTV trend, but an extended Kepler mission will be required to characterize the system via TTVs. We find that the occurrence rate of planet candidates that show TTVs is significantly increased ({approx}68%) for planet candidates transiting stars with multiple transiting planet candidates when compared to planet candidates transiting stars with a single transiting planet candidate.

  17. Deterministic Graphical Games Revisited

    DEFF Research Database (Denmark)

    Andersson, Klas Olof Daniel; Hansen, Kristoffer Arnsfelt; Miltersen, Peter Bro

    2012-01-01

    Starting from Zermelo’s classical formal treatment of chess, we trace through history the analysis of two-player win/lose/draw games with perfect information and potentially infinite play. Such chess-like games have appeared in many different research communities, and methods for solving them......, such as retrograde analysis, have been rediscovered independently. We then revisit Washburn’s deterministic graphical games (DGGs), a natural generalization of chess-like games to arbitrary zero-sum payoffs. We study the complexity of solving DGGs and obtain an almost-linear time comparison-based algorithm...

  18. Irreducible multivariate polynomials obtained from polynomials in ...

    Indian Academy of Sciences (India)

    Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.

  19. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1999-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere....

  20. Better polynomials for GNFS

    OpenAIRE

    Bai , Shi; Bouvier , Cyril; Kruppa , Alexander; Zimmermann , Paul

    2016-01-01

    International audience; The general number field sieve (GNFS) is the most efficient algo-rithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomials for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial tha...

  1. Deterministic indexing for packed strings

    DEFF Research Database (Denmark)

    Bille, Philip; Gørtz, Inge Li; Skjoldjensen, Frederik Rye

    2017-01-01

    Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In the deterministic variant the goal is to solve the string indexing problem without any randomization (at preprocessing time...... or query time). In the packed variant the strings are stored with several character in a single word, giving us the opportunity to read multiple characters simultaneously. Our main result is a new string index in the deterministic and packed setting. Given a packed string S of length n over an alphabet σ...

  2. Branched polynomial covering maps

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2002-01-01

    A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch ...... set. Particular studies are made of branched polynomial covering maps arising from Riemann surfaces and from knots in the 3-sphere. (C) 2001 Elsevier Science B.V. All rights reserved.......A Weierstrass polynomial with multiple roots in certain points leads to a branched covering map. With this as the guiding example, we formally define and study the notion of a branched polynomial covering map. We shall prove that many finite covering maps are polynomial outside a discrete branch...

  3. Application of polynomial preconditioners to conservation laws

    NARCIS (Netherlands)

    Geurts, Bernardus J.; van Buuren, R.; Lu, H.

    2000-01-01

    Polynomial preconditioners which are suitable in implicit time-stepping methods for conservation laws are reviewed and analyzed. The preconditioners considered are either based on a truncation of a Neumann series or on Chebyshev polynomials for the inverse of the system-matrix. The latter class of

  4. Modelling and multi-objective optimization of a variable valve-timing spark-ignition engine using polynomial neural networks and evolutionary algorithms

    International Nuclear Information System (INIS)

    Atashkari, K.; Nariman-Zadeh, N.; Goelcue, M.; Khalkhali, A.; Jamali, A.

    2007-01-01

    The main reason for the efficiency decrease at part load conditions for four-stroke spark-ignition (SI) engines is the flow restriction at the cross-sectional area of the intake system. Traditionally, valve-timing has been designed to optimize operation at high engine-speed and wide open throttle conditions. Several investigations have demonstrated that improvements at part load conditions in engine performance can be accomplished if the valve-timing is variable. Controlling valve-timing can be used to improve the torque and power curve as well as to reduce fuel consumption and emissions. In this paper, a group method of data handling (GMDH) type neural network and evolutionary algorithms (EAs) are firstly used for modelling the effects of intake valve-timing (V t ) and engine speed (N) of a spark-ignition engine on both developed engine torque (T) and fuel consumption (Fc) using some experimentally obtained training and test data. Using such obtained polynomial neural network models, a multi-objective EA (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity preserving mechanism are secondly used for Pareto based optimization of the variable valve-timing engine considering two conflicting objectives such as torque (T) and fuel consumption (Fc). The comparison results demonstrate the superiority of the GMDH type models over feedforward neural network models in terms of the statistical measures in the training data, testing data and the number of hidden neurons. Further, it is shown that some interesting and important relationships, as useful optimal design principles, involved in the performance of the variable valve-timing four-stroke spark-ignition engine can be discovered by the Pareto based multi-objective optimization of the polynomial models. Such important optimal principles would not have been obtained without the use of both the GMDH type neural network modelling and the multi-objective Pareto optimization approach

  5. Weierstrass polynomials for links

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    1997-01-01

    There is a natural way of identifying links in3-space with polynomial covering spaces over thecircle. Thereby any link in 3-space can be definedby a Weierstrass polynomial over the circle. Theequivalence relation for covering spaces over thecircle is, however, completely different from...

  6. Polynomial asymptotic stability of damped stochastic differential equations

    Directory of Open Access Journals (Sweden)

    John Appleby

    2004-08-01

    Full Text Available The paper studies the polynomial convergence of solutions of a scalar nonlinear It\\^{o} stochastic differential equation\\[dX(t = -f(X(t\\,dt + \\sigma(t\\,dB(t\\] where it is known, {\\it a priori}, that $\\lim_{t\\rightarrow\\infty} X(t=0$, a.s. The intensity of the stochastic perturbation $\\sigma$ is a deterministic, continuous and square integrable function, which tends to zero more quickly than a polynomially decaying function. The function $f$ obeys $\\lim_{x\\rightarrow 0}\\mbox{sgn}(xf(x/|x|^\\beta = a$, for some $\\beta>1$, and $a>0$.We study two asymptotic regimes: when $\\sigma$ tends to zero sufficiently quickly the polynomial decay rate of solutions is the same as for the deterministic equation (when $\\sigma\\equiv0$. When $\\sigma$ decays more slowly, a weaker almost sure polynomial upper bound on the decay rate of solutions is established. Results which establish the necessity for $\\sigma$ to decay polynomially in order to guarantee the almost sure polynomial decay of solutions are also proven.

  7. Nonnegativity of uncertain polynomials

    Directory of Open Access Journals (Sweden)

    Šiljak Dragoslav D.

    1998-01-01

    Full Text Available The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

  8. Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

    OpenAIRE

    Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie

    2011-01-01

    In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

  9. Polynomial Heisenberg algebras

    International Nuclear Information System (INIS)

    Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M

    2004-01-01

    Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively

  10. Generalizations of orthogonal polynomials

    Science.gov (United States)

    Bultheel, A.; Cuyt, A.; van Assche, W.; van Barel, M.; Verdonk, B.

    2005-07-01

    We give a survey of recent generalizations of orthogonal polynomials. That includes multidimensional (matrix and vector orthogonal polynomials) and multivariate versions, multipole (orthogonal rational functions) variants, and extensions of the orthogonality conditions (multiple orthogonality). Most of these generalizations are inspired by the applications in which they are applied. We also give a glimpse of these applications, which are usually generalizations of applications where classical orthogonal polynomials also play a fundamental role: moment problems, numerical quadrature, rational approximation, linear algebra, recurrence relations, and random matrices.

  11. Coupled Heuristic Prediction of Long Lead-Time Accumulated Total Inflow of a Reservoir during Typhoons Using Deterministic Recurrent and Fuzzy Inference-Based Neural Network

    Directory of Open Access Journals (Sweden)

    Chien-Lin Huang

    2015-11-01

    Full Text Available This study applies Real-Time Recurrent Learning Neural Network (RTRLNN and Adaptive Network-based Fuzzy Inference System (ANFIS with novel heuristic techniques to develop an advanced prediction model of accumulated total inflow of a reservoir in order to solve the difficulties of future long lead-time highly varied uncertainty during typhoon attacks while using a real-time forecast. For promoting the temporal-spatial forecasted precision, the following original specialized heuristic inputs were coupled: observed-predicted inflow increase/decrease (OPIID rate, total precipitation, and duration from current time to the time of maximum precipitation and direct runoff ending (DRE. This study also investigated the temporal-spatial forecasted error feature to assess the feasibility of the developed models, and analyzed the output sensitivity of both single and combined heuristic inputs to determine whether the heuristic model is susceptible to the impact of future forecasted uncertainty/errors. Validation results showed that the long lead-time–predicted accuracy and stability of the RTRLNN-based accumulated total inflow model are better than that of the ANFIS-based model because of the real-time recurrent deterministic routing mechanism of RTRLNN. Simulations show that the RTRLNN-based model with coupled heuristic inputs (RTRLNN-CHI, average error percentage (AEP/average forecast lead-time (AFLT: 6.3%/49 h can achieve better prediction than the model with non-heuristic inputs (AEP of RTRLNN-NHI and ANFIS-NHI: 15.2%/31.8% because of the full consideration of real-time hydrological initial/boundary conditions. Besides, the RTRLNN-CHI model can promote the forecasted lead-time above 49 h with less than 10% of AEP which can overcome the previous forecasted limits of 6-h AFLT with above 20%–40% of AEP.

  12. Superiority of legendre polynomials to Chebyshev polynomial in ...

    African Journals Online (AJOL)

    In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev, Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev ...

  13. Extended biorthogonal matrix polynomials

    Directory of Open Access Journals (Sweden)

    Ayman Shehata

    2017-01-01

    Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.

  14. On Symmetric Polynomials

    OpenAIRE

    Golden, Ryan; Cho, Ilwoo

    2015-01-01

    In this paper, we study structure theorems of algebras of symmetric functions. Based on a certain relation on elementary symmetric polynomials generating such algebras, we consider perturbation in the algebras. In particular, we understand generators of the algebras as perturbations. From such perturbations, define injective maps on generators, which induce algebra-monomorphisms (or embeddings) on the algebras. They provide inductive structure theorems on algebras of symmetric polynomials. As...

  15. Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

    International Nuclear Information System (INIS)

    Norris, Edward T.; Liu, Xin; Hsieh, Jiang

    2015-01-01

    Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer

  16. ICRP (1991) and deterministic effects

    International Nuclear Information System (INIS)

    Mole, R.H.

    1992-01-01

    A critical review of ICRP Publication 60 (1991) shows that considerable revisions are needed in both language and thinking about deterministic effects (DE). ICRP (1991) makes a welcome and clear distinction between change, caused by irradiation; damage, some degree of deleterious change, for example to cells, but not necessarily deleterious to the exposed individual; harm, clinically observable deleterious effects expressed in individuals or their descendants; and detriment, a complex concept combining the probability, severity and time of expression of harm (para42). (All added emphases come from the author.) Unfortunately these distinctions are not carried through into the discussion of deterministic effects (DE) and two important terms are left undefined. Presumably effect may refer to change, damage, harm or detriment, according to context. Clinically observable is also undefined although its meaning is crucial to any consideration of DE since DE are defined as causing observable harm (para 20). (Author)

  17. BSDEs with polynomial growth generators

    Directory of Open Access Journals (Sweden)

    Philippe Briand

    2000-01-01

    Full Text Available In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

  18. Chromatic polynomials for simplicial complexes

    DEFF Research Database (Denmark)

    Møller, Jesper Michael; Nord, Gesche

    2016-01-01

    In this note we consider s s -chromatic polynomials for finite simplicial complexes. When s=1 s=1 , the 1 1 -chromatic polynomial is just the usual graph chromatic polynomial of the 1 1 -skeleton. In general, the s s -chromatic polynomial depends on the s s -skeleton and its value at r...

  19. Deterministic chaos in the processor load

    International Nuclear Information System (INIS)

    Halbiniak, Zbigniew; Jozwiak, Ireneusz J.

    2007-01-01

    In this article we present the results of research whose purpose was to identify the phenomenon of deterministic chaos in the processor load. We analysed the time series of the processor load during efficiency tests of database software. Our research was done on a Sparc Alpha processor working on the UNIX Sun Solaris 5.7 operating system. The conducted analyses proved the presence of the deterministic chaos phenomenon in the processor load in this particular case

  20. A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

    Energy Technology Data Exchange (ETDEWEB)

    Kersaudy, Pierric, E-mail: pierric.kersaudy@orange.com [Orange Labs, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France); Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France); ESYCOM, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, 77700 Marne-la-Vallée (France); Sudret, Bruno [ETH Zürich, Chair of Risk, Safety and Uncertainty Quantification, Stefano-Franscini-Platz 5, 8093 Zürich (Switzerland); Varsier, Nadège [Orange Labs, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France); Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France); Picon, Odile [ESYCOM, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, 77700 Marne-la-Vallée (France); Wiart, Joe [Orange Labs, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France); Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux (France)

    2015-04-01

    In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.

  1. Deterministic Compressed Sensing

    Science.gov (United States)

    2011-11-01

    39 4.3 Digital Communications . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4 Group Testing ...deterministic de - sign matrices. All bounds ignore the O() constants. . . . . . . . . . . 131 xvi List of Algorithms 1 Iterative Hard Thresholding Algorithm...sensing is information theoretically possible using any (2k, )-RIP sensing matrix . The following celebrated results of Candès, Romberg and Tao [54

  2. Deterministic uncertainty analysis

    International Nuclear Information System (INIS)

    Worley, B.A.

    1987-01-01

    Uncertainties of computer results are of primary interest in applications such as high-level waste (HLW) repository performance assessment in which experimental validation is not possible or practical. This work presents an alternate deterministic approach for calculating uncertainties that has the potential to significantly reduce the number of computer runs required for conventional statistical analysis. 7 refs., 1 fig

  3. RBE for deterministic effects

    International Nuclear Information System (INIS)

    1990-01-01

    In the present report, data on RBE values for effects in tissues of experimental animals and man are analysed to assess whether for specific tissues the present dose limits or annual limits of intake based on Q values, are adequate to prevent deterministic effects. (author)

  4. An arbitrary polynomial chaos-based approach to analyzing the impacts of design parameters on evacuation time under uncertainty

    NARCIS (Netherlands)

    Xie, Q.; Lu, S.; Costola, D.; Hensen, J.L.M.

    2014-01-01

    In performance-based fire protection design of buildings, much attention is paid to design parameters by fire engineers or experts. However, due to the time-consuming evacuation models, it is computationally prohibitive to adopt the conventional Monte Carlo simulation (MCS) to examine the effect of

  5. Deterministic chaos in entangled eigenstates

    Science.gov (United States)

    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.

  6. Deterministic chaos in entangled eigenstates

    Energy Technology Data Exchange (ETDEWEB)

    Schlegel, K.G. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)], E-mail: guenter.schlegel@arcor.de; Foerster, S. [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)

    2008-05-12

    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.

  7. Deterministic chaos in entangled eigenstates

    International Nuclear Information System (INIS)

    Schlegel, K.G.; Foerster, S.

    2008-01-01

    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

  8. A Comparison of State Space LQG, Wiener IMC and Polynomial LQG Discrete Time Feedback Control for Active Vibration Control Purposes

    DEFF Research Database (Denmark)

    Mørkholt, Jakob; Elliott, S.J.; Sors, T.C.

    1997-01-01

    with a piezoceramic patch control actuator and a point velocity sensor and excited by a point force driven by white noise acting as the primary source. The design objective has been to suppress the effect of the primary disturbance on the output by minimising the mean square value of the output. Apart from comparing......A comparison of three ways of designing optimal discrete time feedback controllers has been carried out via computer simulations. The three design methods are similar in that they are all based on the minimisation of a quadratic cost function under certain assumptions about the disturbance noise...... and sensor noise in the system to be controlled. They are also based on (different) models of the plant under control and the disturbance to be suppressed by the controllers. Controllers based on the three methods have been designed from a model of a lightly damped, rectangular plate fitted...

  9. Colouring and knot polynomials

    International Nuclear Information System (INIS)

    Welsh, D.J.A.

    1991-01-01

    These lectures will attempt to explain a connection between the recent advances in knot theory using the Jones and related knot polynomials with classical problems in combinatorics and statistical mechanics. The difficulty of some of these problems will be analysed in the context of their computational complexity. In particular we shall discuss colourings and groups valued flows in graphs, knots and the Jones and Kauffman polynomials, the Ising, Potts and percolation problems of statistical physics, computational complexity of the above problems. (author). 20 refs, 9 figs

  10. Additive and polynomial representations

    CERN Document Server

    Krantz, David H; Suppes, Patrick

    1971-01-01

    Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utiliz

  11. Popov form computation for matrices of Ore polynomials

    DEFF Research Database (Denmark)

    Khochtali, Mohamed; Né Nielsen, Johan Rosenkilde; Storjohann, Arne

    2017-01-01

    Let F[∂; s, d] be a ring of Ore polynomials over a field. We give a new deterministic algorithm for computing the Popov form P of a non-singular matrix A ∈ F[∂; s, d]n×n. Our main focus is to ensure controlled growth in the size of coefficients from F in the case F = k(z), and even k = Q. Our...

  12. Deterministic behavioural models for concurrency

    DEFF Research Database (Denmark)

    Sassone, Vladimiro; Nielsen, Mogens; Winskel, Glynn

    1993-01-01

    This paper offers three candidates for a deterministic, noninterleaving, behaviour model which generalizes Hoare traces to the noninterleaving situation. The three models are all proved equivalent in the rather strong sense of being equivalent as categories. The models are: deterministic labelled...... event structures, generalized trace languages in which the independence relation is context-dependent, and deterministic languages of pomsets....

  13. Deterministic calculations of radiation doses from brachytherapy seeds

    International Nuclear Information System (INIS)

    Reis, Sergio Carneiro dos; Vasconcelos, Vanderley de; Santos, Ana Maria Matildes dos

    2009-01-01

    Brachytherapy is used for treating certain types of cancer by inserting radioactive sources into tumours. CDTN/CNEN is developing brachytherapy seeds to be used mainly in prostate cancer treatment. Dose calculations play a very significant role in the characterization of the developed seeds. The current state-of-the-art of computation dosimetry relies on Monte Carlo methods using, for instance, MCNP codes. However, deterministic calculations have some advantages, as, for example, short computer time to find solutions. This paper presents a software developed to calculate doses in a two-dimensional space surrounding the seed, using a deterministic algorithm. The analysed seeds consist of capsules similar to IMC6711 (OncoSeed), that are commercially available. The exposure rates and absorbed doses are computed using the Sievert integral and the Meisberger third order polynomial, respectively. The software also allows the isodose visualization at the surface plan. The user can choose between four different radionuclides ( 192 Ir, 198 Au, 137 Cs and 60 Co). He also have to enter as input data: the exposure rate constant; the source activity; the active length of the source; the number of segments in which the source will be divided; the total source length; the source diameter; and the actual and effective source thickness. The computed results were benchmarked against results from literature and developed software will be used to support the characterization process of the source that is being developed at CDTN. The software was implemented using Borland Delphi in Windows environment and is an alternative to Monte Carlo based codes. (author)

  14. On the Laurent polynomial rings

    International Nuclear Information System (INIS)

    Stefanescu, D.

    1985-02-01

    We describe some properties of the Laurent polynomial rings in a finite number of indeterminates over a commutative unitary ring. We study some subrings of the Laurent polynomial rings. We finally obtain two cancellation properties. (author)

  15. Computing the Alexander Polynomial Numerically

    DEFF Research Database (Denmark)

    Hansen, Mikael Sonne

    2006-01-01

    Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....

  16. Stochastic Estimation via Polynomial Chaos

    Science.gov (United States)

    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

  17. CSL model checking of deterministic and stochastic Petri nets

    NARCIS (Netherlands)

    Martinez Verdugo, J.M.; Haverkort, Boudewijn R.H.M.; German, R.; Heindl, A.

    2006-01-01

    Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under

  18. Improved multivariate polynomial factoring algorithm

    International Nuclear Information System (INIS)

    Wang, P.S.

    1978-01-01

    A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timing are included

  19. Orthogonal polynomials and random matrices

    CERN Document Server

    Deift, Percy

    2000-01-01

    This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.

  20. Polynomial optimization : Error analysis and applications

    NARCIS (Netherlands)

    Sun, Zhao

    2015-01-01

    Polynomial optimization is the problem of minimizing a polynomial function subject to polynomial inequality constraints. In this thesis we investigate several hierarchies of relaxations for polynomial optimization problems. Our main interest lies in understanding their performance, in particular how

  1. Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    Dias, Kealey

    vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...... of parameter spaces into structurally stable domains, and a description of the bifurcations. For this reason, the talk will focus on these questions for complex polynomial vector fields.......The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...

  2. Roots of the Chromatic Polynomial

    DEFF Research Database (Denmark)

    Perrett, Thomas

    The chromatic polynomial of a graph G is a univariate polynomial whose evaluation at any positive integer q enumerates the proper q-colourings of G. It was introduced in connection with the famous four colour theorem but has recently found other applications in the field of statistical physics...... extend Thomassen’s technique to the Tutte polynomial and as a consequence, deduce a density result for roots of the Tutte polynomial. This partially answers a conjecture of Jackson and Sokal. Finally, we refocus our attention on the chromatic polynomial and investigate the density of chromatic roots...

  3. Polynomials in algebraic analysis

    OpenAIRE

    Multarzyński, Piotr

    2012-01-01

    The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \\cite{DPR}. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear ...

  4. Linear precoding based on polynomial expansion: reducing complexity in massive MIMO

    KAUST Repository

    Mueller, Axel

    2016-02-29

    Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively “antenna-efficient” regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

  5. General Reducibility and Solvability of Polynomial Equations ...

    African Journals Online (AJOL)

    General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...

  6. Introducing Synchronisation in Deterministic Network Models

    DEFF Research Database (Denmark)

    Schiøler, Henrik; Jessen, Jan Jakob; Nielsen, Jens Frederik D.

    2006-01-01

    The paper addresses performance analysis for distributed real time systems through deterministic network modelling. Its main contribution is the introduction and analysis of models for synchronisation between tasks and/or network elements. Typical patterns of synchronisation are presented leading...... to the suggestion of suitable network models. An existing model for flow control is presented and an inherent weakness is revealed and remedied. Examples are given and numerically analysed through deterministic network modelling. Results are presented to highlight the properties of the suggested models...

  7. Polynomial approximation on polytopes

    CERN Document Server

    Totik, Vilmos

    2014-01-01

    Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.

  8. Polynomial intelligent states

    International Nuclear Information System (INIS)

    Milks, Matthew M; Guise, Hubert de

    2005-01-01

    The construction of su(2) intelligent states is simplified using a polynomial representation of su(2). The cornerstone of the new construction is the diagonalization of a 2 x 2 matrix. The method is sufficiently simple to be easily extended to su(3), where one is required to diagonalize a single 3 x 3 matrix. For two perfectly general su(3) operators, this diagonalization is technically possible but the procedure loses much of its simplicity owing to the algebraic form of the roots of a cubic equation. Simplified expressions can be obtained by specializing the choice of su(3) operators. This simpler construction will be discussed in detail

  9. Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

    Directory of Open Access Journals (Sweden)

    Jie Ran

    2015-01-01

    Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

  10. Polynomial chaos functions and stochastic differential equations

    International Nuclear Information System (INIS)

    Williams, M.M.R.

    2006-01-01

    The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

  11. Flowchart Programs, Regular Expressions, and Decidability of Polynomial Growth-Rate

    Directory of Open Access Journals (Sweden)

    Amir M. Ben-Amram

    2016-07-01

    Full Text Available We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely decide if computed values are polynomially bounded as a function of the input; and similarly for the running time. Such complexity properties are undecidable for a Turing-complete programming language, and a common work-around in program analysis is to settle for sound but incomplete solutions. In contrast, we consider a class of programs that is Turing-incomplete, but strong enough to include several challenges for this kind of analysis. For a related language that has well-structured syntax, similar to Meyer and Ritchie's LOOP programs, the problem has been previously proved to be decidable. The analysis relied on the compositionality of programs, hence the challenge in obtaining similar results for flowchart programs with arbitrary control-flow graphs. Our answer to the challenge is twofold: first, we propose a class of loop-annotated flowcharts, which is more general than the class of flowcharts that directly represent structured programs; secondly, we present a technique to reuse the ideas from the work on tructured programs and apply them to such flowcharts. The technique is inspired by the classic translation of non-deterministic automata to regular expressions, but we obviate the exponential cost of constructing such an expression, obtaining a polynomial-time analysis. These ideas may well be applicable to other analysis problems.

  12. Deterministic uncertainty analysis

    International Nuclear Information System (INIS)

    Worley, B.A.

    1987-12-01

    This paper presents a deterministic uncertainty analysis (DUA) method for calculating uncertainties that has the potential to significantly reduce the number of computer runs compared to conventional statistical analysis. The method is based upon the availability of derivative and sensitivity data such as that calculated using the well known direct or adjoint sensitivity analysis techniques. Formation of response surfaces using derivative data and the propagation of input probability distributions are discussed relative to their role in the DUA method. A sample problem that models the flow of water through a borehole is used as a basis to compare the cumulative distribution function of the flow rate as calculated by the standard statistical methods and the DUA method. Propogation of uncertainties by the DUA method is compared for ten cases in which the number of reference model runs was varied from one to ten. The DUA method gives a more accurate representation of the true cumulative distribution of the flow rate based upon as few as two model executions compared to fifty model executions using a statistical approach. 16 refs., 4 figs., 5 tabs

  13. Comparison of some classification algorithms based on deterministic and nondeterministic decision rules

    KAUST Repository

    Delimata, Paweł

    2010-01-01

    We discuss two, in a sense extreme, kinds of nondeterministic rules in decision tables. The first kind of rules, called as inhibitory rules, are blocking only one decision value (i.e., they have all but one decisions from all possible decisions on their right hand sides). Contrary to this, any rule of the second kind, called as a bounded nondeterministic rule, can have on the right hand side only a few decisions. We show that both kinds of rules can be used for improving the quality of classification. In the paper, two lazy classification algorithms of polynomial time complexity are considered. These algorithms are based on deterministic and inhibitory decision rules, but the direct generation of rules is not required. Instead of this, for any new object the considered algorithms extract from a given decision table efficiently some information about the set of rules. Next, this information is used by a decision-making procedure. The reported results of experiments show that the algorithms based on inhibitory decision rules are often better than those based on deterministic decision rules. We also present an application of bounded nondeterministic rules in construction of rule based classifiers. We include the results of experiments showing that by combining rule based classifiers based on minimal decision rules with bounded nondeterministic rules having confidence close to 1 and sufficiently large support, it is possible to improve the classification quality. © 2010 Springer-Verlag.

  14. Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    The two branches of dynamical systems, continuous and discrete, correspond to the study of differential equations (vector fields) and iteration of mappings respectively. In holomorphic dynamics, the systems studied are restricted to those described by holomorphic (complex analytic) functions...... or meromorphic (allowing poles as singularities) functions. There already exists a well-developed theory for iterative holomorphic dynamical systems, and successful relations found between iteration theory and flows of vector fields have been one of the main motivations for the recent interest in holomorphic...... vector fields. Since the class of complex polynomial vector fields in the plane is natural to consider, it is remarkable that its study has only begun very recently. There are numerous fundamental questions that are still open, both in the general classification of these vector fields, the decomposition...

  15. Polynomial methods in combinatorics

    CERN Document Server

    Guth, Larry

    2016-01-01

    This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book. Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accompl...

  16. Polynomial representations of GLn

    CERN Document Server

    Green, James A; Erdmann, Karin

    2007-01-01

    The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

  17. Polynomial representations of GLN

    CERN Document Server

    Green, James A

    1980-01-01

    The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.

  18. Efficient computation of Laguerre polynomials

    NARCIS (Netherlands)

    A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

    2017-01-01

    textabstractAn efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials . Ln(α)(z) are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for . n large and . α small, are used

  19. Optimization over polynomials : Selected topics

    NARCIS (Netherlands)

    Laurent, M.; Jang, Sun Young; Kim, Young Rock; Lee, Dae-Woong; Yie, Ikkwon

    2014-01-01

    Minimizing a polynomial function over a region defined by polynomial inequalities models broad classes of hard problems from combinatorics, geometry and optimization. New algorithmic approaches have emerged recently for computing the global minimum, by combining tools from real algebra (sums of

  20. Height-Deterministic Pushdown Automata

    DEFF Research Database (Denmark)

    Nowotka, Dirk; Srba, Jiri

    2007-01-01

    We define the notion of height-deterministic pushdown automata, a model where for any given input string the stack heights during any (nondeterministic) computation on the input are a priori fixed. Different subclasses of height-deterministic pushdown automata, strictly containing the class...... of regular languages and still closed under boolean language operations, are considered. Several of such language classes have been described in the literature. Here, we suggest a natural and intuitive model that subsumes all the formalisms proposed so far by employing height-deterministic pushdown automata...

  1. Polynomial fuzzy model-based approach for underactuated surface vessels

    DEFF Research Database (Denmark)

    Khooban, Mohammad Hassan; Vafamand, Navid; Dragicevic, Tomislav

    2018-01-01

    The main goal of this study is to introduce a new polynomial fuzzy model-based structure for a class of marine systems with non-linear and polynomial dynamics. The suggested technique relies on a polynomial Takagi–Sugeno (T–S) fuzzy modelling, a polynomial dynamic parallel distributed compensation...... surface vessel (USV). Additionally, in order to overcome the USV control challenges, including the USV un-modelled dynamics, complex nonlinear dynamics, external disturbances and parameter uncertainties, the polynomial fuzzy model representation is adopted. Moreover, the USV-based control structure...... and a sum-of-squares (SOS) decomposition. The new proposed approach is a generalisation of the standard T–S fuzzy models and linear matrix inequality which indicated its effectiveness in decreasing the tracking time and increasing the efficiency of the robust tracking control problem for an underactuated...

  2. Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

    Directory of Open Access Journals (Sweden)

    F. Santonja

    2012-01-01

    Full Text Available Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model.

  3. Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

    Science.gov (United States)

    Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

    2016-08-18

    Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

  4. Deterministic methods in radiation transport

    International Nuclear Information System (INIS)

    Rice, A.F.; Roussin, R.W.

    1992-06-01

    The Seminar on Deterministic Methods in Radiation Transport was held February 4--5, 1992, in Oak Ridge, Tennessee. Eleven presentations were made and the full papers are published in this report, along with three that were submitted but not given orally. These papers represent a good overview of the state of the art in the deterministic solution of radiation transport problems for a variety of applications of current interest to the Radiation Shielding Information Center user community

  5. On generalized Fibonacci and Lucas polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Nalli, Ayse [Department of Mathematics, Faculty of Sciences, Selcuk University, 42075 Campus-Konya (Turkey)], E-mail: aysenalli@yahoo.com; Haukkanen, Pentti [Department of Mathematics, Statistics and Philosophy, 33014 University of Tampere (Finland)], E-mail: mapehau@uta.fi

    2009-12-15

    Let h(x) be a polynomial with real coefficients. We introduce h(x)-Fibonacci polynomials that generalize both Catalan's Fibonacci polynomials and Byrd's Fibonacci polynomials and also the k-Fibonacci numbers, and we provide properties for these h(x)-Fibonacci polynomials. We also introduce h(x)-Lucas polynomials that generalize the Lucas polynomials and present properties of these polynomials. In the last section we introduce the matrix Q{sub h}(x) that generalizes the Q-matrix whose powers generate the Fibonacci numbers.

  6. Parallel Construction of Irreducible Polynomials

    DEFF Research Database (Denmark)

    Frandsen, Gudmund Skovbjerg

    Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....

  7. Orthogonal polynomials in transport theories

    International Nuclear Information System (INIS)

    Dehesa, J.S.

    1981-01-01

    The asymptotical (k→infinity) behaviour of zeros of the polynomials gsub(k)sup((m)(ν)) encountered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude antiwsub(k) of the kth Legendre polynomial needed in the expansion of the scattering function. The parameters antiwsub(k) describe the anisotropy of scattering of the medium considered. In particular, it is shown that the asymptotical density of zeros of the polynomials gsub(k)sup(m)(ν) is an inverted semicircle for the anisotropic non-multiplying scattering medium

  8. Deterministic Automata for Unordered Trees

    Directory of Open Access Journals (Sweden)

    Adrien Boiret

    2014-08-01

    Full Text Available Automata for unordered unranked trees are relevant for defining schemas and queries for data trees in Json or Xml format. While the existing notions are well-investigated concerning expressiveness, they all lack a proper notion of determinism, which makes it difficult to distinguish subclasses of automata for which problems such as inclusion, equivalence, and minimization can be solved efficiently. In this paper, we propose and investigate different notions of "horizontal determinism", starting from automata for unranked trees in which the horizontal evaluation is performed by finite state automata. We show that a restriction to confluent horizontal evaluation leads to polynomial-time emptiness and universality, but still suffers from coNP-completeness of the emptiness of binary intersections. Finally, efficient algorithms can be obtained by imposing an order of horizontal evaluation globally for all automata in the class. Depending on the choice of the order, we obtain different classes of automata, each of which has the same expressiveness as CMso.

  9. Piecewise deterministic processes in biological models

    CERN Document Server

    Rudnicki, Ryszard

    2017-01-01

    This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...

  10. Dynamic optimization deterministic and stochastic models

    CERN Document Server

    Hinderer, Karl; Stieglitz, Michael

    2016-01-01

    This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.

  11. Chaotic time series. Part II. System Identification and Prediction

    Directory of Open Access Journals (Sweden)

    Bjørn Lillekjendlie

    1994-10-01

    Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.

  12. Julia Sets of Orthogonal Polynomials

    DEFF Research Database (Denmark)

    Christiansen, Jacob Stordal; Henriksen, Christian; Petersen, Henrik Laurberg

    2018-01-01

    For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials fPng to properties of the support. More precisely we relate the Julia set of Pn to the outer boundary of the support, the lled Julia...... set to the polynomial convex hull K of the support, and the Green's function associated with Pn to the Green's function for the complement of K....

  13. An introduction to orthogonal polynomials

    CERN Document Server

    Chihara, Theodore S

    1978-01-01

    Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some

  14. Scattering theory and orthogonal polynomials

    International Nuclear Information System (INIS)

    Geronimo, J.S.

    1977-01-01

    The application of the techniques of scattering theory to the study of polynomials orthogonal on the unit circle and a finite segment of the real line is considered. The starting point is the recurrence relations satisfied by the polynomials instead of the orthogonality condition. A set of two two terms recurrence relations for polynomials orthogonal on the real line is presented and used. These recurrence relations play roles analogous to those satisfied by polynomials orthogonal on unit circle. With these recurrence formulas a Wronskian theorem is proved and the Christoffel-Darboux formula is derived. In scattering theory a fundamental role is played by the Jost function. An analogy is deferred of this function and its analytic properties and the locations of its zeros investigated. The role of the analog Jost function in various properties of these orthogonal polynomials is investigated. The techniques of inverse scattering theory are also used. The discrete analogues of the Gelfand-Levitan and Marchenko equations are derived and solved. These techniques are used to calculate asymptotic formulas for the orthogonal polynomials. Finally Szego's theorem on toeplitz and Hankel determinants is proved using the recurrence formulas and some properties of the Jost function. The techniques of inverse scattering theory are used to calculate the correction terms

  15. On factorization of generalized Macdonald polynomials

    International Nuclear Information System (INIS)

    Kononov, Ya.; Morozov, A.

    2016-01-01

    A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W ∞ - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U q (SL N ) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

  16. Deterministic analyses of severe accident issues

    International Nuclear Information System (INIS)

    Dua, S.S.; Moody, F.J.; Muralidharan, R.; Claassen, L.B.

    2004-01-01

    Severe accidents in light water reactors involve complex physical phenomena. In the past there has been a heavy reliance on simple assumptions regarding physical phenomena alongside of probability methods to evaluate risks associated with severe accidents. Recently GE has developed realistic methodologies that permit deterministic evaluations of severe accident progression and of some of the associated phenomena in the case of Boiling Water Reactors (BWRs). These deterministic analyses indicate that with appropriate system modifications, and operator actions, core damage can be prevented in most cases. Furthermore, in cases where core-melt is postulated, containment failure can either be prevented or significantly delayed to allow sufficient time for recovery actions to mitigate severe accidents

  17. Bannai-Ito polynomials and dressing chains

    OpenAIRE

    Derevyagin, Maxim; Tsujimoto, Satoshi; Vinet, Luc; Zhedanov, Alexei

    2012-01-01

    Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by quadratic algebras. The Bannai-Ito polynomials and their kernel polynomials -- the complementary Bannai-Ito polynomials -- are shown to arise in the framework of the SDG maps.

  18. Birth-death processes and associated polynomials

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2003-01-01

    We consider birth-death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth-death polynomials. The sequence of associated polynomials linked with a sequence of birth-death polynomials and its orthogonalizing measure can be used in the analysis

  19. Classifying polynomials and identity testing

    Indian Academy of Sciences (India)

    years, progress has been made in designing deterministic algorithms for restricted ... Research supported by J C Bose Fellowship ...... This method fails if T1 happens to have repeated ..... formulas, maximal-partition discrepancy and mixed-.

  20. On Multiple Polynomials of Capelli Type

    Directory of Open Access Journals (Sweden)

    S.Y. Antonov

    2016-03-01

    Full Text Available This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.

  1. An overview on polynomial approximation of NP-hard problems

    Directory of Open Access Journals (Sweden)

    Paschos Vangelis Th.

    2009-01-01

    Full Text Available The fact that polynomial time algorithm is very unlikely to be devised for an optimal solving of the NP-hard problems strongly motivates both the researchers and the practitioners to try to solve such problems heuristically, by making a trade-off between computational time and solution's quality. In other words, heuristic computation consists of trying to find not the best solution but one solution which is 'close to' the optimal one in reasonable time. Among the classes of heuristic methods for NP-hard problems, the polynomial approximation algorithms aim at solving a given NP-hard problem in poly-nomial time by computing feasible solutions that are, under some predefined criterion, as near to the optimal ones as possible. The polynomial approximation theory deals with the study of such algorithms. This survey first presents and analyzes time approximation algorithms for some classical examples of NP-hard problems. Secondly, it shows how classical notions and tools of complexity theory, such as polynomial reductions, can be matched with polynomial approximation in order to devise structural results for NP-hard optimization problems. Finally, it presents a quick description of what is commonly called inapproximability results. Such results provide limits on the approximability of the problems tackled.

  2. Linear precoding based on polynomial expansion: reducing complexity in massive MIMO

    KAUST Repository

    Mueller, Axel; Kammoun, Abla; Bjö rnson, Emil; Debbah, Mé rouane

    2016-01-01

    By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.

  3. Large level crossings of a random polynomial

    Directory of Open Access Journals (Sweden)

    Kambiz Farahmand

    1987-01-01

    Full Text Available We know the expected number of times that a polynomial of degree n with independent random real coefficients asymptotically crosses the level K, when K is any real value such that (K2/n→0 as n→∞. The present paper shows that, when K is allowed to be large, this expected number of crossings reduces to only one. The coefficients of the polynomial are assumed to be normally distributed. It is shown that it is sufficient to let K≥exp(nf where f is any function of n such that f→∞ as n→∞.

  4. A Polynomial Estimate of Railway Line Delay

    DEFF Research Database (Denmark)

    Cerreto, Fabrizio; Harrod, Steven; Nielsen, Otto Anker

    2017-01-01

    Railway service may be measured by the aggregate delay over a time horizon or due to an event. Timetables for railway service may dampen aggregate delay by addition of additional process time, either supplement time or buffer time. The evaluation of these variables has previously been performed...... by numerical analysis with simulation. This paper proposes an analytical estimate of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. Analysis of the function demonstrates that there should be a balance between the two...

  5. Vanishing of Littlewood-Richardson polynomials is in P

    OpenAIRE

    Adve, Anshul; Robichaux, Colleen; Yong, Alexander

    2017-01-01

    J. DeLoera-T. McAllister and K. D. Mulmuley-H. Narayanan-M. Sohoni independently proved that determining the vanishing of Littlewood-Richardson coefficients has strongly polynomial time computational complexity. Viewing these as Schubert calculus numbers, we prove the generalization to the Littlewood-Richardson polynomials that control equivariant cohomology of Grassmannians. We construct a polytope using the edge-labeled tableau rule of H. Thomas-A. Yong. Our proof then combines a saturation...

  6. Chromatic polynomials of random graphs

    International Nuclear Information System (INIS)

    Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian

    2010-01-01

    Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.

  7. Cosmographic analysis with Chebyshev polynomials

    Science.gov (United States)

    Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

    2018-05-01

    The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

  8. Nonlinear Markov processes: Deterministic case

    International Nuclear Information System (INIS)

    Frank, T.D.

    2008-01-01

    Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution

  9. Exploiting deterministic maintenance opportunity windows created by conservative engineering design rules that result in free time locked into large high-speed coupled production lines with finite buffers

    Directory of Open Access Journals (Sweden)

    Durandt, Casper

    2016-08-01

    Full Text Available Conservative engineering design rules for large serial coupled production processes result in machines having locked-in free time (also called ‘critical downtime’ or ‘maintenance opportunity windows’, which cause idle time if not used. Operators are not able to assess a large production process holistically, and so may not be aware that they form the current bottleneck – or that they have free time available due to interruptions elsewhere. A real-time method is developed to accurately calculate and display free time in location and magnitude, and efficiency improvements are demonstrated in large-scale production runs.

  10. Deterministic Echo State Networks Based Stock Price Forecasting

    Directory of Open Access Journals (Sweden)

    Jingpei Dan

    2014-01-01

    Full Text Available Echo state networks (ESNs, as efficient and powerful computational models for approximating nonlinear dynamical systems, have been successfully applied in financial time series forecasting. Reservoir constructions in standard ESNs rely on trials and errors in real applications due to a series of randomized model building stages. A novel form of ESN with deterministically constructed reservoir is competitive with standard ESN by minimal complexity and possibility of optimizations for ESN specifications. In this paper, forecasting performances of deterministic ESNs are investigated in stock price prediction applications. The experiment results on two benchmark datasets (Shanghai Composite Index and S&P500 demonstrate that deterministic ESNs outperform standard ESN in both accuracy and efficiency, which indicate the prospect of deterministic ESNs for financial prediction.

  11. Polynomial weights and code constructions

    DEFF Research Database (Denmark)

    Massey, J; Costello, D; Justesen, Jørn

    1973-01-01

    polynomial included. This fundamental property is then used as the key to a variety of code constructions including 1) a simplified derivation of the binary Reed-Muller codes and, for any primepgreater than 2, a new extensive class ofp-ary "Reed-Muller codes," 2) a new class of "repeated-root" cyclic codes...... of long constraint length binary convolutional codes derived from2^r-ary Reed-Solomon codes, and 6) a new class ofq-ary "repeated-root" constacyclic codes with an algebraic decoding algorithm.......For any nonzero elementcof a general finite fieldGF(q), it is shown that the polynomials(x - c)^i, i = 0,1,2,cdots, have the "weight-retaining" property that any linear combination of these polynomials with coefficients inGF(q)has Hamming weight at least as great as that of the minimum degree...

  12. Orthogonal Polynomials and Special Functions

    CERN Document Server

    Assche, Walter

    2003-01-01

    The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

  13. Diffusion in Deterministic Interacting Lattice Systems

    Science.gov (United States)

    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.

  14. Need for higher order polynomial basis for polynomial nodal methods employed in LWR calculations

    International Nuclear Information System (INIS)

    Taiwo, T.A.; Palmiotti, G.

    1997-01-01

    The paper evaluates the accuracy and efficiency of sixth order polynomial solutions and the use of one radial node per core assembly for pressurized water reactor (PWR) core power distributions and reactivities. The computer code VARIANT was modified to calculate sixth order polynomial solutions for a hot zero power benchmark problem in which a control assembly along a core axis is assumed to be out of the core. Results are presented for the VARIANT, DIF3D-NODAL, and DIF3D-finite difference codes. The VARIANT results indicate that second order expansion of the within-node source and linear representation of the node surface currents are adequate for this problem. The results also demonstrate the improvement in the VARIANT solution when the order of the polynomial expansion of the within-node flux is increased from fourth to sixth order. There is a substantial saving in computational time for using one radial node per assembly with the sixth order expansion compared to using four or more nodes per assembly and fourth order polynomial solutions. 11 refs., 1 tab

  15. Symmetric functions and orthogonal polynomials

    CERN Document Server

    Macdonald, I G

    1997-01-01

    One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

  16. Deterministic extraction from weak random sources

    CERN Document Server

    Gabizon, Ariel

    2011-01-01

    In this research monograph, the author constructs deterministic extractors for several types of sources, using a methodology of recycling randomness which enables increasing the output length of deterministic extractors to near optimal length.

  17. Deterministic chaos in the pitting phenomena of passivable alloys

    International Nuclear Information System (INIS)

    Hoerle, Stephane

    1998-01-01

    It was shown that electrochemical noise recorded in stable pitting conditions exhibits deterministic (even chaotic) features. The occurrence of deterministic behaviors depend on the material/solution severity. Thus, electrolyte composition ([Cl - ]/[NO 3 - ] ratio, pH), passive film thickness or alloy composition can change the deterministic features. Only one pit is sufficient to observe deterministic behaviors. The electrochemical noise signals are non-stationary, which is a hint of a change with time in the pit behavior (propagation speed or mean). Modifications of electrolyte composition reveals transitions between random and deterministic behaviors. Spontaneous transitions between deterministic behaviors of different features (bifurcation) are also evidenced. Such bifurcations enlighten various routes to chaos. The routes to chaos and the features of chaotic signals allow to suggest the modeling (continuous and discontinuous models are proposed) of the electrochemical mechanisms inside a pit, that describe quite well the experimental behaviors and the effect of the various parameters. The analysis of the chaotic behaviors of a pit leads to a better understanding of propagation mechanisms and give tools for pit monitoring. (author) [fr

  18. Deterministic hydrodynamics: Taking blood apart

    Science.gov (United States)

    Davis, John A.; Inglis, David W.; Morton, Keith J.; Lawrence, David A.; Huang, Lotien R.; Chou, Stephen Y.; Sturm, James C.; Austin, Robert H.

    2006-10-01

    We show the fractionation of whole blood components and isolation of blood plasma with no dilution by using a continuous-flow deterministic array that separates blood components by their hydrodynamic size, independent of their mass. We use the technology we developed of deterministic arrays which separate white blood cells, red blood cells, and platelets from blood plasma at flow velocities of 1,000 μm/sec and volume rates up to 1 μl/min. We verified by flow cytometry that an array using focused injection removed 100% of the lymphocytes and monocytes from the main red blood cell and platelet stream. Using a second design, we demonstrated the separation of blood plasma from the blood cells (white, red, and platelets) with virtually no dilution of the plasma and no cellular contamination of the plasma. cells | plasma | separation | microfabrication

  19. STABILITY SYSTEMS VIA HURWITZ POLYNOMIALS

    Directory of Open Access Journals (Sweden)

    BALTAZAR AGUIRRE HERNÁNDEZ

    2017-01-01

    Full Text Available To analyze the stability of a linear system of differential equations  ẋ = Ax we can study the location of the roots of the characteristic polynomial pA(t associated with the matrix A. We present various criteria - algebraic and geometric - that help us to determine where the roots are located without calculating them directly.

  20. On Modular Counting with Polynomials

    DEFF Research Database (Denmark)

    Hansen, Kristoffer Arnsfelt

    2006-01-01

    For any integers m and l, where m has r sufficiently large (depending on l) factors, that are powers of r distinct primes, we give a construction of a (symmetric) polynomial over Z_m of degree O(\\sqrt n) that is a generalized representation (commonly also called weak representation) of the MODl f...

  1. Global Polynomial Kernel Hazard Estimation

    DEFF Research Database (Denmark)

    Hiabu, Munir; Miranda, Maria Dolores Martínez; Nielsen, Jens Perch

    2015-01-01

    This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically redu...

  2. Congruences concerning Legendre polynomials III

    OpenAIRE

    Sun, Zhi-Hong

    2010-01-01

    Let $p>3$ be a prime, and let $R_p$ be the set of rational numbers whose denominator is coprime to $p$. Let $\\{P_n(x)\\}$ be the Legendre polynomials. In this paper we mainly show that for $m,n,t\\in R_p$ with $m\

  3. Two polynomial division inequalities in

    Directory of Open Access Journals (Sweden)

    Goetgheluck P

    1998-01-01

    Full Text Available This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.

  4. Dirichlet polynomials, majorization, and trumping

    International Nuclear Information System (INIS)

    Pereira, Rajesh; Plosker, Sarah

    2013-01-01

    Majorization and trumping are two partial orders which have proved useful in quantum information theory. We show some relations between these two partial orders and generalized Dirichlet polynomials, Mellin transforms, and completely monotone functions. These relations are used to prove a succinct generalization of Turgut’s characterization of trumping. (paper)

  5. The modified Gauss diagonalization of polynomial matrices

    International Nuclear Information System (INIS)

    Saeed, K.

    1982-10-01

    The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

  6. Sheffer and Non-Sheffer Polynomial Families

    Directory of Open Access Journals (Sweden)

    G. Dattoli

    2012-01-01

    Full Text Available By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.

  7. The finite Fourier transform of classical polynomials

    OpenAIRE

    Dixit, Atul; Jiu, Lin; Moll, Victor H.; Vignat, Christophe

    2014-01-01

    The finite Fourier transform of a family of orthogonal polynomials $A_{n}(x)$, is the usual transform of the polynomial extended by $0$ outside their natural domain. Explicit expressions are given for the Legendre, Jacobi, Gegenbauer and Chebyshev families.

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

    Science.gov (United States)

    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

  9. A Summation Formula for Macdonald Polynomials

    Science.gov (United States)

    de Gier, Jan; Wheeler, Michael

    2016-03-01

    We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.

  10. A New Generalisation of Macdonald Polynomials

    Science.gov (United States)

    Garbali, Alexandr; de Gier, Jan; Wheeler, Michael

    2017-06-01

    We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters ( q, t) and polynomial in a further two parameters ( u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.

  11. Degeneracy of time series models: The best model is not always the correct model

    International Nuclear Information System (INIS)

    Judd, Kevin; Nakamura, Tomomichi

    2006-01-01

    There are a number of good techniques for finding, in some sense, the best model of a deterministic system given a time series of observations. We examine a problem called model degeneracy, which has the consequence that even when a perfect model of a system exists, one does not find it using the best techniques currently available. The problem is illustrated using global polynomial models and the theory of Groebner bases

  12. Associated polynomials and birth-death processes

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2001-01-01

    We consider sequences of orthogonal polynomials with positive zeros, and pursue the question of how (partial) knowledge of the orthogonalizing measure for the {\\it associated polynomials} can lead to information about the orthogonalizing measure for the original polynomials, with a view to

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

    Science.gov (United States)

    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.

  14. Deterministic prediction of surface wind speed variations

    Directory of Open Access Journals (Sweden)

    G. V. Drisya

    2014-11-01

    Full Text Available Accurate prediction of wind speed is an important aspect of various tasks related to wind energy management such as wind turbine predictive control and wind power scheduling. The most typical characteristic of wind speed data is its persistent temporal variations. Most of the techniques reported in the literature for prediction of wind speed and power are based on statistical methods or probabilistic distribution of wind speed data. In this paper we demonstrate that deterministic forecasting methods can make accurate short-term predictions of wind speed using past data, at locations where the wind dynamics exhibit chaotic behaviour. The predictions are remarkably accurate up to 1 h with a normalised RMSE (root mean square error of less than 0.02 and reasonably accurate up to 3 h with an error of less than 0.06. Repeated application of these methods at 234 different geographical locations for predicting wind speeds at 30-day intervals for 3 years reveals that the accuracy of prediction is more or less the same across all locations and time periods. Comparison of the results with f-ARIMA model predictions shows that the deterministic models with suitable parameters are capable of returning improved prediction accuracy and capturing the dynamical variations of the actual time series more faithfully. These methods are simple and computationally efficient and require only records of past data for making short-term wind speed forecasts within practically tolerable margin of errors.

  15. Quantum entanglement via nilpotent polynomials

    International Nuclear Information System (INIS)

    Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, Lorenza

    2006-01-01

    We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed

  16. Multivariate Local Polynomial Regression with Application to Shenzhen Component Index

    Directory of Open Access Journals (Sweden)

    Liyun Su

    2011-01-01

    Full Text Available This study attempts to characterize and predict stock index series in Shenzhen stock market using the concepts of multivariate local polynomial regression. Based on nonlinearity and chaos of the stock index time series, multivariate local polynomial prediction methods and univariate local polynomial prediction method, all of which use the concept of phase space reconstruction according to Takens' Theorem, are considered. To fit the stock index series, the single series changes into bivariate series. To evaluate the results, the multivariate predictor for bivariate time series based on multivariate local polynomial model is compared with univariate predictor with the same Shenzhen stock index data. The numerical results obtained by Shenzhen component index show that the prediction mean squared error of the multivariate predictor is much smaller than the univariate one and is much better than the existed three methods. Even if the last half of the training data are used in the multivariate predictor, the prediction mean squared error is smaller than the univariate predictor. Multivariate local polynomial prediction model for nonsingle time series is a useful tool for stock market price prediction.

  17. Special polynomials associated with some hierarchies

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2008-01-01

    Special polynomials associated with rational solutions of a hierarchy of equations of Painleve type are introduced. The hierarchy arises by similarity reduction from the Fordy-Gibbons hierarchy of partial differential equations. Some relations for these special polynomials are given. Differential-difference hierarchies for finding special polynomials are presented. These formulae allow us to obtain special polynomials associated with the hierarchy studied. It is shown that rational solutions of members of the Schwarz-Sawada-Kotera, the Schwarz-Kaup-Kupershmidt, the Fordy-Gibbons, the Sawada-Kotera and the Kaup-Kupershmidt hierarchies can be expressed through special polynomials of the hierarchy studied

  18. Space complexity in polynomial calculus

    Czech Academy of Sciences Publication Activity Database

    Filmus, Y.; Lauria, M.; Nordström, J.; Ron-Zewi, N.; Thapen, Neil

    2015-01-01

    Roč. 44, č. 4 (2015), s. 1119-1153 ISSN 0097-5397 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : proof complexity * polynomial calculus * lower bounds Subject RIV: BA - General Mathematics Impact factor: 0.841, year: 2015 http://epubs.siam.org/doi/10.1137/120895950

  19. Codimensions of generalized polynomial identities

    International Nuclear Information System (INIS)

    Gordienko, Aleksei S

    2010-01-01

    It is proved that for every finite-dimensional associative algebra A over a field of characteristic zero there are numbers C element of Q + and t element of Z + such that gc n (A)∼Cn t d n as n→∞, where d=PI exp(A) element of Z + . Thus, Amitsur's and Regev's conjectures hold for the codimensions gc n (A) of the generalized polynomial identities. Bibliography: 6 titles.

  20. A deterministic width function model

    Directory of Open Access Journals (Sweden)

    C. E. Puente

    2003-01-01

    Full Text Available Use of a deterministic fractal-multifractal (FM geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States, that the FM approach may also be used to closely approximate existing width functions.

  1. Stable piecewise polynomial vector fields

    Directory of Open Access Journals (Sweden)

    Claudio Pessoa

    2012-09-01

    Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.

  2. Deterministic Predictions of Vessel Responses Based on Past Measurements

    DEFF Research Database (Denmark)

    Nielsen, Ulrik Dam; Jensen, Jørgen Juncher

    2017-01-01

    The paper deals with a prediction procedure from which global wave-induced responses can be deterministically predicted a short time, 10-50 s, ahead of current time. The procedure relies on the autocorrelation function and takes into account prior measurements only; i.e. knowledge about wave...

  3. Safety margins in deterministic safety analysis

    International Nuclear Information System (INIS)

    Viktorov, A.

    2011-01-01

    The concept of safety margins has acquired certain prominence in the attempts to demonstrate quantitatively the level of the nuclear power plant safety by means of deterministic analysis, especially when considering impacts from plant ageing and discovery issues. A number of international or industry publications exist that discuss various applications and interpretations of safety margins. The objective of this presentation is to bring together and examine in some detail, from the regulatory point of view, the safety margins that relate to deterministic safety analysis. In this paper, definitions of various safety margins are presented and discussed along with the regulatory expectations for them. Interrelationships of analysis input and output parameters with corresponding limits are explored. It is shown that the overall safety margin is composed of several components each having different origins and potential uses; in particular, margins associated with analysis output parameters are contrasted with margins linked to the analysis input. While these are separate, it is possible to influence output margins through the analysis input, and analysis method. Preserving safety margins is tantamount to maintaining safety. At the same time, efficiency of operation requires optimization of safety margins taking into account various technical and regulatory considerations. For this, basic definitions and rules for safety margins must be first established. (author)

  4. A mathematical theory for deterministic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Hooft, Gerard ' t [Institute for Theoretical Physics, Utrecht University (Netherlands); Spinoza Institute, Postbox 80.195, 3508 TD Utrecht (Netherlands)

    2007-05-15

    Classical, i.e. deterministic theories underlying quantum mechanics are considered, and it is shown how an apparent quantum mechanical Hamiltonian can be defined in such theories, being the operator that generates evolution in time. It includes various types of interactions. An explanation must be found for the fact that, in the real world, this Hamiltonian is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.

  5. A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

    Science.gov (United States)

    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.

  6. Fractional order differentiation by integration with Jacobi polynomials

    KAUST Repository

    Liu, Dayan

    2012-12-01

    The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

  7. Fractional order differentiation by integration with Jacobi polynomials

    KAUST Repository

    Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem

    2012-01-01

    The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

  8. a Unified Matrix Polynomial Approach to Modal Identification

    Science.gov (United States)

    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.

  9. On factorization of generalized Macdonald polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Kononov, Ya. [Landau Institute for Theoretical Physics, Chernogolovka (Russian Federation); HSE, Math Department, Moscow (Russian Federation); Morozov, A. [ITEP, Moscow (Russian Federation); Institute for Information Transmission Problems, Moscow (Russian Federation); National Research Nuclear University MEPhI, Moscow (Russian Federation)

    2016-08-15

    A remarkable feature of Schur functions - the common eigenfunctions of cut-and-join operators from W{sub ∞} - is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U{sub q}(SL{sub N}) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization - on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding. (orig.)

  10. On factorization of generalized Macdonald polynomials

    Science.gov (United States)

    Kononov, Ya.; Morozov, A.

    2016-08-01

    A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.

  11. Application of grafted polynomial function in forecasting cotton ...

    African Journals Online (AJOL)

    A study was conducted to forecast cotton production trend with the application of a grafted polynomial function in Nigeria from 1985 through 2013. Grafted models are used in econometrics to embark on economic analysis involving time series. In economic time series, the paucity of data and their availability has always ...

  12. Deterministic Diffusion in Delayed Coupled Maps

    International Nuclear Information System (INIS)

    Sozanski, M.

    2005-01-01

    Coupled Map Lattices (CML) are discrete time and discrete space dynamical systems used for modeling phenomena arising in nonlinear systems with many degrees of freedom. In this work, the dynamical and statistical properties of a modified version of the CML with global coupling are considered. The main modification of the model is the extension of the coupling over a set of local map states corresponding to different time iterations. The model with both stochastic and chaotic one-dimensional local maps is studied. Deterministic diffusion in the CML under variation of a control parameter is analyzed for unimodal maps. As a main result, simple relations between statistical and dynamical measures are found for the model and the cases where substituting nonlinear lattices with simpler processes is possible are presented. (author)

  13. Integrated Deterministic-Probabilistic Safety Assessment Methodologies

    Energy Technology Data Exchange (ETDEWEB)

    Kudinov, P.; Vorobyev, Y.; Sanchez-Perea, M.; Queral, C.; Jimenez Varas, G.; Rebollo, M. J.; Mena, L.; Gomez-Magin, J.

    2014-02-01

    IDPSA (Integrated Deterministic-Probabilistic Safety Assessment) is a family of methods which use tightly coupled probabilistic and deterministic approaches to address respective sources of uncertainties, enabling Risk informed decision making in a consistent manner. The starting point of the IDPSA framework is that safety justification must be based on the coupling of deterministic (consequences) and probabilistic (frequency) considerations to address the mutual interactions between stochastic disturbances (e.g. failures of the equipment, human actions, stochastic physical phenomena) and deterministic response of the plant (i.e. transients). This paper gives a general overview of some IDPSA methods as well as some possible applications to PWR safety analyses. (Author)

  14. Deterministic and stochastic CTMC models from Zika disease transmission

    Science.gov (United States)

    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.

  15. Deterministic and efficient quantum cryptography based on Bell's theorem

    International Nuclear Information System (INIS)

    Chen Zengbing; Pan Jianwei; Zhang Qiang; Bao Xiaohui; Schmiedmayer, Joerg

    2006-01-01

    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

  16. Algebraic polynomials with random coefficients

    Directory of Open Access Journals (Sweden)

    K. Farahmand

    2002-01-01

    Full Text Available This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω+a1(ω(n11/2x+a2(ω(n21/2x2+…an(ω(nn1/2xn when n is large. The coefficients {aj(w}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr. A special case of dependent coefficients is also studied.

  17. Fourier series and orthogonal polynomials

    CERN Document Server

    Jackson, Dunham

    2004-01-01

    This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is followe

  18. Killings, duality and characteristic polynomials

    Science.gov (United States)

    Álvarez, Enrique; Borlaf, Javier; León, José H.

    1998-03-01

    In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998

  19. Introduction to Real Orthogonal Polynomials

    Science.gov (United States)

    1992-06-01

    uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC

  20. Local polynomial Whittle estimation of perturbed fractional processes

    DEFF Research Database (Denmark)

    Frederiksen, Per; Nielsen, Frank; Nielsen, Morten Ørregaard

    We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the spectrum of the perturbation as well as that of the short-memory component...... of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal...... for d ε (0, 3/4), and if the spectral density is infinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well in the presence of a serially correlated perturbation term...

  1. Synchronization of generalized Henon map using polynomial controller

    International Nuclear Information System (INIS)

    Lam, H.K.

    2010-01-01

    This Letter presents the chaos synchronization of two discrete-time generalized Henon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.

  2. A companion matrix for 2-D polynomials

    International Nuclear Information System (INIS)

    Boudellioua, M.S.

    1995-08-01

    In this paper, a matrix form analogous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of 2-D linear systems theory. Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form. (author). 6 refs

  3. On polynomial solutions of the Heun equation

    International Nuclear Information System (INIS)

    Gurappa, N; Panigrahi, Prasanta K

    2004-01-01

    By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

  4. A new Arnoldi approach for polynomial eigenproblems

    Energy Technology Data Exchange (ETDEWEB)

    Raeven, F.A.

    1996-12-31

    In this paper we introduce a new generalization of the method of Arnoldi for matrix polynomials. The new approach is compared with the approach of rewriting the polynomial problem into a linear eigenproblem and applying the standard method of Arnoldi to the linearised problem. The algorithm that can be applied directly to the polynomial eigenproblem turns out to be more efficient, both in storage and in computation.

  5. Deterministic Chaos - Complex Chance out of Simple Necessity ...

    Indian Academy of Sciences (India)

    This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...

  6. Simulation of photonic waveguides with deterministic aperiodic nanostructures for biosensing

    DEFF Research Database (Denmark)

    Neustock, Lars Thorben; Paulsen, Moritz; Jahns, Sabrina

    2016-01-01

    Photonic waveguides with deterministic aperiodic corrugations offer rich spectral characteristics under surface-normal illumination. The finite-element method (FEM), the finite-difference time-domain (FDTD) method and a rigorous coupled wave algorithm (RCWA) are compared for computing the near...

  7. Polynomial Approximation Algorithms for the TSP and the QAP with a Factorial Domination Number

    DEFF Research Database (Denmark)

    Gutin, Gregory; Yeo, Anders

    2002-01-01

    Glover and Punnen (J. Oper. Res. Soc. 48 (1997) 502) asked whether there exists a polynomial time algorithm that always produces a tour which is not worse than at least n!/p(n) tours for some polynomial p(n) for every TSP instance on n cities. They conjectured that, unless P = NP, the answer to t...

  8. Primality deterministic and primality probabilistic tests

    Directory of Open Access Journals (Sweden)

    Alfredo Rizzi

    2007-10-01

    Full Text Available In this paper the A. comments the importance of prime numbers in mathematics and in cryptography. He remembers the very important researches of Eulero, Fermat, Legen-re, Rieman and others scholarships. There are many expressions that give prime numbers. Between them Mersenne’s primes have interesting properties. There are also many conjectures that still have to be demonstrated or rejected. The primality deterministic tests are the algorithms that permit to establish if a number is prime or not. There are not applicable in many practical situations, for instance in public key cryptography, because the computer time would be very long. The primality probabilistic tests consent to verify the null hypothesis: the number is prime. In the paper there are comments about the most important statistical tests.

  9. Bayer Demosaicking with Polynomial Interpolation.

    Science.gov (United States)

    Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil

    2016-08-30

    Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.

  10. Fermionic formula for double Kostka polynomials

    OpenAIRE

    Liu, Shiyuan

    2016-01-01

    The $X=M$ conjecture asserts that the $1D$ sum and the fermionic formula coincide up to some constant power. In the case of type $A,$ both the $1D$ sum and the fermionic formula are closely related to Kostka polynomials. Double Kostka polynomials $K_{\\Bla,\\Bmu}(t),$ indexed by two double partitions $\\Bla,\\Bmu,$ are polynomials in $t$ introduced as a generalization of Kostka polynomials. In the present paper, we consider $K_{\\Bla,\\Bmu}(t)$ in the special case where $\\Bmu=(-,\\mu'').$ We formula...

  11. Polynomial sequences generated by infinite Hessenberg matrices

    Directory of Open Access Journals (Sweden)

    Verde-Star Luis

    2017-01-01

    Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

  12. on the performance of Autoregressive Moving Average Polynomial

    African Journals Online (AJOL)

    Timothy Ademakinwa

    estimated using least squares and Newton Raphson iterative methods. To determine the order of the ... r is the degree of polynomial while j is the number of lag of the ..... use a real time series dataset, monthly rainfall and temperature series ...

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

    Energy Technology Data Exchange (ETDEWEB)

    Graham, Emily B. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA; Crump, Alex R. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA; Resch, Charles T. [Geochemistry Department, Pacific Northwest National Laboratory, Richland WA USA; Fansler, Sarah [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA; Arntzen, Evan [Environmental Compliance and Emergency Preparation, Pacific Northwest National Laboratory, Richland WA USA; Kennedy, David W. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA; Fredrickson, Jim K. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA; Stegen, James C. [Biological Sciences Division, Pacific Northwest National Laboratory, Richland WA USA

    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. 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.

  14. Advances in sequential data assimilation and numerical weather forecasting: An Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic ensemble square root filters, and a test of a new time stepping scheme in an atmospheric model

    Science.gov (United States)

    Amezcua, Javier

    This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn't represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion

  15. Stochastic Simulation of Integrated Circuits with Nonlinear Black-Box Components via Augmented Deterministic Equivalents

    Directory of Open Access Journals (Sweden)

    MANFREDI, P.

    2014-11-01

    Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.

  16. Polynomials formalism of quantum numbers

    International Nuclear Information System (INIS)

    Kazakov, K.V.

    2005-01-01

    Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

  17. Polynomial solutions of nonlinear integral equations

    International Nuclear Information System (INIS)

    Dominici, Diego

    2009-01-01

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials

  18. Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

    African Journals Online (AJOL)

    Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

  19. Topological string partition functions as polynomials

    International Nuclear Information System (INIS)

    Yamaguchi, Satoshi; Yau Shingtung

    2004-01-01

    We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one can be expressed as polynomials of five generators. We also compute the explicit polynomial forms of the partition functions for genus 2, 3, and 4. Moreover, some coefficients are written down for all genus. (author)

  20. Polynomial solutions of nonlinear integral equations

    Energy Technology Data Exchange (ETDEWEB)

    Dominici, Diego [Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443 (United States)], E-mail: dominicd@newpaltz.edu

    2009-05-22

    We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.

  1. A generalization of the Bernoulli polynomials

    Directory of Open Access Journals (Sweden)

    Pierpaolo Natalini

    2003-01-01

    Full Text Available A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by means of the factorization method introduced by Infeld and Hull (1951.

  2. The Bessel polynomials and their differential operators

    International Nuclear Information System (INIS)

    Onyango Otieno, V.P.

    1987-10-01

    Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs

  3. Large degree asymptotics of generalized Bessel polynomials

    NARCIS (Netherlands)

    J.L. López; N.M. Temme (Nico)

    2011-01-01

    textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the

  4. Exceptional polynomials and SUSY quantum mechanics

    Indian Academy of Sciences (India)

    Abstract. We show that for the quantum mechanical problem which admit classical Laguerre/. Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional. Laguerre/Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the ...

  5. Connections between the matching and chromatic polynomials

    Directory of Open Access Journals (Sweden)

    E. J. Farrell

    1992-01-01

    Full Text Available The main results established are (i a connection between the matching and chromatic polynomials and (ii a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.

  6. Laguerre polynomials by a harmonic oscillator

    Science.gov (United States)

    Baykal, Melek; Baykal, Ahmet

    2014-09-01

    The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.

  7. Laguerre polynomials by a harmonic oscillator

    International Nuclear Information System (INIS)

    Baykal, Melek; Baykal, Ahmet

    2014-01-01

    The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)

  8. On Generalisation of Polynomials in Complex Plane

    Directory of Open Access Journals (Sweden)

    Maslina Darus

    2010-01-01

    Full Text Available The generalised Bell and Laguerre polynomials of fractional-order in complex z-plane are defined. Some properties are studied. Moreover, we proved that these polynomials are univalent solutions for second order differential equations. Also, the Laguerre-type of some special functions are introduced.

  9. Dual exponential polynomials and linear differential equations

    Science.gov (United States)

    Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

    2018-01-01

    We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

  10. Technique for image interpolation using polynomial transforms

    NARCIS (Netherlands)

    Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.

    1993-01-01

    We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is

  11. On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations

    Science.gov (United States)

    Cima, A.; Gasull, A.; Mañosas, F.

    2017-12-01

    In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. We show that the addressed problems can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then we approach to these equations either applying several tools developed to study extended Fermat problems for polynomial equations, or reducing the question to the computation of the genus of some associated planar algebraic curves.

  12. Weighted Polynomial Approximation for Automated Detection of Inspiratory Flow Limitation

    Directory of Open Access Journals (Sweden)

    Sheng-Cheng Huang

    2017-01-01

    Full Text Available Inspiratory flow limitation (IFL is a critical symptom of sleep breathing disorders. A characteristic flattened flow-time curve indicates the presence of highest resistance flow limitation. This study involved investigating a real-time algorithm for detecting IFL during sleep. Three categories of inspiratory flow shape were collected from previous studies for use as a development set. Of these, 16 cases were labeled as non-IFL and 78 as IFL which were further categorized into minor level (20 cases and severe level (58 cases of obstruction. In this study, algorithms using polynomial functions were proposed for extracting the features of IFL. Methods using first- to third-order polynomial approximations were applied to calculate the fitting curve to obtain the mean absolute error. The proposed algorithm is described by the weighted third-order (w.3rd-order polynomial function. For validation, a total of 1,093 inspiratory breaths were acquired as a test set. The accuracy levels of the classifications produced by the presented feature detection methods were analyzed, and the performance levels were compared using a misclassification cobweb. According to the results, the algorithm using the w.3rd-order polynomial approximation achieved an accuracy of 94.14% for IFL classification. We concluded that this algorithm achieved effective automatic IFL detection during sleep.

  13. Matrix product formula for Macdonald polynomials

    Science.gov (United States)

    Cantini, Luigi; de Gier, Jan; Wheeler, Michael

    2015-09-01

    We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik-Zamolodchikov equations, which arise by considering representations of the Zamolodchikov-Faddeev and Yang-Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.

  14. Matrix product formula for Macdonald polynomials

    International Nuclear Information System (INIS)

    Cantini, Luigi; Gier, Jan de; Michael Wheeler

    2015-01-01

    We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik–Zamolodchikov equations, which arise by considering representations of the Zamolodchikov–Faddeev and Yang–Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1. (paper)

  15. Arabic text classification using Polynomial Networks

    Directory of Open Access Journals (Sweden)

    Mayy M. Al-Tahrawi

    2015-10-01

    Full Text Available In this paper, an Arabic statistical learning-based text classification system has been developed using Polynomial Neural Networks. Polynomial Networks have been recently applied to English text classification, but they were never used for Arabic text classification. In this research, we investigate the performance of Polynomial Networks in classifying Arabic texts. Experiments are conducted on a widely used Arabic dataset in text classification: Al-Jazeera News dataset. We chose this dataset to enable direct comparisons of the performance of Polynomial Networks classifier versus other well-known classifiers on this dataset in the literature of Arabic text classification. Results of experiments show that Polynomial Networks classifier is a competitive algorithm to the state-of-the-art ones in the field of Arabic text classification.

  16. Deterministic and unambiguous dense coding

    International Nuclear Information System (INIS)

    Wu Shengjun; Cohen, Scott M.; Sun Yuqing; Griffiths, Robert B.

    2006-01-01

    Optimal dense coding using a partially-entangled pure state of Schmidt rank D and a noiseless quantum channel of dimension D is studied both in the deterministic case where at most L d messages can be transmitted with perfect fidelity, and in the unambiguous case where when the protocol succeeds (probability τ x ) Bob knows for sure that Alice sent message x, and when it fails (probability 1-τ x ) he knows it has failed. Alice is allowed any single-shot (one use) encoding procedure, and Bob any single-shot measurement. For D≤D a bound is obtained for L d in terms of the largest Schmidt coefficient of the entangled state, and is compared with published results by Mozes et al. [Phys. Rev. A71, 012311 (2005)]. For D>D it is shown that L d is strictly less than D 2 unless D is an integer multiple of D, in which case uniform (maximal) entanglement is not needed to achieve the optimal protocol. The unambiguous case is studied for D≤D, assuming τ x >0 for a set of DD messages, and a bound is obtained for the average . A bound on the average requires an additional assumption of encoding by isometries (unitaries when D=D) that are orthogonal for different messages. Both bounds are saturated when τ x is a constant independent of x, by a protocol based on one-shot entanglement concentration. For D>D it is shown that (at least) D 2 messages can be sent unambiguously. Whether unitary (isometric) encoding suffices for optimal protocols remains a major unanswered question, both for our work and for previous studies of dense coding using partially-entangled states, including noisy (mixed) states

  17. Deterministic quantitative risk assessment development

    Energy Technology Data Exchange (ETDEWEB)

    Dawson, Jane; Colquhoun, Iain [PII Pipeline Solutions Business of GE Oil and Gas, Cramlington Northumberland (United Kingdom)

    2009-07-01

    Current risk assessment practice in pipeline integrity management is to use a semi-quantitative index-based or model based methodology. This approach has been found to be very flexible and provide useful results for identifying high risk areas and for prioritizing physical integrity assessments. However, as pipeline operators progressively adopt an operating strategy of continual risk reduction with a view to minimizing total expenditures within safety, environmental, and reliability constraints, the need for quantitative assessments of risk levels is becoming evident. Whereas reliability based quantitative risk assessments can be and are routinely carried out on a site-specific basis, they require significant amounts of quantitative data for the results to be meaningful. This need for detailed and reliable data tends to make these methods unwieldy for system-wide risk k assessment applications. This paper describes methods for estimating risk quantitatively through the calibration of semi-quantitative estimates to failure rates for peer pipeline systems. The methods involve the analysis of the failure rate distribution, and techniques for mapping the rate to the distribution of likelihoods available from currently available semi-quantitative programs. By applying point value probabilities to the failure rates, deterministic quantitative risk assessment (QRA) provides greater rigor and objectivity than can usually be achieved through the implementation of semi-quantitative risk assessment results. The method permits a fully quantitative approach or a mixture of QRA and semi-QRA to suit the operator's data availability and quality, and analysis needs. For example, consequence analysis can be quantitative or can address qualitative ranges for consequence categories. Likewise, failure likelihoods can be output as classical probabilities or as expected failure frequencies as required. (author)

  18. Comparison of deterministic and Monte Carlo methods in shielding design.

    Science.gov (United States)

    Oliveira, A D; Oliveira, C

    2005-01-01

    In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.

  19. Comparison of deterministic and Monte Carlo methods in shielding design

    International Nuclear Information System (INIS)

    Oliveira, A. D.; Oliveira, C.

    2005-01-01

    In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions. (authors)

  20. Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

    DEFF Research Database (Denmark)

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

    2018-01-01

    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......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......-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertainty 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...

  1. Expected number of real roots for random linear combinations of orthogonal polynomials associated with radial weights

    OpenAIRE

    Bayraktar, Turgay

    2017-01-01

    In this note, we obtain asymptotic expected number of real zeros for random polynomials of the form $$f_n(z)=\\sum_{j=0}^na^n_jc^n_jz^j$$ where $a^n_j$ are independent and identically distributed real random variables with bounded $(2+\\delta)$th absolute moment and the deterministic numbers $c^n_j$ are normalizing constants for the monomials $z^j$ within a weighted $L^2$-space induced by a radial weight function satisfying suitable smoothness and growth conditions.

  2. Deterministic secure communication protocol without using entanglement

    OpenAIRE

    Cai, Qing-yu

    2003-01-01

    We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.

  3. on the performance of Autoregressive Moving Average Polynomial

    African Journals Online (AJOL)

    Timothy Ademakinwa

    Distributed Lag (PDL) model, Autoregressive Polynomial Distributed Lag ... Moving Average Polynomial Distributed Lag (ARMAPDL) model. ..... Global Journal of Mathematics and Statistics. Vol. 1. ... Business and Economic Research Center.

  4. Risk-based and deterministic regulation

    International Nuclear Information System (INIS)

    Fischer, L.E.; Brown, N.W.

    1995-07-01

    Both risk-based and deterministic methods are used for regulating the nuclear industry to protect the public safety and health from undue risk. The deterministic method is one where performance standards are specified for each kind of nuclear system or facility. The deterministic performance standards address normal operations and design basis events which include transient and accident conditions. The risk-based method uses probabilistic risk assessment methods to supplement the deterministic one by (1) addressing all possible events (including those beyond the design basis events), (2) using a systematic, logical process for identifying and evaluating accidents, and (3) considering alternative means to reduce accident frequency and/or consequences. Although both deterministic and risk-based methods have been successfully applied, there is need for a better understanding of their applications and supportive roles. This paper describes the relationship between the two methods and how they are used to develop and assess regulations in the nuclear industry. Preliminary guidance is suggested for determining the need for using risk based methods to supplement deterministic ones. However, it is recommended that more detailed guidance and criteria be developed for this purpose

  5. Neck curve polynomials in neck rupture model

    International Nuclear Information System (INIS)

    Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

    2012-01-01

    The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of 280 X 90 with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

  6. Deterministic Approach to Detect Heart Sound Irregularities

    Directory of Open Access Journals (Sweden)

    Richard Mengko

    2017-07-01

    Full Text Available A new method to detect heart sound that does not require machine learning is proposed. The heart sound is a time series event which is generated by the heart mechanical system. From the analysis of heart sound S-transform and the understanding of how heart works, it can be deducted that each heart sound component has unique properties in terms of timing, frequency, and amplitude. Based on these facts, a deterministic method can be designed to identify each heart sound components. The recorded heart sound then can be printed with each component correctly labeled. This greatly help the physician to diagnose the heart problem. The result shows that most known heart sounds were successfully detected. There are some murmur cases where the detection failed. This can be improved by adding more heuristics including setting some initial parameters such as noise threshold accurately, taking into account the recording equipment and also the environmental condition. It is expected that this method can be integrated into an electronic stethoscope biomedical system.

  7. Deterministic chaos at the ocean surface: applications and interpretations

    Directory of Open Access Journals (Sweden)

    A. J. Palmer

    1998-01-01

    Full Text Available Ocean surface, grazing-angle radar backscatter data from two separate experiments, one of which provided coincident time series of measured surface winds, were found to exhibit signatures of deterministic chaos. Evidence is presented that the lowest dimensional underlying dynamical system responsible for the radar backscatter chaos is that which governs the surface wind turbulence. Block-averaging time was found to be an important parameter for determining the degree of determinism in the data as measured by the correlation dimension, and by the performance of an artificial neural network in retrieving wind and stress from the radar returns, and in radar detection of an ocean internal wave. The correlation dimensions are lowered and the performance of the deterministic retrieval and detection algorithms are improved by averaging out the higher dimensional surface wave variability in the radar returns.

  8. Deterministic Brownian motion generated from differential delay equations.

    Science.gov (United States)

    Lei, Jinzhi; Mackey, Michael C

    2011-10-01

    This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.

  9. Progress in nuclear well logging modeling using deterministic transport codes

    International Nuclear Information System (INIS)

    Kodeli, I.; Aldama, D.L.; Maucec, M.; Trkov, A.

    2002-01-01

    Further studies in continuation of the work presented in 2001 in Portoroz were performed in order to study and improve the performances, precission and domain of application of the deterministic transport codes with respect to the oil well logging analysis. These codes are in particular expected to complement the Monte Carlo solutions, since they can provide a detailed particle flux distribution in the whole geometry in a very reasonable CPU time. Real-time calculation can be envisaged. The performances of deterministic transport methods were compared to those of the Monte Carlo method. IRTMBA generic benchmark was analysed using the codes MCNP-4C and DORT/TORT. Centric as well as excentric casings were considered using 14 MeV point neutron source and NaI scintillation detectors. Neutron and gamma spectra were compared at two detector positions.(author)

  10. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tempone, Raul; Wolfers, Sö ren

    2017-01-01

    , obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose

  11. Polynomials in finite geometries and combinatorics

    NARCIS (Netherlands)

    Blokhuis, A.; Walker, K.

    1993-01-01

    It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.

  12. Polynomial analysis of ambulatory blood pressure measurements

    NARCIS (Netherlands)

    Zwinderman, A. H.; Cleophas, T. A.; Cleophas, T. J.; van der Wall, E. E.

    2001-01-01

    In normotensive subjects blood pressures follow a circadian rhythm. A circadian rhythm in hypertensive patients is less well established, and may be clinically important, particularly with rigorous treatments of daytime blood pressures. Polynomial analysis of ambulatory blood pressure monitoring

  13. Handbook on semidefinite, conic and polynomial optimization

    CERN Document Server

    Anjos, Miguel F

    2012-01-01

    This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.

  14. Transversals of Complex Polynomial Vector Fields

    DEFF Research Database (Denmark)

    Dias, Kealey

    Vector fields in the complex plane are defined by assigning the vector determined by the value P(z) to each point z in the complex plane, where P is a polynomial of one complex variable. We consider special families of so-called rotated vector fields that are determined by a polynomial multiplied...... by rotational constants. Transversals are a certain class of curves for such a family of vector fields that represent the bifurcation states for this family of vector fields. More specifically, transversals are curves that coincide with a homoclinic separatrix for some rotation of the vector field. Given...... a concrete polynomial, it seems to take quite a bit of work to prove that it is generic, i.e. structurally stable. This has been done for a special class of degree d polynomial vector fields having simple equilibrium points at the d roots of unity, d odd. In proving that such vector fields are generic...

  15. Generalized catalan numbers, sequences and polynomials

    OpenAIRE

    KOÇ, Cemal; GÜLOĞLU, İsmail; ESİN, Songül

    2010-01-01

    In this paper we present an algebraic interpretation for generalized Catalan numbers. We describe them as dimensions of certain subspaces of multilinear polynomials. This description is of utmost importance in the investigation of annihilators in exterior algebras.

  16. Schur Stability Regions for Complex Quadratic Polynomials

    Science.gov (United States)

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  17. Evaluation of Deterministic and Stochastic Components of Traffic Counts

    Directory of Open Access Journals (Sweden)

    Ivan Bošnjak

    2012-10-01

    Full Text Available Traffic counts or statistical evidence of the traffic processare often a characteristic of time-series data. In this paper fundamentalproblem of estimating deterministic and stochasticcomponents of a traffic process are considered, in the context of"generalised traffic modelling". Different methods for identificationand/or elimination of the trend and seasonal componentsare applied for concrete traffic counts. Further investigationsand applications of ARIMA models, Hilbert space formulationsand state-space representations are suggested.

  18. About the solvability of matrix polynomial equations

    OpenAIRE

    Netzer, Tim; Thom, Andreas

    2016-01-01

    We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

  19. Two polynomial representations of experimental design

    OpenAIRE

    Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera

    2007-01-01

    In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Groebner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch between them. Examples include fractions of full factorial designs and designs for mixture experiments.

  20. Rotation of 2D orthogonal polynomials

    Czech Academy of Sciences Publication Activity Database

    Yang, B.; Flusser, Jan; Kautský, J.

    2018-01-01

    Roč. 102, č. 1 (2018), s. 44-49 ISSN 0167-8655 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : Rotation invariants * Orthogonal polynomials * Recurrent relation * Hermite-like polynomials * Hermite moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.995, year: 2016 http://library.utia.cas.cz/separaty/2017/ZOI/flusser-0483250.pdf

  1. Vertex models, TASEP and Grothendieck polynomials

    International Nuclear Information System (INIS)

    Motegi, Kohei; Sakai, Kazumitsu

    2013-01-01

    We examine the wavefunctions and their scalar products of a one-parameter family of integrable five-vertex models. At a special point of the parameter, the model investigated is related to an irreversible interacting stochastic particle system—the so-called totally asymmetric simple exclusion process (TASEP). By combining the quantum inverse scattering method with a matrix product representation of the wavefunctions, the on-/off-shell wavefunctions of the five-vertex models are represented as a certain determinant form. Up to some normalization factors, we find that the wavefunctions are given by Grothendieck polynomials, which are a one-parameter deformation of Schur polynomials. Introducing a dual version of the Grothendieck polynomials, and utilizing the determinant representation for the scalar products of the wavefunctions, we derive a generalized Cauchy identity satisfied by the Grothendieck polynomials and their duals. Several representation theoretical formulae for the Grothendieck polynomials are also presented. As a byproduct, the relaxation dynamics such as Green functions for the periodic TASEP are found to be described in terms of the Grothendieck polynomials. (paper)

  2. Many-body orthogonal polynomial systems

    International Nuclear Information System (INIS)

    Witte, N.S.

    1997-03-01

    The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)

  3. Design of deterministic interleaver for turbo codes

    International Nuclear Information System (INIS)

    Arif, M.A.; Sheikh, N.M.; Sheikh, A.U.H.

    2008-01-01

    The choice of suitable interleaver for turbo codes can improve the performance considerably. For long block lengths, random interleavers perform well, but for some applications it is desirable to keep the block length shorter to avoid latency. For such applications deterministic interleavers perform better. The performance and design of a deterministic interleaver for short frame turbo codes is considered in this paper. The main characteristic of this class of deterministic interleaver is that their algebraic design selects the best permutation generator such that the points in smaller subsets of the interleaved output are uniformly spread over the entire range of the information data frame. It is observed that the interleaver designed in this manner improves the minimum distance or reduces the multiplicity of first few spectral lines of minimum distance spectrum. Finally we introduce a circular shift in the permutation function to reduce the correlation between the parity bits corresponding to the original and interleaved data frames to improve the decoding capability of MAP (Maximum A Posteriori) probability decoder. Our solution to design a deterministic interleaver outperforms the semi-random interleavers and the deterministic interleavers reported in the literature. (author)

  4. Relations between Möbius and coboundary polynomials

    NARCIS (Netherlands)

    Jurrius, R.P.M.J.

    2012-01-01

    It is known that, in general, the coboundary polynomial and the Möbius polynomial of a matroid do not determine each other. Less is known about more specific cases. In this paper, we will investigate if it is possible that the Möbius polynomial of a matroid, together with the Möbius polynomial of

  5. Some Formulas for the Polynomials and Topological Indices of Nanostructures

    Directory of Open Access Journals (Sweden)

    Soleimani Najmeh

    2016-12-01

    Full Text Available In this paper, we focus on the structure of Polycyclic Aromatic Hydrocarbons (PAHs and calculate the Omega and its related counting polynomials of nanostructures. Also, the exact expressions for the Theta, Sadhana, Pi, Hyper Zagreb and Forgotten Zagreb indices of linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori were computed for the first time. These indices can be used in QSAR/QSPR studies.

  6. Anti-deterministic behaviour of discrete systems that are less predictable than noise

    Science.gov (United States)

    Urbanowicz, Krzysztof; Kantz, Holger; Holyst, Janusz A.

    2005-05-01

    We present a new type of deterministic dynamical behaviour that is less predictable than white noise. We call it anti-deterministic (AD) because time series corresponding to the dynamics of such systems do not generate deterministic lines in recurrence plots for small thresholds. We show that although the dynamics is chaotic in the sense of exponential divergence of nearby initial conditions and although some properties of AD data are similar to white noise, the AD dynamics is in fact, less predictable than noise and hence is different from pseudo-random number generators.

  7. Deterministic blade row interactions in a centrifugal compressor stage

    Science.gov (United States)

    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.

  8. Proving Non-Deterministic Computations in Agda

    Directory of Open Access Journals (Sweden)

    Sergio Antoy

    2017-01-01

    Full Text Available We investigate proving properties of Curry programs using Agda. First, we address the functional correctness of Curry functions that, apart from some syntactic and semantic differences, are in the intersection of the two languages. Second, we use Agda to model non-deterministic functions with two distinct and competitive approaches incorporating the non-determinism. The first approach eliminates non-determinism by considering the set of all non-deterministic values produced by an application. The second approach encodes every non-deterministic choice that the application could perform. We consider our initial experiment a success. Although proving properties of programs is a notoriously difficult task, the functional logic paradigm does not seem to add any significant layer of difficulty or complexity to the task.

  9. Deterministic dense coding with partially entangled states

    Science.gov (United States)

    Mozes, Shay; Oppenheim, Jonathan; Reznik, Benni

    2005-01-01

    The utilization of a d -level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding schemes for certain classes of nonmaximally entangled states, and numerically obtain schemes in the general case. We study the dependency of the maximal alphabet size of such schemes on the partially entangled state shared by the two parties. Surprisingly, for d>2 it is possible to have deterministic dense coding with less than one ebit. In this case the number of alphabet letters that can be communicated by a single particle is between d and 2d . In general, we numerically find that the maximal alphabet size is any integer in the range [d,d2] with the possible exception of d2-1 . We also find that states with less entanglement can have a greater deterministic communication capacity than other more entangled states.

  10. Special polynomials associated with rational solutions of some hierarchies

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2009-01-01

    New special polynomials associated with rational solutions of the Painleve hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey-Dodd-Gibbon, the Kaup-Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials.

  11. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials

    Directory of Open Access Journals (Sweden)

    Paul Barry

    2013-01-01

    Full Text Available The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection coefficients as well as recurrence relations that define them.

  12. New polynomial-based molecular descriptors with low degeneracy.

    Directory of Open Access Journals (Sweden)

    Matthias Dehmer

    Full Text Available In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power.

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

    Science.gov (United States)

    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.

  14. DETERMINISTIC METHODS USED IN FINANCIAL ANALYSIS

    Directory of Open Access Journals (Sweden)

    MICULEAC Melania Elena

    2014-06-01

    Full Text Available The deterministic methods are those quantitative methods that have as a goal to appreciate through numerical quantification the creation and expression mechanisms of factorial and causal, influence and propagation relations of effects, where the phenomenon can be expressed through a direct functional relation of cause-effect. The functional and deterministic relations are the causal relations where at a certain value of the characteristics corresponds a well defined value of the resulting phenomenon. They can express directly the correlation between the phenomenon and the influence factors, under the form of a function-type mathematical formula.

  15. Optimal Deterministic Investment Strategies for Insurers

    Directory of Open Access Journals (Sweden)

    Ulrich Rieder

    2013-11-01

    Full Text Available We consider an insurance company whose risk reserve is given by a Brownian motion with drift and which is able to invest the money into a Black–Scholes financial market. As optimization criteria, we treat mean-variance problems, problems with other risk measures, exponential utility and the probability of ruin. Following recent research, we assume that investment strategies have to be deterministic. This leads to deterministic control problems, which are quite easy to solve. Moreover, it turns out that there are some interesting links between the optimal investment strategies of these problems. Finally, we also show that this approach works in the Lévy process framework.

  16. A new class of generalized polynomials associated with Hermite and Bernoulli polynomials

    Directory of Open Access Journals (Sweden)

    M. A. Pathan

    2015-05-01

    Full Text Available In this paper, we introduce a new class of generalized  polynomials associated with  the modified Milne-Thomson's polynomials Φ_{n}^{(α}(x,ν of degree n and order α introduced by  Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli polynomials  B_n(x, generalized Bernoulli numbers B_n(a,b, generalized Bernoulli polynomials  B_n(x;a,b,c of Luo et al, Hermite-Bernoulli polynomials  {_HB}_n(x,y of Dattoli et al and {_HB}_n^{(α} (x,y of Pathan  are generalized to the one   {_HB}_n^{(α}(x,y,a,b,c which is called  the generalized  polynomial depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B_n, B_n(x, B_n(a,b, B_n(x;a,b,c and {}_HB_n^{(α}(x,y;a,b,c  are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Bernoulli numbers and polynomials

  17. Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

    KAUST Repository

    Ait-Haddou, Rachid; Goldman, Ron

    2015-01-01

    We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.

  18. Certain non-linear differential polynomials sharing a non zero polynomial

    Directory of Open Access Journals (Sweden)

    Majumder Sujoy

    2015-10-01

    functions sharing a nonzero polynomial and obtain two results which improves and generalizes the results due to L. Liu [Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 56 (2008, 3236-3245.] and P. Sahoo [Uniqueness and weighted value sharing of meromorphic functions, Applied. Math. E-Notes., 11 (2011, 23-32.].

  19. Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

    KAUST Repository

    Ait-Haddou, Rachid

    2015-06-07

    We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials. © 2015 Elsevier Inc. All rights reserved.

  20. Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation

    International Nuclear Information System (INIS)

    Demina, Maria V; Kudryashov, Nikolai A

    2012-01-01

    Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of any system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is also obtained that translating relative equilibria of point vortices with arbitrary circulations can be constructed using a generalization of the Tkachenko equation. Roots of any pair of polynomials solving the Tkachenko equation and the generalized Tkachenko equation are proved to give positions of point vortices in stationary and translating relative equilibria accordingly. These results are valid even if the polynomials in a pair have multiple or common roots. It is obtained that the Adler–Moser polynomial provides non-unique polynomial solutions of the Tkachenko equation. It is shown that the generalized Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers. (paper)

  1. Global sensitivity analysis by polynomial dimensional decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Rahman, Sharif, E-mail: rahman@engineering.uiowa.ed [College of Engineering, The University of Iowa, Iowa City, IA 52242 (United States)

    2011-07-15

    This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.

  2. Remarks on determinants and the classical polynomials

    International Nuclear Information System (INIS)

    Henning, J.J.; Kranold, H.U.; Louw, D.F.B.

    1986-01-01

    As motivation for this formal analysis the problem of Landau damping of Bernstein modes is discussed. It is shown that in the case of a weak but finite constant external magnetic field, the analytical structure of the dispersion relations is of such a nature that longitudinal waves propagating orthogonal to the external magnetic field are also damped, contrary to normal belief. In the treatment of the linearized Vlasov equation it is found convenient to generate certain polynomials by the problem at hand and to explicitly write down expressions for these polynomials. In the course of this study methods are used that relate to elementary but fairly unknown functional relationships between power sums and coefficients of polynomials. These relationships, also called Waring functions, are derived. They are then used in other applications to give explicit expressions for the generalized Laguerre polynomials in terms of determinant functions. The properties of polynomials generated by a wide class of generating functions are investigated. These relationships are also used to obtain explicit forms for the cumulants of a distribution in terms of its moments. It is pointed out that cumulants (or moments, for that matter) do not determine a distribution function

  3. Multilevel weighted least squares polynomial approximation

    KAUST Repository

    Haji-Ali, Abdul-Lateef

    2017-06-30

    Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi-optimal approximation in a given polynomial subspace scales, up to a logarithmic factor, linearly in the dimension of this space. However, in many applications, the computation of samples includes a numerical discretization error. Thus, obtaining polynomial approximations with a single level method can become prohibitively expensive, as it requires a sufficiently large number of samples, each computed with a sufficiently small discretization error. As a solution to this problem, we propose a multilevel method that utilizes samples computed with different accuracies and is able to match the accuracy of single-level approximations with reduced computational cost. We derive complexity bounds under certain assumptions about polynomial approximability and sample work. Furthermore, we propose an adaptive algorithm for situations where such assumptions cannot be verified a priori. Finally, we provide an efficient algorithm for the sampling from optimal distributions and an analysis of computationally favorable alternative distributions. Numerical experiments underscore the practical applicability of our method.

  4. Comparison of Deterministic and Probabilistic Radial Distribution Systems Load Flow

    Science.gov (United States)

    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.

  5. Deterministic and stochastic models for middle east respiratory syndrome (MERS)

    Science.gov (United States)

    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.

  6. Applicability of deterministic methods in seismic site effects modeling

    International Nuclear Information System (INIS)

    Cioflan, C.O.; Radulian, M.; Apostol, B.F.; Ciucu, C.

    2005-01-01

    The up-to-date information related to local geological structure in the Bucharest urban area has been integrated in complex analyses of the seismic ground motion simulation using deterministic procedures. The data recorded for the Vrancea intermediate-depth large earthquakes are supplemented with synthetic computations all over the city area. The hybrid method with a double-couple seismic source approximation and a relatively simple regional and local structure models allows a satisfactory reproduction of the strong motion records in the frequency domain (0.05-1)Hz. The new geological information and a deterministic analytical method which combine the modal summation technique, applied to model the seismic wave propagation between the seismic source and the studied sites, with the mode coupling approach used to model the seismic wave propagation through the local sedimentary structure of the target site, allows to extend the modelling to higher frequencies of earthquake engineering interest. The results of these studies (synthetic time histories of the ground motion parameters, absolute and relative response spectra etc) for the last 3 Vrancea strong events (August 31,1986 M w =7.1; May 30,1990 M w = 6.9 and October 27, 2004 M w = 6.0) can complete the strong motion database used for the microzonation purposes. Implications and integration of the deterministic results into the urban planning and disaster management strategies are also discussed. (authors)

  7. A Theory of Deterministic Event Structures

    NARCIS (Netherlands)

    Lee, I.; Rensink, Arend; Smolka, S.A.

    1995-01-01

    We present an w-complete algebra of a class of deterministic event structures which are labelled prime event structures where the labelling function satises a certain distinctness condition. The operators of the algebra are summation sequential composition and join. Each of these gives rise to a

  8. A Numerical Simulation for a Deterministic Compartmental ...

    African Journals Online (AJOL)

    In this work, an earlier deterministic mathematical model of HIV/AIDS is revisited and numerical solutions obtained using Eulers numerical method. Using hypothetical values for the parameters, a program was written in VISUAL BASIC programming language to generate series for the system of difference equations from the ...

  9. Minimal residual method stronger than polynomial preconditioning

    Energy Technology Data Exchange (ETDEWEB)

    Faber, V.; Joubert, W.; Knill, E. [Los Alamos National Lab., NM (United States)] [and others

    1994-12-31

    Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.

  10. Fast beampattern evaluation by polynomial rooting

    Science.gov (United States)

    Häcker, P.; Uhlich, S.; Yang, B.

    2011-07-01

    Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

  11. New realisation of Preisach model using adaptive polynomial approximation

    Science.gov (United States)

    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.

  12. Twisted Polynomials and Forgery Attacks on GCM

    DEFF Research Database (Denmark)

    Abdelraheem, Mohamed Ahmed A. M. A.; Beelen, Peter; Bogdanov, Andrey

    2015-01-01

    Polynomial hashing as an instantiation of universal hashing is a widely employed method for the construction of MACs and authenticated encryption (AE) schemes, the ubiquitous GCM being a prominent example. It is also used in recent AE proposals within the CAESAR competition which aim at providing...... in an improved key recovery algorithm. As cryptanalytic applications of our twisted polynomials, we develop the first universal forgery attacks on GCM in the weak-key model that do not require nonce reuse. Moreover, we present universal weak-key forgeries for the nonce-misuse resistant AE scheme POET, which...

  13. Polynomial Vector Fields in One Complex Variable

    DEFF Research Database (Denmark)

    Branner, Bodil

    In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias.......In recent years Adrien Douady was interested in polynomial vector fields, both in relation to iteration theory and as a topic on their own. This talk is based on his work with Pierrette Sentenac, work of Xavier Buff and Tan Lei, and my own joint work with Kealey Dias....

  14. The chromatic polynomial and list colorings

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2009-01-01

    We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph.......We prove that, if a graph has a list of k available colors at every vertex, then the number of list-colorings is at least the chromatic polynomial evaluated at k when k is sufficiently large compared to the number of vertices of the graph....

  15. Complex centers of polynomial differential equations

    Directory of Open Access Journals (Sweden)

    Mohamad Ali M. Alwash

    2007-07-01

    Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

  16. Differential recurrence formulae for orthogonal polynomials

    Directory of Open Access Journals (Sweden)

    Anton L. W. von Bachhaus

    1995-11-01

    Full Text Available Part I - By combining a general 2nd-order linear homogeneous ordinary differential equation with the three-term recurrence relation possessed by all orthogonal polynomials, it is shown that sequences of orthogonal polynomials which satisfy a differential equation of the above mentioned type necessarily have a differentiation formula of the type: gn(xY'n(x=fn(xYn(x+Yn-1(x. Part II - A recurrence formula of the form: rn(xY'n(x+sn(xY'n+1(x+tn(xY'n-1(x=0, is derived using the result of Part I.

  17. Polynomial regression analysis and significance test of the regression function

    International Nuclear Information System (INIS)

    Gao Zhengming; Zhao Juan; He Shengping

    2012-01-01

    In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)

  18. Nonclassical Orthogonal Polynomials and Corresponding Quadratures

    CERN Document Server

    Fukuda, H; Alt, E O; Matveenko, A V

    2004-01-01

    We construct nonclassical orthogonal polynomials and calculate abscissas and weights of Gaussian quadrature for arbitrary weight and interval. The program is written by Mathematica and it works if moment integrals are given analytically. The result is a FORTRAN subroutine ready to utilize the quadrature.

  19. Intrinsic Diophantine approximation on general polynomial surfaces

    DEFF Research Database (Denmark)

    Tiljeset, Morten Hein

    2017-01-01

    We study the Hausdorff measure and dimension of the set of intrinsically simultaneously -approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done...

  20. Quantum Hilbert matrices and orthogonal polynomials

    DEFF Research Database (Denmark)

    Andersen, Jørgen Ellegaard; Berg, Christian

    2009-01-01

    Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

  1. Algebraic polynomial system solving and applications

    NARCIS (Netherlands)

    Bleylevens, I.W.M.

    2010-01-01

    The problem of computing the solutions of a system of multivariate polynomial equations can be approached by the Stetter-Möller matrix method which casts the problem into a large eigenvalue problem. This Stetter-Möller matrix method forms the starting point for the development of computational

  2. Information-theoretic lengths of Jacobi polynomials

    Energy Technology Data Exchange (ETDEWEB)

    Guerrero, A; Dehesa, J S [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, Granada (Spain); Sanchez-Moreno, P, E-mail: agmartinez@ugr.e, E-mail: pablos@ugr.e, E-mail: dehesa@ugr.e [Instituto ' Carlos I' de Fisica Teorica y Computacional, Universidad de Granada, Granada (Spain)

    2010-07-30

    The information-theoretic lengths of the Jacobi polynomials P{sup ({alpha}, {beta})}{sub n}(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [- 1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. The explicit expressions of the Fisher length are given. The Renyi lengths are found by the use of the combinatorial multivariable Bell polynomials in terms of the polynomial degree n and the parameters ({alpha}, {beta}). The Shannon length, which cannot be exactly calculated because of its logarithmic functional form, is bounded from below by using sharp upper bounds to general densities on [- 1, +1] given in terms of various expectation values; moreover, its asymptotics is also pointed out. Finally, several computational issues relative to these three quantities are carefully analyzed.

  3. Indecomposability of polynomials via Jacobian matrix

    International Nuclear Information System (INIS)

    Cheze, G.; Najib, S.

    2007-12-01

    Uni-multivariate decomposition of polynomials is a special case of absolute factorization. Recently, thanks to the Ruppert's matrix some effective results about absolute factorization have been improved. Here we show that with a jacobian matrix we can get sharper bounds for the special case of uni-multivariate decomposition. (author)

  4. On selfadjoint functors satisfying polynomial relations

    DEFF Research Database (Denmark)

    Agerholm, Troels; Mazorchuk, Volodomyr

    2011-01-01

    We study selfadjoint functors acting on categories of finite dimen- sional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint func- tors satisfying several easy relations, in particular, idempotents and square roots of a sum...

  5. Polynomial Variables and the Jacobian Problem

    Indian Academy of Sciences (India)

    algebra and algebraic geometry, and ... algebraically, to making the change of variables (X, Y) r--t. (X +p, Y ... aX + bY + p and eX + dY + q are linear polynomials in X, Y. ..... [5] T T Moh, On the Jacobian conjecture and the confipration of roots,.

  6. Function approximation with polynomial regression slines

    International Nuclear Information System (INIS)

    Urbanski, P.

    1996-01-01

    Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author)

  7. Polynomial stabilization of some dissipative hyperbolic systems

    Czech Academy of Sciences Publication Activity Database

    Ammari, K.; Feireisl, Eduard; Nicaise, S.

    2014-01-01

    Roč. 34, č. 11 (2014), s. 4371-4388 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : exponential stability * polynomial stability * observability inequality Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9924

  8. Polynomial Asymptotes of the Second Kind

    Science.gov (United States)

    Dobbs, David E.

    2011-01-01

    This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…

  9. Characteristic polynomials of linear polyacenes and their ...

    Indian Academy of Sciences (India)

    Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal's triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP's. Thus it ...

  10. Coherent states for polynomial su(2) algebra

    International Nuclear Information System (INIS)

    Sadiq, Muhammad; Inomata, Akira

    2007-01-01

    A class of generalized coherent states is constructed for a polynomial su(2) algebra in a group-free manner. As a special case, the coherent states for the cubic su(2) algebra are discussed. The states so constructed reduce to the usual SU(2) coherent states in the linear limit

  11. Bernoulli Polynomials, Fourier Series and Zeta Numbers

    DEFF Research Database (Denmark)

    Scheufens, Ernst E

    2013-01-01

    Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent...

  12. Euler Polynomials, Fourier Series and Zeta Numbers

    DEFF Research Database (Denmark)

    Scheufens, Ernst E

    2012-01-01

    Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....

  13. Automatic Control Systems Modeling by Volterra Polynomials

    Directory of Open Access Journals (Sweden)

    S. V. Solodusha

    2012-01-01

    Full Text Available The problem of the existence of the solutions of polynomial Volterra integral equations of the first kind of the second degree is considered. An algorithm of the numerical solution of one class of Volterra nonlinear systems of the first kind is developed. Numerical results for test examples are presented.

  14. Spectral properties of birth-death polynomials

    NARCIS (Netherlands)

    van Doorn, Erik A.

    2015-01-01

    We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by

  15. Spectral properties of birth-death polynomials

    NARCIS (Netherlands)

    van Doorn, Erik A.

    We consider sequences of polynomials that are defined by a three-terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis. By a famous result of Karlin and McGregor such sequences are instrumental in the analysis of birth-death processes. Inspired by

  16. Optimization of Cubic Polynomial Functions without Calculus

    Science.gov (United States)

    Taylor, Ronald D., Jr.; Hansen, Ryan

    2008-01-01

    In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…

  17. transformation of independent variables in polynomial regression ...

    African Journals Online (AJOL)

    Ada

    preferable when possible to work with a simple functional form in transformed variables rather than with a more complicated form in the original variables. In this paper, it is shown that linear transformations applied to independent variables in polynomial regression models affect the t ratio and hence the statistical ...

  18. Inequalities for a Polynomial and its Derivative

    Indian Academy of Sciences (India)

    Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 110; Issue 2. Inequalities for a Polynomial and its Derivative. V K Jain. Volume 110 Issue 2 May 2000 pp 137- ...

  19. Integral Inequalities for Self-Reciprocal Polynomials

    Indian Academy of Sciences (India)

    Annual Meetings · Mid Year Meetings · Discussion Meetings · Public Lectures · Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. Integral Inequalities for Self-Reciprocal Polynomials. Horst Alzer. Volume 120 Issue 2 April 2010 ...

  20. Deterministic nonlinear systems a short course

    CERN Document Server

    Anishchenko, Vadim S; Strelkova, Galina I

    2014-01-01

    This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems.  This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.

  1. Deterministic nanoparticle assemblies: from substrate to solution

    International Nuclear Information System (INIS)

    Barcelo, Steven J; Gibson, Gary A; Yamakawa, Mineo; Li, Zhiyong; Kim, Ansoon; Norris, Kate J

    2014-01-01

    The deterministic assembly of metallic nanoparticles is an exciting field with many potential benefits. Many promising techniques have been developed, but challenges remain, particularly for the assembly of larger nanoparticles which often have more interesting plasmonic properties. Here we present a scalable process combining the strengths of top down and bottom up fabrication to generate deterministic 2D assemblies of metallic nanoparticles and demonstrate their stable transfer to solution. Scanning electron and high-resolution transmission electron microscopy studies of these assemblies suggested the formation of nanobridges between touching nanoparticles that hold them together so as to maintain the integrity of the assembly throughout the transfer process. The application of these nanoparticle assemblies as solution-based surface-enhanced Raman scattering (SERS) materials is demonstrated by trapping analyte molecules in the nanoparticle gaps during assembly, yielding uniformly high enhancement factors at all stages of the fabrication process. (paper)

  2. Deterministic dynamics of plasma focus discharges

    International Nuclear Information System (INIS)

    Gratton, J.; Alabraba, M.A.; Warmate, A.G.; Giudice, G.

    1992-04-01

    The performance (neutron yield, X-ray production, etc.) of plasma focus discharges fluctuates strongly in series performed with fixed experimental conditions. Previous work suggests that these fluctuations are due to a deterministic ''internal'' dynamics involving degrees of freedom not controlled by the operator, possibly related to adsorption and desorption of impurities from the electrodes. According to these dynamics the yield of a discharge depends on the outcome of the previous ones. We study 8 series of discharges in three different facilities, with various electrode materials and operating conditions. More evidence of a deterministic internal dynamics is found. The fluctuation pattern depends on the electrode materials and other characteristics of the experiment. A heuristic mathematical model that describes adsorption and desorption of impurities from the electrodes and their consequences on the yield is presented. The model predicts steady yield or periodic and chaotic fluctuations, depending on parameters related to the experimental conditions. (author). 27 refs, 7 figs, 4 tabs

  3. Advances in stochastic and deterministic global optimization

    CERN Document Server

    Zhigljavsky, Anatoly; Žilinskas, Julius

    2016-01-01

    Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and mu...

  4. Understanding deterministic diffusion by correlated random walks

    International Nuclear Information System (INIS)

    Klages, R.; Korabel, N.

    2002-01-01

    Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulae we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coefficients in terms of dynamical correlations. (author)

  5. Deterministic geologic processes and stochastic modeling

    International Nuclear Information System (INIS)

    Rautman, C.A.; Flint, A.L.

    1992-01-01

    This paper reports that recent outcrop sampling at Yucca Mountain, Nevada, has produced significant new information regarding the distribution of physical properties at the site of a potential high-level nuclear waste repository. consideration of the spatial variability indicates that her are a number of widespread deterministic geologic features at the site that have important implications for numerical modeling of such performance aspects as ground water flow and radionuclide transport. Because the geologic processes responsible for formation of Yucca Mountain are relatively well understood and operate on a more-or-less regional scale, understanding of these processes can be used in modeling the physical properties and performance of the site. Information reflecting these deterministic geologic processes may be incorporated into the modeling program explicitly using geostatistical concepts such as soft information, or implicitly, through the adoption of a particular approach to modeling

  6. Deterministic automata for extended regular expressions

    Directory of Open Access Journals (Sweden)

    Syzdykov Mirzakhmet

    2017-12-01

    Full Text Available In this work we present the algorithms to produce deterministic finite automaton (DFA for extended operators in regular expressions like intersection, subtraction and complement. The method like “overriding” of the source NFA(NFA not defined with subset construction rules is used. The past work described only the algorithm for AND-operator (or intersection of regular languages; in this paper the construction for the MINUS-operator (and complement is shown.

  7. Density of Real Zeros of the Tutte Polynomial

    DEFF Research Database (Denmark)

    Ok, Seongmin; Perrett, Thomas

    2018-01-01

    The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

  8. Density of Real Zeros of the Tutte Polynomial

    DEFF Research Database (Denmark)

    Ok, Seongmin; Perrett, Thomas

    2017-01-01

    The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This ....... This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.......The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane...

  9. Some Polynomials Associated with the r-Whitney Numbers

    Indian Academy of Sciences (India)

    26

    Abstract. In the present article we study three families of polynomials associated with ... [29, 39] for their relations with the Bernoulli and generalized Bernoulli polynomials and ... generating functions in a similar way as in the classical cases.

  10. On an Inequality Concerning the Polar Derivative of a Polynomial

    Indian Academy of Sciences (India)

    Abstract. In this paper, we present a correct proof of an -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zygmund's inequality to the polar derivative of a polynomial.

  11. Polynomial Digital Control of a Series Equal Liquid Tanks

    Directory of Open Access Journals (Sweden)

    Bobála Vladimír

    2016-01-01

    Full Text Available Time-delays are mainly caused by the time required to transport mass, energy or information, but they can also be caused by processing time or accumulation. Typical examples of such processes are e.g. pumps, liquid storing tanks, distillation columns or some types of chemical reactors. In many cases time-delay is caused by the effect produced by the accumulation of a large number of low-order systems. Several industrial processes have the time-delay effect produced by the accumulation of a great number of low-order systems with the identical dynamic. The dynamic behavior of series these low-order systems is expressed by high-order system. One of possibilities of control of such processes is their approximation by low-order model with time-delay. The paper is focused on the design of the digital polynomial control of a set of equal liquid cylinder atmospheric tanks. The designed control algorithms are realized using the digital Smith Predictor (SP based on polynomial approach – by minimization of the Linear Quadratic (LQ criterion. The LQ criterion was combined with pole assignment.

  12. Deterministic and efficient quantum cryptography based on Bell's theorem

    International Nuclear Information System (INIS)

    Chen, Z.-B.; Zhang, Q.; Bao, X.-H.; Schmiedmayer, J.; Pan, J.-W.

    2005-01-01

    Full text: We propose a novel 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 a key bit with the help of classical communications. Eavesdropping can be detected by checking the violation of local realism for the detected events. We also show that our protocol allows a robust implementation under current technology. (author)

  13. Deterministic Mean-Field Ensemble Kalman Filtering

    KAUST Repository

    Law, Kody

    2016-05-03

    The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

  14. Deterministic Mean-Field Ensemble Kalman Filtering

    KAUST Repository

    Law, Kody; Tembine, Hamidou; Tempone, Raul

    2016-01-01

    The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence k between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d<2k. The fidelity of approximation of the true distribution is also established using an extension of the total variation metric to random measures. This is limited by a Gaussian bias term arising from nonlinearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.

  15. Forced Translocation of Polymer through Nanopore: Deterministic Model and Simulations

    Science.gov (United States)

    Wang, Yanqian; Panyukov, Sergey; Liao, Qi; Rubinstein, Michael

    2012-02-01

    We propose a new theoretical model of forced translocation of a polymer chain through a nanopore. We assume that DNA translocation at high fields proceeds too fast for the chain to relax, and thus the chain unravels loop by loop in an almost deterministic way. So the distribution of translocation times of a given monomer is controlled by the initial conformation of the chain (the distribution of its loops). Our model predicts the translocation time of each monomer as an explicit function of initial polymer conformation. We refer to this concept as ``fingerprinting''. The width of the translocation time distribution is determined by the loop distribution in initial conformation as well as by the thermal fluctuations of the polymer chain during the translocation process. We show that the conformational broadening δt of translocation times of m-th monomer δtm^1.5 is stronger than the thermal broadening δtm^1.25 The predictions of our deterministic model were verified by extensive molecular dynamics simulations

  16. 2-variable Laguerre matrix polynomials and Lie-algebraic techniques

    International Nuclear Information System (INIS)

    Khan, Subuhi; Hassan, Nader Ali Makboul

    2010-01-01

    The authors introduce 2-variable forms of Laguerre and modified Laguerre matrix polynomials and derive their special properties. Further, the representations of the special linear Lie algebra sl(2) and the harmonic oscillator Lie algebra G(0,1) are used to derive certain results involving these polynomials. Furthermore, the generating relations for the ordinary as well as matrix polynomials related to these matrix polynomials are derived as applications.

  17. Algebraic limit cycles in polynomial systems of differential equations

    International Nuclear Information System (INIS)

    Llibre, Jaume; Zhao Yulin

    2007-01-01

    Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

  18. The generalized Yablonskii-Vorob'ev polynomials and their properties

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2008-01-01

    Rational solutions of the generalized second Painleve hierarchy are classified. Representation of the rational solutions in terms of special polynomials, the generalized Yablonskii-Vorob'ev polynomials, is introduced. Differential-difference relations satisfied by the polynomials are found. Hierarchies of differential equations related to the generalized second Painleve hierarchy are derived. One of these hierarchies is a sequence of differential equations satisfied by the generalized Yablonskii-Vorob'ev polynomials

  19. Polynomial selection in number field sieve for integer factorization

    Directory of Open Access Journals (Sweden)

    Gireesh Pandey

    2016-09-01

    Full Text Available The general number field sieve (GNFS is the fastest algorithm for factoring large composite integers which is made up by two prime numbers. Polynomial selection is an important step of GNFS. The asymptotic runtime depends on choice of good polynomial pairs. In this paper, we present polynomial selection algorithm that will be modelled with size and root properties. The correlations between polynomial coefficient and number of relations have been explored with experimental findings.

  20. Contributions to fuzzy polynomial techniques for stability analysis and control

    OpenAIRE

    Pitarch Pérez, José Luis

    2014-01-01

    The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...

  1. Orthogonal polynomials in Stein's method

    NARCIS (Netherlands)

    Schoutens, W.

    2001-01-01

    Stein's method provides a way of finding approximations to the distribution, ¿ say, of a random variable, which at the same time gives estimates of the approximation error involved. In essence the method is based on a defining equation, or equivalently an operator, of the distribution ¿ and a

  2. Interlacing of zeros of quasi-orthogonal meixner polynomials | Driver ...

    African Journals Online (AJOL)

    ... interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed. Mathematics Subject Classication (2010): 33C45, 42C05. Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner

  3. Strong result for real zeros of random algebraic polynomials

    Directory of Open Access Journals (Sweden)

    T. Uno

    2001-01-01

    Full Text Available An estimate is given for the lower bound of real zeros of random algebraic polynomials whose coefficients are non-identically distributed dependent Gaussian random variables. Moreover, our estimated measure of the exceptional set, which is independent of the degree of the polynomials, tends to zero as the degree of the polynomial tends to infinity.

  4. On the Lorentz degree of a product of polynomials

    KAUST Repository

    Ait-Haddou, Rachid

    2015-01-01

    In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence of a result of Barnard et al. (1991) on polynomials with nonnegative coefficients.

  5. A Determinant Expression for the Generalized Bessel Polynomials

    Directory of Open Access Journals (Sweden)

    Sheng-liang Yang

    2013-01-01

    Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

  6. On the estimation of the degree of regression polynomial

    International Nuclear Information System (INIS)

    Toeroek, Cs.

    1997-01-01

    The mathematical functions most commonly used to model curvature in plots are polynomials. Generally, the higher the degree of the polynomial, the more complex is the trend that its graph can represent. We propose a new statistical-graphical approach based on the discrete projective transformation (DPT) to estimating the degree of polynomial that adequately describes the trend in the plot

  7. Zeros and uniqueness of Q-difference polynomials of meromorphic ...

    Indian Academy of Sciences (India)

    Meromorphic functions; Nevanlinna theory; logarithmic order; uniqueness problem; difference-differential polynomial. Abstract. In this paper, we investigate the value distribution of -difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials ...

  8. Uniqueness and zeros of q-shift difference polynomials

    Indian Academy of Sciences (India)

    In this paper, we consider the zero distributions of -shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to -shift difference polynomials. We also investigate the uniqueness problem of -shift ...

  9. Polynomially Riesz elements | Živković-Zlatanović | Quaestiones ...

    African Journals Online (AJOL)

    A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp ∈ B is quasinilpotent. Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, ...

  10. Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials

    International Nuclear Information System (INIS)

    Tratnik, M.V.

    1990-01-01

    Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

  11. Commutators with idempotent values on multilinear polynomials in ...

    Indian Academy of Sciences (India)

    Multilinear polynomial; derivations; generalized polynomial identity; prime ring; right ideal. Abstract. Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R , f ( x 1 , … , x n ) a multilinear polynomial over C , ϱ a nonzero right ideal of R and m > 1 a fixed integer such that.

  12. Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

    Science.gov (United States)

    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…

  13. Degenerate r-Stirling Numbers and r-Bell Polynomials

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

  15. Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

    Science.gov (United States)

    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.

  16. Deterministic quantum state transfer and remote entanglement using microwave photons.

    Science.gov (United States)

    Kurpiers, P; Magnard, P; Walter, T; Royer, B; Pechal, M; Heinsoo, J; Salathé, Y; Akin, A; Storz, S; Besse, J-C; Gasparinetti, S; Blais, A; Wallraff, A

    2018-06-01

    Sharing information coherently between nodes of a quantum network is fundamental to distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers that are connected by classical and quantum channels 1 . A direct quantum channel, which connects nodes deterministically rather than probabilistically, achieves larger entanglement rates between nodes and is advantageous for distributed fault-tolerant quantum computation 2 . Here we implement deterministic state-transfer and entanglement protocols between two superconducting qubits fabricated on separate chips. Superconducting circuits 3 constitute a universal quantum node 4 that is capable of sending, receiving, storing and processing quantum information 5-8 . Our implementation is based on an all-microwave cavity-assisted Raman process 9 , which entangles or transfers the qubit state of a transmon-type artificial atom 10 with a time-symmetric itinerant single photon. We transfer qubit states by absorbing these itinerant photons at the receiving node, with a probability of 98.1 ± 0.1 per cent, achieving a transfer-process fidelity of 80.02 ± 0.07 per cent for a protocol duration of only 180 nanoseconds. We also prepare remote entanglement on demand with a fidelity as high as 78.9 ± 0.1 per cent at a rate of 50 kilohertz. Our results are in excellent agreement with numerical simulations based on a master-equation description of the system. This deterministic protocol has the potential to be used for quantum computing distributed across different nodes of a cryogenic network.

  17. Sparse DOA estimation with polynomial rooting

    DEFF Research Database (Denmark)

    Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren

    2015-01-01

    Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...

  18. Quantum Hurwitz numbers and Macdonald polynomials

    Science.gov (United States)

    Harnad, J.

    2016-11-01

    Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

  19. Polynomial chaos representation of databases on manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Soize, C., E-mail: christian.soize@univ-paris-est.fr [Université Paris-Est, Laboratoire Modélisation et Simulation Multi-Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-La-Vallée, Cedex 2 (France); Ghanem, R., E-mail: ghanem@usc.edu [University of Southern California, 210 KAP Hall, Los Angeles, CA 90089 (United States)

    2017-04-15

    Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.

  20. Polynomial structures in one-loop amplitudes

    International Nuclear Information System (INIS)

    Britto, Ruth; Feng Bo; Yang Gang

    2008-01-01

    A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients of (4-2ε)-dimensional master integrals; these formulas depend on an additional variable, u, which encodes the dimensional shift. Second, convert the u-dependent coefficients of (4-2ε)-dimensional master integrals to explicit coefficients of dimensionally shifted master integrals. This procedure requires the initial formulas for coefficients to have polynomial dependence on u. Here, we give a proof of this property in the case of massless propagators. The proof is constructive. Thus, as a byproduct, we produce different algebraic expressions for the scalar integral coefficients, in which the polynomial property is apparent. In these formulas, the box and pentagon contributions are separated explicitly.

  1. Link polynomial, crossing multiplier and surgery formula

    International Nuclear Information System (INIS)

    Deguchi, Tetsuo; Yamada, Yasuhiko.

    1989-01-01

    Relations between link polynomials constructed from exactly solvable lattice models and topological field theory are reviewed. It is found that the surgery formula for a three-sphere S 3 with Wilson lines corresponds to the Markov trace constructed from the exactly solvable models. This indicates that knot theory intimately relates various important subjects such as exactly solvable models, conformal field theories and topological quantum field theories. (author)

  2. Completeness of the ring of polynomials

    DEFF Research Database (Denmark)

    Thorup, Anders

    2015-01-01

    Consider the polynomial ring R:=k[X1,…,Xn]R:=k[X1,…,Xn] in n≥2n≥2 variables over an uncountable field k. We prove that R   is complete in its adic topology, that is, the translation invariant topology in which the non-zero ideals form a fundamental system of neighborhoods of 0. In addition we pro...

  3. Moments, positive polynomials and their applications

    CERN Document Server

    Lasserre, Jean Bernard

    2009-01-01

    Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP) . This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones,

  4. Polynomials and identities on real Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Kraus, M.

    2012-01-01

    Roč. 385, č. 2 (2012), s. 1015-1026 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : Polynomials on Banach spaces Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11006743

  5. A DETERMINISTIC METHOD FOR TRANSIENT, THREE-DIMENSIONAL NUETRON TRANSPORT

    International Nuclear Information System (INIS)

    S. GOLUOGLU, C. BENTLEY, R. DEMEGLIO, M. DUNN, K. NORTON, R. PEVEY I.SUSLOV AND H.L. DODDS

    1998-01-01

    A deterministic method for solving the time-dependent, three-dimensional Boltzmam transport equation with explicit representation of delayed neutrons has been developed and evaluated. The methodology used in this study for the time variable of the neutron flux is known as the improved quasi-static (IQS) method. The position, energy, and angle-dependent neutron flux is computed deterministically by using the three-dimensional discrete ordinates code TORT. This paper briefly describes the methodology and selected results. The code developed at the University of Tennessee based on this methodology is called TDTORT. TDTORT can be used to model transients involving voided and/or strongly absorbing regions that require transport theory for accuracy. This code can also be used to model either small high-leakage systems, such as space reactors, or asymmetric control rod movements. TDTORT can model step, ramp, step followed by another step, and step followed by ramp type perturbations. It can also model columnwise rod movement can also be modeled. A special case of columnwise rod movement in a three-dimensional model of a boiling water reactor (BWR) with simple adiabatic feedback is also included. TDTORT is verified through several transient one-dimensional, two-dimensional, and three-dimensional benchmark problems. The results show that the transport methodology and corresponding code developed in this work have sufficient accuracy and speed for computing the dynamic behavior of complex multidimensional neutronic systems

  6. Eye aberration analysis with Zernike polynomials

    Science.gov (United States)

    Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.

    1998-06-01

    New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.

  7. Deterministic effects of the ionizing radiation

    International Nuclear Information System (INIS)

    Raslawski, Elsa C.

    2001-01-01

    Full text: The deterministic effect is the somatic damage that appears when radiation dose is superior to the minimum value or 'threshold dose'. Over this threshold dose, the frequency and seriousness of the damage increases with the amount given. Sixteen percent of patients younger than 15 years of age with the diagnosis of cancer have the possibility of a cure. The consequences of cancer treatment in children are very serious, as they are physically and emotionally developing. The seriousness of the delayed effects of radiation therapy depends on three factors: a)- The treatment ( dose of radiation, schedule of treatment, time of treatment, beam energy, treatment volume, distribution of the dose, simultaneous chemotherapy, etc.); b)- The patient (state of development, patient predisposition, inherent sensitivity of tissue, the present of other alterations, etc.); c)- The tumor (degree of extension or infiltration, mechanical effects, etc.). The effect of radiation on normal tissue is related to cellular activity and the maturity of the tissue irradiated. Children have a mosaic of tissues in different stages of maturity at different moments in time. On the other hand, each tissue has a different pattern of development, so that sequelae are different in different irradiated tissues of the same patient. We should keep in mind that all the tissues are affected in some degree. Bone tissue evidences damage with growth delay and degree of calcification. Damage is small at 10 Gy; between 10 and 20 Gy growth arrest is partial, whereas at doses larger than 20 Gy growth arrest is complete. The central nervous system is the most affected because the radiation injuries produce demyelination with or without focal or diffuse areas of necrosis in the white matter causing character alterations, lower IQ and functional level, neuro cognitive impairment,etc. The skin is also affected, showing different degrees of erythema such as ulceration and necrosis, different degrees of

  8. Deterministic and probabilistic approach to safety analysis

    International Nuclear Information System (INIS)

    Heuser, F.W.

    1980-01-01

    The examples discussed in this paper show that reliability analysis methods fairly well can be applied in order to interpret deterministic safety criteria in quantitative terms. For further improved extension of applied reliability analysis it has turned out that the influence of operational and control systems and of component protection devices should be considered with the aid of reliability analysis methods in detail. Of course, an extension of probabilistic analysis must be accompanied by further development of the methods and a broadening of the data base. (orig.)

  9. A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes

    International Nuclear Information System (INIS)

    Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

    2013-01-01

    We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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

  12. When to conduct probabilistic linkage vs. deterministic linkage? A simulation study.

    Science.gov (United States)

    Zhu, Ying; Matsuyama, Yutaka; Ohashi, Yasuo; Setoguchi, Soko

    2015-08-01

    When unique identifiers are unavailable, successful record linkage depends greatly on data quality and types of variables available. While probabilistic linkage theoretically captures more true matches than deterministic linkage by allowing imperfection in identifiers, studies have shown inconclusive results likely due to variations in data quality, implementation of linkage methodology and validation method. The simulation study aimed to understand data characteristics that affect the performance of probabilistic vs. deterministic linkage. We created ninety-six scenarios that represent real-life situations using non-unique identifiers. We systematically introduced a range of discriminative power, rate of missing and error, and file size to increase linkage patterns and difficulties. We assessed the performance difference of linkage methods using standard validity measures and computation time. Across scenarios, deterministic linkage showed advantage in PPV while probabilistic linkage showed advantage in sensitivity. Probabilistic linkage uniformly outperformed deterministic linkage as the former generated linkages with better trade-off between sensitivity and PPV regardless of data quality. However, with low rate of missing and error in data, deterministic linkage performed not significantly worse. The implementation of deterministic linkage in SAS took less than 1min, and probabilistic linkage took 2min to 2h depending on file size. Our simulation study demonstrated that the intrinsic rate of missing and error of linkage variables was key to choosing between linkage methods. In general, probabilistic linkage was a better choice, but for exceptionally good quality data (<5% error), deterministic linkage was a more resource efficient choice. Copyright © 2015 Elsevier Inc. All rights reserved.

  13. Linear flow of heat in an infinite region and hermite polynomials

    International Nuclear Information System (INIS)

    Al-Hawaj, A.Y.

    1991-01-01

    The problem of linear flow of heat in an infinite region occupies a prominent place in the field of conduction of heat in solids. A number of solutions to this problem, have been given from time to time by several mathematicians. The object of this paper is to derive the solutions of the problem of linear flow of heat in an infinite region, which lead to Hermite Polynomials. The author further presents three linear combinations of his solutions and their particular cases. The region (- ∞ < x < ∞) of the problem led him to investigate the solutions of the problem in terms of Hermite Polynomials

  14. Optimization of structures subjected to dynamic load: deterministic and probabilistic methods

    Directory of Open Access Journals (Sweden)

    Élcio Cassimiro Alves

    Full Text Available Abstract This paper deals with the deterministic and probabilistic optimization of structures against bending when submitted to dynamic loads. The deterministic optimization problem considers the plate submitted to a time varying load while the probabilistic one takes into account a random loading defined by a power spectral density function. The correlation between the two problems is made by one Fourier Transformed. The finite element method is used to model the structures. The sensitivity analysis is performed through the analytical method and the optimization problem is dealt with by the method of interior points. A comparison between the deterministic optimisation and the probabilistic one with a power spectral density function compatible with the time varying load shows very good results.

  15. Streamflow disaggregation: a nonlinear deterministic approach

    Directory of Open Access Journals (Sweden)

    B. Sivakumar

    2004-01-01

    Full Text Available This study introduces a nonlinear deterministic approach for streamflow disaggregation. According to this approach, the streamflow transformation process from one scale to another is treated as a nonlinear deterministic process, rather than a stochastic process as generally assumed. The approach follows two important steps: (1 reconstruction of the scalar (streamflow series in a multi-dimensional phase-space for representing the transformation dynamics; and (2 use of a local approximation (nearest neighbor method for disaggregation. The approach is employed for streamflow disaggregation in the Mississippi River basin, USA. Data of successively doubled resolutions between daily and 16 days (i.e. daily, 2-day, 4-day, 8-day, and 16-day are studied, and disaggregations are attempted only between successive resolutions (i.e. 2-day to daily, 4-day to 2-day, 8-day to 4-day, and 16-day to 8-day. Comparisons between the disaggregated values and the actual values reveal excellent agreements for all the cases studied, indicating the suitability of the approach for streamflow disaggregation. A further insight into the results reveals that the best results are, in general, achieved for low embedding dimensions (2 or 3 and small number of neighbors (less than 50, suggesting possible presence of nonlinear determinism in the underlying transformation process. A decrease in accuracy with increasing disaggregation scale is also observed, a possible implication of the existence of a scaling regime in streamflow.

  16. Design of deterministic OS for SPLC

    International Nuclear Information System (INIS)

    Son, Choul Woong; Kim, Dong Hoon; Son, Gwang Seop

    2012-01-01

    Existing safety PLCs for using in nuclear power plants operates based on priority based scheduling, in which the highest priority task runs first. This type of scheduling scheme determines processing priorities when multiple requests for processing or when there is a lack of resources available for processing, guaranteeing execution of higher priority tasks. This type of scheduling is prone to exhaustion of resources and continuous preemptions by devices with high priorities, and therefore there is uncertainty every period in terms of smooth running of the overall system. Hence, it is difficult to apply this type of scheme to where deterministic operation is required, such as in nuclear power plant. Also, existing PLCs either have no output logic with regard to devices' redundant selection or it was set in a fixed way, and as a result it was extremely inefficient to use them for redundant systems such as that of a nuclear power plant and their use was limited. Therefore, functional modules that can manage and control all devices need to be developed by improving on the way priorities are assigned among the devices, making it more flexible. A management module should be able to schedule all devices of the system, manage resources, analyze states of the devices, and give warnings in case of abnormal situations, such as device fail or resource scarcity and decide on how to handle it. Also, the management module should have output logic for device redundancy, as well as deterministic processing capabilities, such as with regard to device interrupt events

  17. Deterministic sensitivity analysis for the numerical simulation of contaminants transport

    International Nuclear Information System (INIS)

    Marchand, E.

    2007-12-01

    The questions of safety and uncertainty are central to feasibility studies for an underground nuclear waste storage site, in particular the evaluation of uncertainties about safety indicators which are due to uncertainties concerning properties of the subsoil or of the contaminants. The global approach through probabilistic Monte Carlo methods gives good results, but it requires a large number of simulations. The deterministic method investigated here is complementary. Based on the Singular Value Decomposition of the derivative of the model, it gives only local information, but it is much less demanding in computing time. The flow model follows Darcy's law and the transport of radionuclides around the storage site follows a linear convection-diffusion equation. Manual and automatic differentiation are compared for these models using direct and adjoint modes. A comparative study of both probabilistic and deterministic approaches for the sensitivity analysis of fluxes of contaminants through outlet channels with respect to variations of input parameters is carried out with realistic data provided by ANDRA. Generic tools for sensitivity analysis and code coupling are developed in the Caml language. The user of these generic platforms has only to provide the specific part of the application in any language of his choice. We also present a study about two-phase air/water partially saturated flows in hydrogeology concerning the limitations of the Richards approximation and of the global pressure formulation used in petroleum engineering. (author)

  18. A study of deterministic models for quantum mechanics

    International Nuclear Information System (INIS)

    Sutherland, R.

    1980-01-01

    A theoretical investigation is made into the difficulties encountered in constructing a deterministic model for quantum mechanics and into the restrictions that can be placed on the form of such a model. The various implications of the known impossibility proofs are examined. A possible explanation for the non-locality required by Bell's proof is suggested in terms of backward-in-time causality. The efficacy of the Kochen and Specker proof is brought into doubt by showing that there is a possible way of avoiding its implications in the only known physically realizable situation to which it applies. A new thought experiment is put forward to show that a particle's predetermined momentum and energy values cannot satisfy the laws of momentum and energy conservation without conflicting with the predictions of quantum mechanics. Attention is paid to a class of deterministic models for which the individual outcomes of measurements are not dependent on hidden variables associated with the measuring apparatus and for which the hidden variables of a particle do not need to be randomized after each measurement

  19. Integrated deterministic and probabilistic safety assessment: Concepts, challenges, research directions

    International Nuclear Information System (INIS)

    Zio, Enrico

    2014-01-01

    Highlights: • IDPSA contributes to robust risk-informed decision making in nuclear safety. • IDPSA considers time-dependent interactions among component failures and system process. • Also, IDPSA considers time-dependent interactions among control and operator actions. • Computational efficiency by advanced Monte Carlo and meta-modelling simulations. • Efficient post-processing of IDPSA output by clustering and data mining. - Abstract: Integrated deterministic and probabilistic safety assessment (IDPSA) is conceived as a way to analyze the evolution of accident scenarios in complex dynamic systems, like nuclear, aerospace and process ones, accounting for the mutual interactions between the failure and recovery of system components, the evolving physical processes, the control and operator actions, the software and firmware. In spite of the potential offered by IDPSA, several challenges need to be effectively addressed for its development and practical deployment. In this paper, we give an overview of these and discuss the related implications in terms of research perspectives

  20. Analysis of deterministic cyclic gene regulatory network models with delays

    CERN Document Server

    Ahsen, Mehmet Eren; Niculescu, Silviu-Iulian

    2015-01-01

    This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.

  1. Integrated deterministic and probabilistic safety assessment: Concepts, challenges, research directions

    Energy Technology Data Exchange (ETDEWEB)

    Zio, Enrico, E-mail: enrico.zio@ecp.fr [Ecole Centrale Paris and Supelec, Chair on System Science and the Energetic Challenge, European Foundation for New Energy – Electricite de France (EDF), Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex (France); Dipartimento di Energia, Politecnico di Milano, Via Ponzio 34/3, 20133 Milano (Italy)

    2014-12-15

    Highlights: • IDPSA contributes to robust risk-informed decision making in nuclear safety. • IDPSA considers time-dependent interactions among component failures and system process. • Also, IDPSA considers time-dependent interactions among control and operator actions. • Computational efficiency by advanced Monte Carlo and meta-modelling simulations. • Efficient post-processing of IDPSA output by clustering and data mining. - Abstract: Integrated deterministic and probabilistic safety assessment (IDPSA) is conceived as a way to analyze the evolution of accident scenarios in complex dynamic systems, like nuclear, aerospace and process ones, accounting for the mutual interactions between the failure and recovery of system components, the evolving physical processes, the control and operator actions, the software and firmware. In spite of the potential offered by IDPSA, several challenges need to be effectively addressed for its development and practical deployment. In this paper, we give an overview of these and discuss the related implications in terms of research perspectives.

  2. Development of a model for unsteady deterministic stresses adapted to the multi-stages turbomachines simulation; Developpement d'un modele de tensions deterministes instationnaires adapte a la simulation de turbomachines multi-etagees

    Energy Technology Data Exchange (ETDEWEB)

    Charbonnier, D.

    2004-12-15

    The physical phenomena observed in turbomachines are generally three-dimensional and unsteady. A recent study revealed that a three-dimensional steady simulation can reproduce the time-averaged unsteady phenomena, since the steady flow field equations integrate deterministic stresses. The objective of this work is thus to develop an unsteady deterministic stresses model. The analogy with turbulence makes it possible to write transport equations for these stresses. The equations are implemented in steady flow solver and e model for the energy deterministic fluxes is also developed and implemented. Finally, this work shows that a three-dimensional steady simulation, by taking into account unsteady effects with transport equations of deterministic stresses, increases the computing time by only approximately 30 %, which remains very interesting compared to an unsteady simulation. (author)

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

    Energy Technology Data Exchange (ETDEWEB)

    Abraham, Simon, E-mail: Simon.Abraham@ulb.ac.be [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium); Raisee, Mehrdad [School of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box: 11155-4563, Tehran (Iran, Islamic Republic of); Ghorbaniasl, Ghader; Contino, Francesco; Lacor, Chris [Vrije Universiteit Brussel (VUB), Department of Mechanical Engineering, Research Group Fluid Mechanics and Thermodynamics, Pleinlaan 2, 1050 Brussels (Belgium)

    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 selection 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.

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

    Science.gov (United States)

    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.

  5. Crossover ensembles of random matrices and skew-orthogonal polynomials

    International Nuclear Information System (INIS)

    Kumar, Santosh; Pandey, Akhilesh

    2011-01-01

    Highlights: → We study crossover ensembles of Jacobi family of random matrices. → We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. → We use the method of skew-orthogonal polynomials and quaternion determinants. → We prove universality of spectral correlations in crossover ensembles. → We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.

  6. Conditional Density Approximations with Mixtures of Polynomials

    DEFF Research Database (Denmark)

    Varando, Gherardo; López-Cruz, Pedro L.; Nielsen, Thomas Dyhre

    2015-01-01

    Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce...... two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities...

  7. A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

    Directory of Open Access Journals (Sweden)

    Stefano Chinaglia

    2017-09-01

    Full Text Available Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.

  8. Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

    International Nuclear Information System (INIS)

    Feng Yi-Fu; Zhang Qing-Ling; Feng De-Zhi

    2012-01-01

    The global stability problem of Takagi—Sugeno (T—S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov—Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches

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

    Science.gov (United States)

    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.

  10. Polynomial curve fitting for control rod worth using least square numerical analysis

    International Nuclear Information System (INIS)

    Muhammad Husamuddin Abdul Khalil; Mark Dennis Usang; Julia Abdul Karim; Mohd Amin Sharifuldin Salleh

    2012-01-01

    RTP must have sufficient excess reactivity to compensate the negative reactivity feedback effects such as those caused by the fuel temperature and power defects of reactivity, fuel burn-up and to allow full power operation for predetermined period of time. To compensate this excess reactivity, it is necessary to introduce an amount of negative reactivity by adjusting or controlling the control rods at will. Control rod worth depends largely upon the value of the neutron flux at the location of the rod and reflected by a polynomial curve. Purpose of this paper is to rule out the polynomial curve fitting using least square numerical techniques via MATLAB compatible language. (author)

  11. Analytical theory for artificial satellites. [nominal orbit expressed by means of Chebyshev polynomials

    Science.gov (United States)

    Deprit, A.

    1975-01-01

    A theory for generating segmented ephemerides is discussed as a means for fast generation and simple retrieval of nominal orbit data. Over a succession of finite intervals of time, the orbit is represented by a best approximation expressed by Chebyshev polynomials. Storage of coefficients tables for Chebyshev polynomials is seen as a method to reduce data and decrease transmission costs. A general algorithm was constructed and computer programs were designed. The possibility of storing an ephemeris for a few days in the on-board computer, or in microprocessors attached to the data collectors is suggested.

  12. A Synoptic of Software Implementation for Shift Registers Based on 16th Degree Primitive Polynomials

    Directory of Open Access Journals (Sweden)

    Mirella Amelia Mioc

    2016-08-01

    Full Text Available Almost all of the major applications in the specific Fields of Communication used a well-known device called Linear Feedback Shift Register. Usually LFSR functions in a Galois Field GF(2n, meaning that all the operations are done with arithmetic modulo n degree Irreducible  and especially  Primitive Polynomials. Storing data in Galois Fields allows effective and manageable manipulation, mainly in computer cryptographic applications. The analysis of functioning for Primitive Polynomials of 16th degree shows that almost all the obtained results are in the same time distribution.

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

    Science.gov (United States)

    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.

  14. Inferring hierarchical clustering structures by deterministic annealing

    International Nuclear Information System (INIS)

    Hofmann, T.; Buhmann, J.M.

    1996-01-01

    The unsupervised detection of hierarchical structures is a major topic in unsupervised learning and one of the key questions in data analysis and representation. We propose a novel algorithm for the problem of learning decision trees for data clustering and related problems. In contrast to many other methods based on successive tree growing and pruning, we propose an objective function for tree evaluation and we derive a non-greedy technique for tree growing. Applying the principles of maximum entropy and minimum cross entropy, a deterministic annealing algorithm is derived in a meanfield approximation. This technique allows us to canonically superimpose tree structures and to fit parameters to averaged or open-quote fuzzified close-quote trees

  15. Mechanics from Newton's laws to deterministic chaos

    CERN Document Server

    Scheck, Florian

    2018-01-01

    This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science.   Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics.   The book contains more than 150 problems ...

  16. Deterministic effects of interventional radiology procedures

    International Nuclear Information System (INIS)

    Shope, Thomas B.

    1997-01-01

    The purpose of this paper is to describe deterministic radiation injuries reported to the Food and Drug Administration (FDA) that resulted from therapeutic, interventional procedures performed under fluoroscopic guidance, and to investigate the procedure or equipment-related factors that may have contributed to the injury. Reports submitted to the FDA under both mandatory and voluntary reporting requirements which described radiation-induced skin injuries from fluoroscopy were investigated. Serious skin injuries, including moist desquamation and tissues necrosis, have occurred since 1992. These injuries have resulted from a variety of interventional procedures which have required extended periods of fluoroscopy compared to typical diagnostic procedures. Facilities conducting therapeutic interventional procedures need to be aware of the potential for patient radiation injury and take appropriate steps to limit the potential for injury. (author)

  17. Deterministic SLIR model for tuberculosis disease mapping

    Science.gov (United States)

    Aziz, Nazrina; Diah, Ijlal Mohd; Ahmad, Nazihah; Kasim, Maznah Mat

    2017-11-01

    Tuberculosis (TB) occurs worldwide. It can be transmitted to others directly through air when active TB persons sneeze, cough or spit. In Malaysia, it was reported that TB cases had been recognized as one of the most infectious disease that lead to death. Disease mapping is one of the methods that can be used as the prevention strategies since it can displays clear picture for the high-low risk areas. Important thing that need to be considered when studying the disease occurrence is relative risk estimation. The transmission of TB disease is studied through mathematical model. Therefore, in this study, deterministic SLIR models are used to estimate relative risk for TB disease transmission.

  18. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    International Nuclear Information System (INIS)

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

    2003-01-01

    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

  19. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    Science.gov (United States)

    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.

  20. Polynomial solutions of the Monge-Ampère equation

    Energy Technology Data Exchange (ETDEWEB)

    Aminov, Yu A [B.Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar' kov (Ukraine)

    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 of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.

  1. Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials

    International Nuclear Information System (INIS)

    Gruenbaum, F A; Vinet, Luc; Zhedanov, Alexei

    2004-01-01

    We study operator pencils on generators of the Lie algebras sl 2 and the oscillator algebra. These pencils are linear in a spectral parameter λ. The corresponding generalized eigenvalue problem gives rise to some sets of orthogonal polynomials and Laurent biorthogonal polynomials (LBP) expressed in terms of the Gauss 2 F 1 and degenerate 1 F 1 hypergeometric functions. For special choices of the parameters of the pencils, we identify the resulting polynomials with the Hendriksen-van Rossum LBP which are widely believed to be the biorthogonal analogues of the classical orthogonal polynomials. This places these examples under the umbrella of the generalized bispectral problem which is considered here. Other (non-bispectral) cases give rise to some 'nonclassical' orthogonal polynomials including Tricomi-Carlitz and random-walk polynomials. An application to solutions of relativistic Toda chain is considered

  2. Least squares orthogonal polynomial approximation in several independent variables

    International Nuclear Information System (INIS)

    Caprari, R.S.

    1992-06-01

    This paper begins with an exposition of a systematic technique for generating orthonormal polynomials in two independent variables by application of the Gram-Schmidt orthogonalization procedure of linear algebra. It is then demonstrated how a linear least squares approximation for experimental data or an arbitrary function can be generated from these polynomials. The least squares coefficients are computed without recourse to matrix arithmetic, which ensures both numerical stability and simplicity of implementation as a self contained numerical algorithm. The Gram-Schmidt procedure is then utilised to generate a complete set of orthogonal polynomials of fourth degree. A theory for the transformation of the polynomial representation from an arbitrary basis into the familiar sum of products form is presented, together with a specific implementation for fourth degree polynomials. Finally, the computational integrity of this algorithm is verified by reconstructing arbitrary fourth degree polynomials from their values at randomly chosen points in their domain. 13 refs., 1 tab

  3. Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks

    Czech Academy of Sciences Publication Activity Database

    Knížek, J.; Tichý, Petr; Beránek, L.; Šindelář, Jan; Vojtěšek, B.; Bouchal, P.; Nenutil, R.; Dedík, O.

    2010-01-01

    Roč. 7, č. 10 (2010), s. 48-60 ISSN 0974-5718 Grant - others:GA MZd(CZ) NS9812; GA ČR(CZ) GAP304/10/0868 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10750506 Keywords : polynomial regression * orthogonalization * numerical methods * markers * biomarkers Subject RIV: BA - General Mathematics

  4. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    OpenAIRE

    Ndayiragije, François; Van Assche, Walter

    2013-01-01

    Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to $r>1$ different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Followi...

  5. On Roots of Polynomials and Algebraically Closed Fields

    Directory of Open Access Journals (Sweden)

    Schwarzweller Christoph

    2017-10-01

    Full Text Available In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

  6. Open Problems Related to the Hurwitz Stability of Polynomials Segments

    Directory of Open Access Journals (Sweden)

    Baltazar Aguirre-Hernández

    2018-01-01

    Full Text Available In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.

  7. General quantum polynomials: irreducible modules and Morita equivalence

    International Nuclear Information System (INIS)

    Artamonov, V A

    1999-01-01

    In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials

  8. Applications of polynomial optimization in financial risk investment

    Science.gov (United States)

    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.

  9. Root and Critical Point Behaviors of Certain Sums of Polynomials

    Indian Academy of Sciences (India)

    13

    There is an extensive literature concerning roots of sums of polynomials. Many papers and books([5], [6],. [7]) have written about these polynomials. Perhaps the most immediate question of sums of polynomials,. A + B = C, is “given bounds for the roots of A and B, what bounds can be given for the roots of C?” By. Fell [3], if ...

  10. Measures of thermodynamic irreversibility in deterministic and stochastic dynamics

    International Nuclear Information System (INIS)

    Ford, Ian J

    2015-01-01

    It is generally observed that if a dynamical system is sufficiently complex, then as time progresses it will share out energy and other properties amongst its component parts to eliminate any initial imbalances, retaining only fluctuations. This is known as energy dissipation and it is closely associated with the concept of thermodynamic irreversibility, measured by the increase in entropy according to the second law. It is of interest to quantify such behaviour from a dynamical rather than a thermodynamic perspective and to this end stochastic entropy production and the time-integrated dissipation function have been introduced as analogous measures of irreversibility, principally for stochastic and deterministic dynamics, respectively. We seek to compare these measures. First we modify the dissipation function to allow it to measure irreversibility in situations where the initial probability density function (pdf) of the system is asymmetric as well as symmetric in velocity. We propose that it tests for failure of what we call the obversibility of the system, to be contrasted with reversibility, the failure of which is assessed by stochastic entropy production. We note that the essential difference between stochastic entropy production and the time-integrated modified dissipation function lies in the sequence of procedures undertaken in the associated tests of irreversibility. We argue that an assumed symmetry of the initial pdf with respect to velocity inversion (within a framework of deterministic dynamics) can be incompatible with the Past Hypothesis, according to which there should be a statistical distinction between the behaviour of certain properties of an isolated system as it evolves into the far future and the remote past. Imposing symmetry on a velocity distribution is acceptable for many applications of statistical physics, but can introduce difficulties when discussing irreversible behaviour. (paper)

  11. Simulation of aspheric tolerance with polynomial fitting

    Science.gov (United States)

    Li, Jing; Cen, Zhaofeng; Li, Xiaotong

    2018-01-01

    The shape of the aspheric lens changes caused by machining errors, resulting in a change in the optical transfer function, which affects the image quality. At present, there is no universally recognized tolerance criterion standard for aspheric surface. To study the influence of aspheric tolerances on the optical transfer function, the tolerances of polynomial fitting are allocated on the aspheric surface, and the imaging simulation is carried out by optical imaging software. Analysis is based on a set of aspheric imaging system. The error is generated in the range of a certain PV value, and expressed as a form of Zernike polynomial, which is added to the aspheric surface as a tolerance term. Through optical software analysis, the MTF of optical system can be obtained and used as the main evaluation index. Evaluate whether the effect of the added error on the MTF of the system meets the requirements of the current PV value. Change the PV value and repeat the operation until the acceptable maximum allowable PV value is obtained. According to the actual processing technology, consider the error of various shapes, such as M type, W type, random type error. The new method will provide a certain development for the actual free surface processing technology the reference value.

  12. Quadratic polynomial interpolation on triangular domain

    Science.gov (United States)

    Li, Ying; Zhang, Congcong; Yu, Qian

    2018-04-01

    In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

  13. Positive trigonometric polynomials and signal processing applications

    CERN Document Server

    Dumitrescu, Bogdan

    2017-01-01

    This revised edition is made up of two parts: theory and applications. Though many of the fundamental results are still valid and used, new and revised material is woven throughout the text. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly. The applications section is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semi-definite programming form, ready to be solved with algorithms freely available, like those from the libraries SeDuMi, CVX and Pos3Poly. A new chapter discusses applications in super-resolution theory, where Bounded Real Lemma for trigonometric polynomials is an important tool. This revision is written to be more appealing and easier to use for new readers. < Features updated information on LMI...

  14. From sequences to polynomials and back, via operator orderings

    Energy Technology Data Exchange (ETDEWEB)

    Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)

    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.

  15. On Multiple Interpolation Functions of the -Genocchi Polynomials

    Directory of Open Access Journals (Sweden)

    Jin Jeong-Hee

    2010-01-01

    Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.

  16. Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials

    Directory of Open Access Journals (Sweden)

    Oksana Bihun

    2018-01-01

    Full Text Available Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived. The generalization is based on a modification of pseudospectral matrix representations of linear differential operators proposed in the paper, which allows these representations to depend on two, rather than one, sets of interpolation nodes. The identities hold for every polynomial family pνxν=0∞ orthogonal with respect to a measure supported on the real line that satisfies some standard assumptions, as long as the polynomials in the family satisfy differential equations Apν(x=qν(xpν(x, where A is a linear differential operator and each qν(x is a polynomial of degree at most n0∈N; n0 does not depend on ν. The proposed identities generalize known identities for classical and Krall orthogonal polynomials, to the case of the nonclassical orthogonal polynomials that belong to the class described above. The generalized pseudospectral representations of the differential operator A for the case of the Sonin-Markov orthogonal polynomials, also known as generalized Hermite polynomials, are presented. The general result is illustrated by new algebraic relations satisfied by the zeros of the Sonin-Markov polynomials.

  17. A deterministic algorithm for fitting a step function to a weighted point-set

    KAUST Repository

    Fournier, Hervé ; Vigneron, Antoine E.

    2013-01-01

    Given a set of n points in the plane, each point having a positive weight, and an integer k>0, we present an optimal O(nlogn)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance

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

    Science.gov (United States)

    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 ...

  19. Distributed Design of a Central Service to Ensure Deterministic Behavior

    Directory of Open Access Journals (Sweden)

    Imran Ali Jokhio

    2012-10-01

    Full Text Available A central authentication service to EPC (Electronic Product Code system architecture is proposed in our previous work. A challenge for a central service always arises that how it can ensure a certain level of delay while processing emergent data. The increasing data in the EPC system architecture is tags data. Therefore, authenticating increasing number of tag in the central authentication service with a deterministic time response is investigated and a distributed authentication service is designed in a layered approach. A distributed design of tag searching services in SOA (Service Oriented Architecture style is also presented. Using the SOA architectural style a self-adaptive authentication service over Cloud is also proposed for the central authentication service, that may also be extended for other applications.

  20. Molecular dynamics with deterministic and stochastic numerical methods

    CERN Document Server

    Leimkuhler, Ben

    2015-01-01

    This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.  Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method...

  1. Polynomial pseudosupersymmetry underlying a two-level atom in an external electromagnetic field

    International Nuclear Information System (INIS)

    Samsonov, B.F.; Shamshutdinova, V.V.; Gitman, D.M.

    2005-01-01

    Chains of transformations introduced previously were studied in order to obtain electric fields with a time-dependent frequency for which the equation of motion of a two-level atom in the presence of these fields can be solved exactly. It is shown that a polynomial pseudosupersymmetry may be associated to such chains

  2. A Gradient Weighted Moving Finite-Element Method with Polynomial Approximation of Any Degree

    Directory of Open Access Journals (Sweden)

    Ali R. Soheili

    2009-01-01

    Full Text Available A gradient weighted moving finite element method (GWMFE based on piecewise polynomial of any degree is developed to solve time-dependent problems in two space dimensions. Numerical experiments are employed to test the accuracy and effciency of the proposed method with nonlinear Burger equation.

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

  5. Deterministic Earthquake Hazard Assessment by Public Agencies in California

    Science.gov (United States)

    Mualchin, L.

    2005-12-01

    Even in its short recorded history, California has experienced a number of damaging earthquakes that have resulted in new codes and other legislation for public safety. In particular, the 1971 San Fernando earthquake produced some of the most lasting results such as the Hospital Safety Act, the Strong Motion Instrumentation Program, the Alquist-Priolo Special Studies Zone Act, and the California Department of Transportation (Caltrans') fault-based deterministic seismic hazard (DSH) map. The latter product provides values for earthquake ground motions based on Maximum Credible Earthquakes (MCEs), defined as the largest earthquakes that can reasonably be expected on faults in the current tectonic regime. For surface fault rupture displacement hazards, detailed study of the same faults apply. Originally, hospital, dam, and other critical facilities used seismic design criteria based on deterministic seismic hazard analyses (DSHA). However, probabilistic methods grew and took hold by introducing earthquake design criteria based on time factors and quantifying "uncertainties", by procedures such as logic trees. These probabilistic seismic hazard analyses (PSHA) ignored the DSH approach. Some agencies were influenced to adopt only the PSHA method. However, deficiencies in the PSHA method are becoming recognized, and the use of the method is now becoming a focus of strong debate. Caltrans is in the process of producing the fourth edition of its DSH map. The reason for preferring the DSH method is that Caltrans believes it is more realistic than the probabilistic method for assessing earthquake hazards that may affect critical facilities, and is the best available method for insuring public safety. Its time-invariant values help to produce robust design criteria that are soundly based on physical evidence. And it is the method for which there is the least opportunity for unwelcome surprises.

  6. Improving Deterministic Reserve Requirements for Security Constrained Unit Commitment and Scheduling Problems in Power Systems

    Science.gov (United States)

    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

  7. Experimental aspects of deterministic secure quantum key distribution

    Energy Technology Data Exchange (ETDEWEB)

    Walenta, Nino; Korn, Dietmar; Puhlmann, Dirk; Felbinger, Timo; Hoffmann, Holger; Ostermeyer, Martin [Universitaet Potsdam (Germany). Institut fuer Physik; Bostroem, Kim [Universitaet Muenster (Germany)

    2008-07-01

    Most common protocols for quantum key distribution (QKD) use non-deterministic algorithms to establish a shared key. But deterministic implementations can allow for higher net key transfer rates and eavesdropping detection rates. The Ping-Pong coding scheme by Bostroem and Felbinger[1] employs deterministic information encoding in entangled states with its characteristic quantum channel from Bob to Alice and back to Bob. Based on a table-top implementation of this protocol with polarization-entangled photons fundamental advantages as well as practical issues like transmission losses, photon storage and requirements for progress towards longer transmission distances are discussed and compared to non-deterministic protocols. Modifications of common protocols towards a deterministic quantum key distribution are addressed.

  8. Relations between zeros of special polynomials associated with the Painleve equations

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2007-01-01

    A method for finding relations of roots of polynomials is presented. Our approach allows us to get a number of relations between the zeros of the classical polynomials as well as the roots of special polynomials associated with rational solutions of the Painleve equations. We apply the method to obtain the relations for the zeros of several polynomials. These are: the Hermite polynomials, the Laguerre polynomials, the Yablonskii-Vorob'ev polynomials, the generalized Okamoto polynomials, and the generalized Hermite polynomials. All the relations found can be considered as analogues of generalized Stieltjes relations

  9. Exploring the stochastic and deterministic aspects of cyclic emission variability on a high speed spark-ignition engine

    International Nuclear Information System (INIS)

    Karvountzis-Kontakiotis, A.; Dimaratos, A.; Ntziachristos, L.; Samaras, Z.

    2017-01-01

    This study contributes to the understanding of cycle-to-cycle emissions variability (CEV) in premixed spark-ignition combustion engines. A number of experimental investigations of cycle-to-cycle combustion variability (CCV) exist in published literature; however only a handful of studies deal with CEV. This study experimentally investigates the impact of CCV on CEV of NO and CO, utilizing experimental results from a high-speed spark-ignition engine. Both CEV and CCV are shown to comprise a deterministic and a stochastic component. Results show that at maximum break torque (MBT) operation, the indicated mean effective pressure (IMEP) maximizes and its coefficient of variation (COV_I_M_E_P) minimizes, leading to minimum variation of NO. NO variability and hence mean NO levels can be reduced by more than 50% and 30%, respectively, at advanced ignition timing, by controlling the deterministic CCV using cycle resolved combustion control. The deterministic component of CEV increases at lean combustion (lambda = 1.12) and this overall increases NO variability. CEV was also found to decrease with engine load. At steady speed, increasing throttle position from 20% to 80%, decreased COV_I_M_E_P, COV_N_O and COV_C_O by 59%, 46%, and 6% respectively. Highly resolved engine control, by means of cycle-to-cycle combustion control, appears as key to limit the deterministic feature of cyclic variability and by that to overall reduce emission levels. - Highlights: • Engine emissions variability comprise both stochastic and deterministic components. • Lean and diluted combustion conditions increase emissions variability. • Advanced ignition timing enhances the deterministic component of variability. • Load increase decreases the deterministic component of variability. • The deterministic component can be reduced by highly resolved combustion control.

  10. Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

    Science.gov (United States)

    Dobronets, B. S.; Popova, O. A.

    2018-05-01

    Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.

  11. Current advances on polynomial resultant formulations

    Science.gov (United States)

    Sulaiman, Surajo; Aris, Nor'aini; Ahmad, Shamsatun Nahar

    2017-08-01

    Availability of computer algebra systems (CAS) lead to the resurrection of the resultant method for eliminating one or more variables from the polynomials system. The resultant matrix method has advantages over the Groebner basis and Ritt-Wu method due to their high complexity and storage requirement. This paper focuses on the current resultant matrix formulations and investigates their ability or otherwise towards producing optimal resultant matrices. A determinantal formula that gives exact resultant or a formulation that can minimize the presence of extraneous factors in the resultant formulation is often sought for when certain conditions that it exists can be determined. We present some applications of elimination theory via resultant formulations and examples are given to explain each of the presented settings.

  12. Differential operators associated with Hermite polynomials

    International Nuclear Information System (INIS)

    Onyango Otieno, V.P.

    1989-09-01

    This paper considers the boundary value problems for the Hermite differential equation -(e -x2 y'(x))'+e -x2 y(x)=λe -x2 y(x), (x is an element of (-∞, ∞)) in both the so-called right-definite and left-definite cases based partly on a classical approach due to E.C. Titchmarsh. We then link the Titchmarsh approach with operator theoretic results in the spaces L w 2 (-∞, ∞) and H p,q 2 (-∞, ∞). The results in the left-definite case provide an indirect proof of the completeness of the Hermite polynomials in L w 2 (-∞, ∞). (author). 17 refs

  13. Absorbing phase transitions in deterministic fixed-energy sandpile models

    Science.gov (United States)

    Park, Su-Chan

    2018-03-01

    We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010), 10.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a microscopic absorbing phase transition, or a so-called spreading dynamics, of the BTW-FES, to find that the phase transition in this setting is related to the dynamical isotropic percolation process rather than self-organized criticality. In particular, we argue that choosing recurrent configurations of the corresponding ASM as an initial configuration does not allow for a nontrivial APT in the DFES.

  14. Connection coefficients between Boas-Buck polynomial sets

    Science.gov (United States)

    Cheikh, Y. Ben; Chaggara, H.

    2006-07-01

    In this paper, a general method to express explicitly connection coefficients between two Boas-Buck polynomial sets is presented. As application, we consider some generalized hypergeometric polynomials, from which we derive some well-known results including duplication and inversion formulas.

  15. Mathematical Use Of Polynomials Of Different End Periods Of ...

    African Journals Online (AJOL)

    This paper focused on how polynomials of different end period of random numbers can be used in the application of encryption and decryption of a message. Eight steps were used in generating information on how polynomials of different end periods of random numbers in the application of encryption and decryption of a ...

  16. On the Lorentz degree of a product of polynomials

    KAUST Repository

    Ait-Haddou, Rachid

    2015-01-01

    In this note, we negatively answer two questions of T. Erdélyi (1991, 2010) on possible lower bounds on the Lorentz degree of product of two polynomials. We show that the correctness of one question for degree two polynomials is a direct consequence

  17. On polynomial selection for the general number field sieve

    Science.gov (United States)

    Kleinjung, Thorsten

    2006-12-01

    The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

  18. A Combinatorial Proof of a Result on Generalized Lucas Polynomials

    Directory of Open Access Journals (Sweden)

    Laugier Alexandre

    2016-09-01

    Full Text Available We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2. The initial values are 〈0〉 = 2; 〈1〉= s, respectively.

  19. Animating Nested Taylor Polynomials to Approximate a Function

    Science.gov (United States)

    Mazzone, Eric F.; Piper, Bruce R.

    2010-01-01

    The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…

  20. Some Results on the Independence Polynomial of Unicyclic Graphs

    Directory of Open Access Journals (Sweden)

    Oboudi Mohammad Reza

    2018-05-01

    Full Text Available Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x=∑k=0ns(G,kxk$I(G,x = \\sum\

  1. Generalized Freud's equation and level densities with polynomial

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.

  2. Deterministic models for energy-loss straggling

    International Nuclear Information System (INIS)

    Prinja, A.K.; Gleicher, F.; Dunham, G.; Morel, J.E.

    1999-01-01

    Inelastic ion interactions with target electrons are dominated by extremely small energy transfers that are difficult to resolve numerically. The continuous-slowing-down (CSD) approximation is then commonly employed, which, however, only preserves the mean energy loss per collision through the stopping power, S(E) = ∫ 0 ∞ dEprime (E minus Eprime) σ s (E → Eprime). To accommodate energy loss straggling, a Gaussian distribution with the correct mean-squared energy loss (akin to a Fokker-Planck approximation in energy) is commonly used in continuous-energy Monte Carlo codes. Although this model has the unphysical feature that ions can be upscattered, it nevertheless yields accurate results. A multigroup model for energy loss straggling was recently presented for use in multigroup Monte Carlo codes or in deterministic codes that use multigroup data. The method has the advantage that the mean and mean-squared energy loss are preserved without unphysical upscatter and hence is computationally efficient. Results for energy spectra compared extremely well with Gaussian distributions under the idealized conditions for which the Gaussian may be considered to be exact. Here, the authors present more consistent comparisons by extending the method to accommodate upscatter and, further, compare both methods with exact solutions obtained from an analog Monte Carlo simulation, for a straight-ahead transport problem

  3. A Deterministic Approach to Earthquake Prediction

    Directory of Open Access Journals (Sweden)

    Vittorio Sgrigna

    2012-01-01

    Full Text Available The paper aims at giving suggestions for a deterministic approach to investigate possible earthquake prediction and warning. A fundamental contribution can come by observations and physical modeling of earthquake precursors aiming at seeing in perspective the phenomenon earthquake within the framework of a unified theory able to explain the causes of its genesis, and the dynamics, rheology, and microphysics of its preparation, occurrence, postseismic relaxation, and interseismic phases. Studies based on combined ground and space observations of earthquake precursors are essential to address the issue. Unfortunately, up to now, what is lacking is the demonstration of a causal relationship (with explained physical processes and looking for a correlation between data gathered simultaneously and continuously by space observations and ground-based measurements. In doing this, modern and/or new methods and technologies have to be adopted to try to solve the problem. Coordinated space- and ground-based observations imply available test sites on the Earth surface to correlate ground data, collected by appropriate networks of instruments, with space ones detected on board of Low-Earth-Orbit (LEO satellites. Moreover, a new strong theoretical scientific effort is necessary to try to understand the physics of the earthquake.

  4. Deterministic dense coding and entanglement entropy

    International Nuclear Information System (INIS)

    Bourdon, P. S.; Gerjuoy, E.; McDonald, J. P.; Williams, H. T.

    2008-01-01

    We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of nonmaximally entangled qudits in a pure state |ψ>. Our results include the following: (i) We prove that it is possible for a state |ψ> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d=3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d+j messages, 2≤j≤d-1; moreover, we show that the j=2 and j=d-1 cases of the conjecture are valid in all dimensions. (iii) Given that |ψ> allows the sending of K messages and has √(λ 0 ) as its largest Schmidt coefficient, we show that the inequality λ 0 ≤d/K, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form λ 0 < d/K if K=d+1, while our constructions of local unitaries show that equality can be realized if K=d+2 or K=2d-1

  5. Analysis of pinching in deterministic particle separation

    Science.gov (United States)

    Risbud, Sumedh; Luo, Mingxiang; Frechette, Joelle; Drazer, German

    2011-11-01

    We investigate the problem of spherical particles vertically settling parallel to Y-axis (under gravity), through a pinching gap created by an obstacle (spherical or cylindrical, center at the origin) and a wall (normal to X axis), to uncover the physics governing microfluidic separation techniques such as deterministic lateral displacement and pinched flow fractionation: (1) theoretically, by linearly superimposing the resistances offered by the wall and the obstacle separately, (2) computationally, using the lattice Boltzmann method for particulate systems and (3) experimentally, by conducting macroscopic experiments. Both, theory and simulations, show that for a given initial separation between the particle centre and the Y-axis, presence of a wall pushes the particles closer to the obstacle, than its absence. Experimentally, this is expected to result in an early onset of the short-range repulsive forces caused by solid-solid contact. We indeed observe such an early onset, which we quantify by measuring the asymmetry in the trajectories of the spherical particles around the obstacle. This work is partially supported by the National Science Foundation Grant Nos. CBET- 0731032, CMMI-0748094, and CBET-0954840.

  6. Higher order branching of periodic orbits from polynomial isochrones

    Directory of Open Access Journals (Sweden)

    B. Toni

    1999-09-01

    Full Text Available We discuss the higher order local bifurcations of limit cycles from polynomial isochrones (linearizable centers when the linearizing transformation is explicitly known and yields a polynomial perturbation one-form. Using a method based on the relative cohomology decomposition of polynomial one-forms complemented with a step reduction process, we give an explicit formula for the overall upper bound of branch points of limit cycles in an arbitrary $n$ degree polynomial perturbation of the linear isochrone, and provide an algorithmic procedure to compute the upper bound at successive orders. We derive a complete analysis of the nonlinear cubic Hamiltonian isochrone and show that at most nine branch points of limit cycles can bifurcate in a cubic polynomial perturbation. Moreover, perturbations with exactly two, three, four, six, and nine local families of limit cycles may be constructed.

  7. Describing Quadratic Cremer Point Polynomials by Parabolic Perturbations

    DEFF Research Database (Denmark)

    Sørensen, Dan Erik Krarup

    1996-01-01

    We describe two infinite order parabolic perturbation proceduresyielding quadratic polynomials having a Cremer fixed point. The main ideais to obtain the polynomial as the limit of repeated parabolic perturbations.The basic tool at each step is to control the behaviour of certain externalrays.......Polynomials of the Cremer type correspond to parameters at the boundary of ahyperbolic component of the Mandelbrot set. In this paper we concentrate onthe main cardioid component. We investigate the differences between two-sided(i.e. alternating) and one-sided parabolic perturbations.In the two-sided case, we prove...... the existence of polynomials having an explicitlygiven external ray accumulating both at the Cremer point and at its non-periodicpreimage. We think of the Julia set as containing a "topologists double comb".In the one-sided case we prove a weaker result: the existence of polynomials havingan explicitly given...

  8. q-analogue of the Krawtchouk and Meixner orthogonal polynomials

    International Nuclear Information System (INIS)

    Campigotto, C.; Smirnov, Yu.F.; Enikeev, S.G.

    1993-06-01

    The comparative analysis of Krawtchouk polynomials on a uniform grid with Wigner D-functions for the SU(2) group is presented. As a result the partnership between corresponding properties of the polynomials and D-functions is established giving the group-theoretical interpretation of the Krawtchouk polynomials properties. In order to extend such an analysis on the quantum groups SU q (2) and SU q (1,1), q-analogues of Krawtchouk and Meixner polynomials of a discrete variable are studied. The total set of characteristics of these polynomials is calculated, including the orthogonality condition, normalization factor, recurrent relation, the explicit analytic expression, the Rodrigues formula, the difference derivative formula and various particular cases and values. (R.P.) 22 refs.; 2 tabs

  9. Primitive polynomials selection method for pseudo-random number generator

    Science.gov (United States)

    Anikin, I. V.; Alnajjar, Kh

    2018-01-01

    In this paper we suggested the method for primitive polynomials selection of special type. This kind of polynomials can be efficiently used as a characteristic polynomials for linear feedback shift registers in pseudo-random number generators. The proposed method consists of two basic steps: finding minimum-cost irreducible polynomials of the desired degree and applying primitivity tests to get the primitive ones. Finally two primitive polynomials, which was found by the proposed method, used in pseudorandom number generator based on fuzzy logic (FRNG) which had been suggested before by the authors. The sequences generated by new version of FRNG have low correlation magnitude, high linear complexity, less power consumption, is more balanced and have better statistical properties.

  10. Orthogonal polynomials derived from the tridiagonal representation approach

    Science.gov (United States)

    Alhaidari, A. D.

    2018-01-01

    The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose properties give the structure and dynamics of the corresponding physical system. For a certain range of parameters, one of these polynomials has a mix of continuous and discrete spectra making it suitable for describing physical systems with both scattering and bound states. In this work, we define these polynomials by their recursion relations and highlight some of their properties using numerical means. Due to the prime significance of these polynomials in physics, we hope that our short expose will encourage experts in the field of orthogonal polynomials to study them and derive their properties (weight functions, generating functions, asymptotics, orthogonality relations, zeros, etc.) analytically.

  11. Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

    International Nuclear Information System (INIS)

    Ndayiragije, F; Van Assche, W

    2013-01-01

    Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind. (paper)

  12. A note on some identities of derangement polynomials.

    Science.gov (United States)

    Kim, Taekyun; Kim, Dae San; Jang, Gwan-Woo; Kwon, Jongkyum

    2018-01-01

    The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255-258, 1978, Clarke and Sved in Math. Mag. 66(5):299-303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1-11 2018. A derangement is a permutation that has no fixed points, and the derangement number [Formula: see text] is the number of fixed-point-free permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higher-order and r -derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higher-order derangement polynomials by using umbral calculus.

  13. A dynamically adaptive wavelet approach to stochastic computations based on polynomial chaos - capturing all scales of random modes on independent grids

    International Nuclear Information System (INIS)

    Ren Xiaoan; Wu Wenquan; Xanthis, Leonidas S.

    2011-01-01

    Highlights: → New approach for stochastic computations based on polynomial chaos. → Development of dynamically adaptive wavelet multiscale solver using space refinement. → Accurate capture of steep gradients and multiscale features in stochastic problems. → All scales of each random mode are captured on independent grids. → Numerical examples demonstrate the need for different space resolutions per mode. - Abstract: In stochastic computations, or uncertainty quantification methods, the spectral approach based on the polynomial chaos expansion in random space leads to a coupled system of deterministic equations for the coefficients of the expansion. The size of this system increases drastically when the number of independent random variables and/or order of polynomial chaos expansions increases. This is invariably the case for large scale simulations and/or problems involving steep gradients and other multiscale features; such features are variously reflected on each solution component or random/uncertainty mode requiring the development of adaptive methods for their accurate resolution. In this paper we propose a new approach for treating such problems based on a dynamically adaptive wavelet methodology involving space-refinement on physical space that allows all scales of each solution component to be refined independently of the rest. We exemplify this using the convection-diffusion model with random input data and present three numerical examples demonstrating the salient features of the proposed method. Thus we establish a new, elegant and flexible approach for stochastic problems with steep gradients and multiscale features based on polynomial chaos expansions.

  14. Equivalence relations between deterministic and quantum mechanical systems

    International Nuclear Information System (INIS)

    Hooft, G.

    1988-01-01

    Several quantum mechanical models are shown to be equivalent to certain deterministic systems because a basis can be found in terms of which the wave function does not spread. This suggests that apparently indeterministic behavior typical for a quantum mechanical world can be the result of locally deterministic laws of physics. We show how certain deterministic systems allow the construction of a Hilbert space and a Hamiltonian so that at long distance scales they may appear to behave as quantum field theories, including interactions but as yet no mass term. These observations are suggested to be useful for building theories at the Planck scale

  15. Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes

    DEFF Research Database (Denmark)

    Starke, Jens; Reichert, Christian; Eiswirth, Markus

    2007-01-01

    Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...

  16. Operational State Complexity of Deterministic Unranked Tree Automata

    Directory of Open Access Journals (Sweden)

    Xiaoxue Piao

    2010-08-01

    Full Text Available We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic tree automata are obtained. For tree concatenation we establish a tight upper bound that is of a different order than the known state complexity of concatenation of regular string languages. We show that (n+1 ( (m+12^n-2^(n-1 -1 vertical states are sufficient, and necessary in the worst case, to recognize the concatenation of tree languages recognized by (strongly or weakly deterministic automata with, respectively, m and n vertical states.

  17. ZERODUR: deterministic approach for strength design

    Science.gov (United States)

    Hartmann, Peter

    2012-12-01

    There is an increasing request for zero expansion glass ceramic ZERODUR substrates being capable of enduring higher operational static loads or accelerations. The integrity of structures such as optical or mechanical elements for satellites surviving rocket launches, filigree lightweight mirrors, wobbling mirrors, and reticle and wafer stages in microlithography must be guaranteed with low failure probability. Their design requires statistically relevant strength data. The traditional approach using the statistical two-parameter Weibull distribution suffered from two problems. The data sets were too small to obtain distribution parameters with sufficient accuracy and also too small to decide on the validity of the model. This holds especially for the low failure probability levels that are required for reliable applications. Extrapolation to 0.1% failure probability and below led to design strengths so low that higher load applications seemed to be not feasible. New data have been collected with numbers per set large enough to enable tests on the applicability of the three-parameter Weibull distribution. This distribution revealed to provide much better fitting of the data. Moreover it delivers a lower threshold value, which means a minimum value for breakage stress, allowing of removing statistical uncertainty by introducing a deterministic method to calculate design strength. Considerations taken from the theory of fracture mechanics as have been proven to be reliable with proof test qualifications of delicate structures made from brittle materials enable including fatigue due to stress corrosion in a straight forward way. With the formulae derived, either lifetime can be calculated from given stress or allowable stress from minimum required lifetime. The data, distributions, and design strength calculations for several practically relevant surface conditions of ZERODUR are given. The values obtained are significantly higher than those resulting from the two

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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.

  20. vs. a polynomial chaos-based MCMC

    KAUST Repository

    Siripatana, Adil

    2014-08-01

    Bayesian Inference of Manning\\'s n coefficient in a Storm Surge Model Framework: comparison between Kalman lter and polynomial based method Adil Siripatana Conventional coastal ocean models solve the shallow water equations, which describe the conservation of mass and momentum when the horizontal length scale is much greater than the vertical length scale. In this case vertical pressure gradients in the momentum equations are nearly hydrostatic. The outputs of coastal ocean models are thus sensitive to the bottom stress terms de ned through the formulation of Manning\\'s n coefficients. This thesis considers the Bayesian inference problem of the Manning\\'s n coefficient in the context of storm surge based on the coastal ocean ADCIRC model. In the first part of the thesis, we apply an ensemble-based Kalman filter, the singular evolutive interpolated Kalman (SEIK) filter to estimate both a constant Manning\\'s n coefficient and a 2-D parameterized Manning\\'s coefficient on one ideal and one of more realistic domain using observation system simulation experiments (OSSEs). We study the sensitivity of the system to the ensemble size. we also access the benefits from using an in ation factor on the filter performance. To study the limitation of the Guassian restricted assumption on the SEIK lter, 5 we also implemented in the second part of this thesis a Markov Chain Monte Carlo (MCMC) method based on a Generalized Polynomial chaos (gPc) approach for the estimation of the 1-D and 2-D Mannning\\'s n coe cient. The gPc is used to build a surrogate model that imitate the ADCIRC model in order to make the computational cost of implementing the MCMC with the ADCIRC model reasonable. We evaluate the performance of the MCMC-gPc approach and study its robustness to di erent OSSEs scenario. we also compare its estimates with those resulting from SEIK in term of parameter estimates and full distributions. we present a full analysis of the solution of these two methods, of the

  1. Dynamic scheduling and analysis of real time systems with multiprocessors

    Directory of Open Access Journals (Sweden)

    M.D. Nashid Anjum

    2016-08-01

    Full Text Available This research work considers a scenario of cloud computing job-shop scheduling problems. We consider m realtime jobs with various lengths and n machines with different computational speeds and costs. Each job has a deadline to be met, and the profit of processing a packet of a job differs from other jobs. Moreover, considered deadlines are either hard or soft and a penalty is applied if a deadline is missed where the penalty is considered as an exponential function of time. The scheduling problem has been formulated as a mixed integer non-linear programming problem whose objective is to maximize net-profit. The formulated problem is computationally hard and not solvable in deterministic polynomial time. This research work proposes an algorithm named the Tube-tap algorithm as a solution to this scheduling optimization problem. Extensive simulation shows that the proposed algorithm outperforms existing solutions in terms of maximizing net-profit and preserving deadlines.

  2. Topological quantum information, virtual Jones polynomials and Khovanov homology

    International Nuclear Information System (INIS)

    Kauffman, Louis H

    2011-01-01

    In this paper, we give a quantum statistical interpretation of the bracket polynomial state sum 〈K〉, the Jones polynomial V K (t) and virtual knot theory versions of the Jones polynomial, including the arrow polynomial. We use these quantum mechanical interpretations to give new quantum algorithms for these Jones polynomials. In those cases where the Khovanov homology is defined, the Hilbert space C(K) of our model is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. There is a natural unitary transformation U:C(K) → C(K) such that 〈K〉 = Trace(U), where 〈K〉 denotes the evaluation of the state sum model for the corresponding polynomial. We show that for the Khovanov boundary operator ∂:C(K) → C(K), we have the relationship ∂U + U∂ = 0. Consequently, the operator U acts on the Khovanov homology, and we obtain a direct relationship between the Khovanov homology and this quantum algorithm for the Jones polynomial. (paper)

  3. Constructing general partial differential equations using polynomial and neural networks.

    Science.gov (United States)

    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.

  4. Fisher-Wright model with deterministic seed bank and selection.

    Science.gov (United States)

    Koopmann, Bendix; Müller, Johannes; Tellier, Aurélien; Živković, Daniel

    2017-04-01

    Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached. Copyright © 2016 Elsevier Inc. All rights reserved.

  5. The cointegrated vector autoregressive model with general deterministic terms

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Morten Ørregaard

    2017-01-01

    In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)=Z(t) Y(t), where Z(t) belongs to a large class...... of deterministic regressors and Y(t) is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended...... model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are X 2 -distributed....

  6. The cointegrated vector autoregressive model with general deterministic terms

    DEFF Research Database (Denmark)

    Johansen, Søren; Nielsen, Morten Ørregaard

    In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class...... of deterministic regressors and Y(t) is a zero-mean CVAR. We suggest an extended model that can be estimated by reduced rank regression and give a condition for when the additive and extended models are asymptotically equivalent, as well as an algorithm for deriving the additive model parameters from the extended...... model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are khi squared distributed....

  7. Method to deterministically study photonic nanostructures in different experimental instruments

    NARCIS (Netherlands)

    Husken, B.H.; Woldering, L.A.; Blum, Christian; Tjerkstra, R.W.; Vos, Willem L.

    2009-01-01

    We describe an experimental method to recover a single, deterministically fabricated nanostructure in various experimental instruments without the use of artificially fabricated markers, with the aim to study photonic structures. Therefore, a detailed map of the spatial surroundings of the

  8. Pseudo-random number generator based on asymptotic deterministic randomness

    Science.gov (United States)

    Wang, Kai; Pei, Wenjiang; Xia, Haishan; Cheung, Yiu-ming

    2008-06-01

    A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks.

  9. Pseudo-random number generator based on asymptotic deterministic randomness

    International Nuclear Information System (INIS)

    Wang Kai; Pei Wenjiang; Xia Haishan; Cheung Yiuming

    2008-01-01

    A novel approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness constructed by the piecewise linear map and the noninvertible nonlinearity transform, and then give the discretized systems in the finite digitized state space. The statistic characteristics of the asymptotic deterministic randomness are investigated numerically, such as stationary probability density function and random-like behavior. Furthermore, we analyze the dynamics of the symbolic sequence. Both theoretical and experimental results show that the symbolic sequence of the asymptotic deterministic randomness possesses very good cryptographic properties, which improve the security of chaos based PRBGs and increase the resistance against entropy attacks and symbolic dynamics attacks

  10. Non deterministic finite automata for power systems fault diagnostics

    Directory of Open Access Journals (Sweden)

    LINDEN, R.

    2009-06-01

    Full Text Available This paper introduces an application based on finite non-deterministic automata for power systems diagnosis. Automata for the simpler faults are presented and the proposed system is compared with an established expert system.

  11. Transmission power control in WSNs : from deterministic to cognitive methods

    NARCIS (Netherlands)

    Chincoli, M.; Liotta, A.; Gravina, R.; Palau, C.E.; Manso, M.; Liotta, A.; Fortino, G.

    2018-01-01

    Communications in Wireless Sensor Networks (WSNs) are affected by dynamic environments, variable signal fluctuations and interference. Thus, prompt actions are necessary to achieve dependable communications and meet Quality of Service (QoS) requirements. To this end, the deterministic algorithms

  12. The probabilistic approach and the deterministic licensing procedure

    International Nuclear Information System (INIS)

    Fabian, H.; Feigel, A.; Gremm, O.

    1984-01-01

    If safety goals are given, the creativity of the engineers is necessary to transform the goals into actual safety measures. That is, safety goals are not sufficient for the derivation of a safety concept; the licensing process asks ''What does a safe plant look like.'' The answer connot be given by a probabilistic procedure, but need definite deterministic statements; the conclusion is, that the licensing process needs a deterministic approach. The probabilistic approach should be used in a complementary role in cases where deterministic criteria are not complete, not detailed enough or not consistent and additional arguments for decision making in connection with the adequacy of a specific measure are necessary. But also in these cases the probabilistic answer has to be transformed into a clear deterministic statement. (orig.)

  13. A new modelling of the multigroup scattering cross section in deterministic codes for neutron transport

    International Nuclear Information System (INIS)

    Calloo, A.A.

    2012-01-01

    In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law using Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy respectively). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with non-zero values for a very small range of the cosine of the scattering angle. Besides, the finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of this cross section. As such, the Legendre expansion is less suited to represent the scattering law. Furthermore, this model induces negative values which are non-physical. In this work, various scattering laws are briefly described and the limitations of the existing model are pointed out. Hence, piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. The discrete ordinates method which is widely employed to solve the transport equation has been adapted. Thus, the finite volume method for angular discretization has been developed and implemented in Paris environment which hosts the S n solver, Snatch. The angular finite volume method has been compared to the collocation method with Legendre moments to ensure its proper performance. Moreover, unlike the latter, this method is adapted for both the Legendre moments and the piecewise-constant functions representations of the scattering cross section. This hybrid-source method has been validated for different cases: fuel cell in infinite lattice

  14. Dynamics of polynomial Chaplygin gas warm inflation

    Energy Technology Data Exchange (ETDEWEB)

    Jawad, Abdul [COMSATS Institute of Information Technology, Department of Mathematics, Lahore (Pakistan); Chaudhary, Shahid [Sharif College of Engineering and Technology, Department of Mathematics, Lahore (Pakistan); Videla, Nelson [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile)

    2017-11-15

    In the present work, we study the consequences of a recently proposed polynomial inflationary potential in the context of the generalized, modified, and generalized cosmic Chaplygin gas models. In addition, we consider dissipative effects by coupling the inflation field to radiation, i.e., the inflationary dynamics is studied in the warm inflation scenario. We take into account a general parametrization of the dissipative coefficient Γ for describing the decay of the inflaton field into radiation. By studying the background and perturbative dynamics in the weak and strong dissipative regimes of warm inflation separately for the positive and negative quadratic and quartic potentials, we obtain expressions for the most relevant inflationary observables as the scalar power spectrum, the scalar spectral, and the tensor-to-scalar ratio. We construct the trajectories in the n{sub s}-r plane for several expressions of the dissipative coefficient and compare with the two-dimensional marginalized contours for (n{sub s}, r) from the latest Planck data. We find that our results are in agreement with WMAP9 and Planck 2015 data. (orig.)

  15. Global sensitivity analysis using polynomial chaos expansions

    International Nuclear Information System (INIS)

    Sudret, Bruno

    2008-01-01

    Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression-based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices

  16. Global sensitivity analysis using polynomial chaos expansions

    Energy Technology Data Exchange (ETDEWEB)

    Sudret, Bruno [Electricite de France, R and D Division, Site des Renardieres, F 77818 Moret-sur-Loing Cedex (France)], E-mail: bruno.sudret@edf.fr

    2008-07-15

    Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol' indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to build surrogate models that allow one to compute the Sobol' indices analytically as a post-processing of the PCE coefficients. Thus the computational cost of the sensitivity indices practically reduces to that of estimating the PCE coefficients. An original non intrusive regression-based approach is proposed, together with an experimental design of minimal size. Various application examples illustrate the approach, both from the field of global SA (i.e. well-known benchmark problems) and from the field of stochastic mechanics. The proposed method gives accurate results for various examples that involve up to eight input random variables, at a computational cost which is 2-3 orders of magnitude smaller than the traditional Monte Carlo-based evaluation of the Sobol' indices.

  17. Polynomial Chaos Surrogates for Bayesian Inference

    KAUST Repository

    Le Maitre, Olivier

    2016-01-06

    The Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.

  18. Scattering amplitudes from multivariate polynomial division

    Energy Technology Data Exchange (ETDEWEB)

    Mastrolia, Pierpaolo, E-mail: pierpaolo.mastrolia@cern.ch [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Dipartimento di Fisica e Astronomia, Universita di Padova, Padova (Italy); INFN Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Mirabella, Edoardo, E-mail: mirabell@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Ossola, Giovanni, E-mail: GOssola@citytech.cuny.edu [New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Peraro, Tiziano, E-mail: peraro@mppmu.mpg.de [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)

    2012-11-15

    We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Groebner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

  19. q-Bernoulli numbers and q-Bernoulli polynomials revisited

    Directory of Open Access Journals (Sweden)

    Kim Taekyun

    2011-01-01

    Full Text Available Abstract This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010, some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math 48, 73-86, 1994 (see Equation 9, some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification (2000 11B68, 11S40, 11S80

  20. Generalized Freud's equation and level densities with polynomial potential

    Science.gov (United States)

    Boobna, Akshat; Ghosh, Saugata

    2013-08-01

    We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.