New results on robust exponential stability of integral delay systems
NASA Astrophysics Data System (ADS)
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
NASA Astrophysics Data System (ADS)
Mao, Yanbing; Zhang, Hongbin
2014-05-01
This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov-Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
On the Stability of Exponential Backoff
Song, Nah-Oak; Kwak, Byung-Jae; Miller, Leonard E.
2003-01-01
Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 − e−1) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed. PMID:25481670
Cauchy Problem and Exponential Stability for the Inhomogeneous Landau Equation
NASA Astrophysics Data System (ADS)
Carrapatoso, Kleber; Tristani, Isabelle; Wu, Kung-Chien
2016-07-01
This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, Maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated semigroup. We then turn to the nonlinear equation and we use the linearized semigroup decay in order to construct solutions in a close-to-equilibrium setting. Finally, we prove an exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay.
On exponential stability of gravity driven viscoelastic flows
NASA Astrophysics Data System (ADS)
Jiang, Fei; Wu, Guochun; Zhong, Xin
2016-05-01
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω ⊂R3 of class C3. First, we establish a critical number κC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ >κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ bar is a Rayleigh-Taylor (RT) type and ρbar‧ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
NASA Astrophysics Data System (ADS)
Chen, Huabin; Zhao, Yang
2015-10-01
This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov-Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.
NASA Astrophysics Data System (ADS)
Chen, Zhaohui; Huang, Qi
2016-01-01
This paper focuses on the problems of globally exponential stability and stabilization with H∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.
Zhang, Yunong; Wang, Jun
2002-01-01
Global exponential stability is the most desirable stability property of recurrent neural networks. The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment. The theoretical analysis focuses on the global exponential stability, convergence rates, and selection of design parameters. The theoretical results are further substantiated by simulation results conducted for synthesizing linear feedback control systems with different specifications and design requirements. PMID:18244461
Robust Stabilization Control for an Electric Bicycle
NASA Astrophysics Data System (ADS)
Kawamura, Takuro; Murakami, Toshiyuki
Recently, bicycles have gained immense popularity because they have high mobility and are an environment-friendly means of transport. However, many people tend to avoid riding a bicycle because it is unstable. In order to solve this problem, stabilization control for a bicycle has been researched. The aim of this study is improvement of the robustness in stabilization control. To achieve this goal, control systems that use a camber angle disturbance observer (CADO) are proposed. Two kinds of CADOs are proposed in this paper, and the performances of these two observers are compared. The proposed control systems provide higher robustness than does the conventional method. The validity of the proposed methods is confirmed by the experimental results.
NASA Astrophysics Data System (ADS)
Mohamad, Sannay
2008-05-01
This paper demonstrates that there is a discrete-time analogue which does not require any restriction on the size of the time-step in order to preserve the exponential stability of an artificial neural network with distributed delays. The analysis exploits an appropriate Lyapunov sequence and a discrete-time system of Halanay inequalities, and also either a Young inequality or a geometric-arithmetic mean inequality, to derive several sufficient conditions on the network parameters for the exponential stability of the analogue. The sufficiency conditions are independent of the time-step, and they correspond to those that establish the exponential stability of the continuous-time network.
Numerical robust stability estimation in milling process
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Zhu, Limin; Ding, Han; Xiong, Youlun
2012-09-01
The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.
Adaptive control: Stability, convergence, and robustness
NASA Technical Reports Server (NTRS)
Sastry, Shankar; Bodson, Marc
1989-01-01
The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.
Stability, complexity and robustness in population dynamics.
Demongeot, J; Hazgui, H; Ben Amor, H; Waku, J
2014-09-01
The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. PMID:25107273
Exponential Stability for Stochastic Neural Networks of Neutral Type with Impulsive Effects
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Samidurai, R.; Anthoni, S. Marshal
This paper is concerned with the exponential stability of stochastic neural networks of neutral type with impulsive effects. By employing the Lyapunov functional and stochastic analysis, a new stability criterion for the stochastic neural network is derived in terms of linear matrix inequality. A numerical example is provided to show the effectiveness and applicability of the obtained result.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
On exponential stability of linear Levin-Nohel integro-differential equations
NASA Astrophysics Data System (ADS)
Tien Dung, Nguyen
2015-02-01
The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].
Exponential stability of an elastic string with local Kelvin-Voigt damping
NASA Astrophysics Data System (ADS)
Zhang, Qiong
2010-12-01
This paper is devoted to analyzing an elastic string with local Kelvin-Voigt damping. We prove the exponential stability of the system when the material coefficient function near the interface is smooth enough. Our method is based on the frequency method and semigroup theory.
NASA Astrophysics Data System (ADS)
Devianto, Dodi
2016-02-01
It is constructed convolution of generated random variable from independent and identically exponential distribution with stabilizer constant. The characteristic function of this distribution is obtained by using Laplace-Stieltjes transform. The uniform continuity property of characteristic function from this convolution is obtained by using analytical methods as basic properties.
Chen, Huabin; Shi, Peng; Lim, Cheng-Chew; Hu, Peng
2016-06-01
In this paper, the exponential stability in p th( p > 1 )-moment for neutral stochastic Markov systems with time-varying delay is studied. The derived stability conditions comprise two forms: 1) the delay-independent stability criteria which are obtained by establishing an integral inequality and 2) the delay-dependent stability criteria which are captured by using the theory of the functional differential equations. As its applications, the obtained stability results are used to investigate the exponential stability in p th( p > 1 )-moment for the neutral stochastic neural networks with time-varying delay and Markov switching, and the globally exponential adaptive synchronization for the neutral stochastic complex dynamical systems with time-varying delay and Markov switching, respectively. On the delay-independent criteria, sufficient conditions are given in terms of M -matrix and thus are easy to check. The delay-dependent criteria are presented in the forms of the algebraic inequalities, and the least upper bound of the time-varying delay is also provided. The primary advantages of these obtained results over some recent and similar works are that the differentiability or continuity of the delay function is not required, and that the difficulty stemming from the presence of the neutral item and the Markov switching is overcome. Three numerical examples are provided to examine the effectiveness and potential of the theoretic results obtained. PMID:27187938
Robust three-axis attitude stabilization for inertial pointing spacecraft using magnetorquers
NASA Astrophysics Data System (ADS)
Celani, Fabio
2015-02-01
In this work feedback control laws are designed for achieving three-axis attitude stabilization of inertial pointing spacecraft using only magnetic torquers. The designs are based on an almost periodic model of geomagnetic field along the spacecraft's orbit. Both attitude plus attitude rate feedback and attitude only feedback are proposed. Both feedback laws achieve local exponential stability robustly with respect to large uncertainties in the spacecraft's inertia matrix. The latter properties are proved using general averaging and Lyapunov stability. Simulations are included to validate the effectiveness of the proposed control algorithms.
Computation of robustly stabilizing PID controllers for interval systems.
Matušů, Radek; Prokop, Roman
2016-01-01
The paper is focused on the computation of all possible robustly stabilizing Proportional-Integral-Derivative (PID) controllers for plants with interval uncertainty. The main idea of the proposed method is based on Tan's (et al.) technique for calculation of (nominally) stabilizing PI and PID controllers or robustly stabilizing PI controllers by means of plotting the stability boundary locus in either P-I plane or P-I-D space. Refinement of the existing method by consideration of 16 segment plants instead of 16 Kharitonov plants provides an elegant and efficient tool for finding all robustly stabilizing PID controllers for an interval system. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example in which the uncertain mathematical model of an experimental oblique wing aircraft is robustly stabilized. PMID:27350931
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples. PMID:27164266
Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins
NASA Technical Reports Server (NTRS)
Brenner, Marty; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.
On-Line Robust Modal Stability Prediction using Wavelet Processing
NASA Technical Reports Server (NTRS)
Brenner, Martin J.; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.
The Role of a Steepness Parameter in the Exponential Stability of a Model Problem. Numerical Aspects
NASA Astrophysics Data System (ADS)
Todorovic, N.
2011-06-01
The Nekhoroshev theorem considers quasi integrable Hamiltonians providing stability of actions in exponentially long times. One of the hypothesis required by the theorem is a mathematical condition called steepness. Nekhoroshev conjectured that different steepness properties should imply numerically observable differences in the stability times. After a recent study on this problem (Guzzo et al. 2011, Todorovic et al. 2011) we show some additional numerical results on the change of resonances and the diffusion laws produced by the increasing effect of steepness. The experiments are performed on a 4-dimensional steep symplectic map designed in a way that a parameter smoothly regulates the steepness properties in the model.
Yang, Shiju; Li, Chuandong; Huang, Tingwen
2016-03-01
The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results. PMID:26797471
Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis
NASA Astrophysics Data System (ADS)
Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah
2016-06-01
Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-07-01
In this paper, the global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and using matrix inequality technique, several sufficient conditions in complex-valued linear matrix inequality form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the considered neural networks. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The proposed stability results are less conservative than some recently known ones in the literatures, which is demonstrated via two examples with simulations. PMID:27136664
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1994-01-01
This progress report gives current progress of the research in nonlinear robust control using positive real concept. The progress is documented in a draft paper. In the paper, the manipulator dynamics is reformulated differently from the existing equations of motion for free base robots. This new formulation gives a compact form of the dynamic equations for easy computation. The nonlinear terms are now considered. The results show that for an additional nonlinear friction term, the feedback controller designed using passivity concept works quite well. Although design of such a controller requires simulation of the dynamics for the example shown in the following draft, this design procedure is feasible.
Yielding Elastic Tethers Stabilize Robust Cell Adhesion
Whitfield, Matt J.; Luo, Jonathon P.; Thomas, Wendy E.
2014-01-01
Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds. PMID:25473833
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
NASA Astrophysics Data System (ADS)
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Robust stability of positive switched systems with dwell time
NASA Astrophysics Data System (ADS)
Liu, Jinjin; Zhang, Kanjian; Wei, Haikun
2016-08-01
This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.
NASA Astrophysics Data System (ADS)
Wu, Ailong; Zeng, Zhigang
2015-03-01
Modeling and related characterization of memristive neurodynamic systems becomes a critical pathway towards neuromorphic system designs. This paper presents a general class of memristive neural networks with time-varying delays. Some improved algebraic criteria for global exponential stability of memristive neural networks are obtained. The criteria improve some previous results and are easy to be verified with the physical parameters of system itself. The proposed framework for theoretical analysis of memristive neurodynamic systems may be useful in developing nanoscale memristor device as synapse in neuromorphic computing architectures.
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-08-01
This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.
Robust stability of stochastic delayed additive neural networks with Markovian switching.
Huang, He; Ho, Daniel W C; Qu, Yuzhong
2007-09-01
This paper is concerned with the problem of robust stability for stochastic interval delayed additive neural networks (SIDANN) with Markovian switching. The time delay is assumed to be time-varying. In such neural networks, the features of stochastic systems, interval systems, time-varying delay systems and Markovian switching are taken into account. The mathematical model of this kind of neural networks is first proposed. Secondly, the global exponential stability in the mean square is studied for the SIDANN with Markovian switching. Based on the Lyapunov method, several stability conditions are presented, which can be expressed in terms of linear matrix inequalities. As a subsequent result, the stochastic interval additive neural networks with time-varying delay are also discussed. A sufficient condition is given to determine its stability. Finally, two simulation examples are provided to illustrate the effectiveness of the results developed. PMID:17714914
Exponential stability analysis of linear systems with multiple successive delay components
NASA Astrophysics Data System (ADS)
Lin, Chun-Pi; Fong, I.-Kong
2013-06-01
A general class of linear systems with multiple successive delay components is considered in this article. The delays are assumed to vary in intervals, and delay-dependent exponential stability conditions are derived in terms of linear matrix inequalities. To reduce conservativeness, a new Lyapunov-Krasovskii functional is designed to contain more complete state information, so that a derivation procedure with time-varying delays treated as uncertain parameters can be adopted. Usage of slack variables and inequalities are refrained as much as possible when bounds on the Lyapunov derivative are sought. The stability criteria are tested by two popular numerical examples, with less conservative results obtained in all the checked cases. Besides, a practical application of the derived conditions is illustrated.
Robust local stability of multilayer recurrent neural networks.
Suykens, J K; De Moor, B; Vandewalle, J
2000-01-01
In this paper we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers. The stability condition follows from linking theory about linearization, robustness analysis of linear systems under nonlinear perturbation and matrix inequalities. A characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic Lyapunov function. In a similar way like for NL theory, local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion, while the proven basin of attraction is relatively small due to conservatism of the criterion. Modifying dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples. PMID:18249754
High-Spin Organic Diradical with Robust Stability.
Gallagher, Nolan M; Bauer, Jackson J; Pink, Maren; Rajca, Suchada; Rajca, Andrzej
2016-08-01
Triplet ground-state organic molecules are interesting with respect to several emerging technologies but typically exhibit limited stability. We report two organic diradicals, one of which possesses a triplet ground state (2J/kB = 234 ± 36 K) and robust stability at elevated temperatures. We are able to sublime this high-spin diradical under high vacuum at 140 °C with no significant decomposition. PMID:27430499
Use of a genetic algorithm to analyze robust stability problems
Murdock, T.M.; Schmitendorf, W.E.; Forrest, S.
1990-01-01
This note resents a genetic algorithm technique for testing the stability of a characteristic polynomial whose coefficients are functions of unknown but bounded parameters. This technique is fast and can handle a large number of parametric uncertainties. We also use this method to determine robust stability margins for uncertain polynomials. Several benchmark examples are included to illustrate the two uses of the algorithm. 27 refs., 4 figs.
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
NASA Technical Reports Server (NTRS)
Gupta, Sandeep
1996-01-01
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-09-01
This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results. PMID:27239891
Li, Yongkun; Li, Bing
2016-01-01
In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using a fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies model and its discrete-time analogue have the same dynamical behaviors. PMID:27468397
Sun, Xi-Ming; Wang, Xue-Fang; Tan, Ying; Wang, Xiao-Liang; Wang, Wei
2016-06-01
This paper provides a design strategy for temperature control of the gas chromatograph. Usually gas chromatograph is modeled by a simple first order system with a time-delay, and a proportion integration (PI) controller is widely used to regulate the output of the gas chromatograph to the desired temperature. As the characteristics of the gas chromatograph varies at the different temperature range, the single-model based PI controller cannot work well when output temperature varies from one range to another. Moreover, the presence of various disturbance will further deteriorate the performance. In order to improve the accuracy of the temperature control, multiple models are used at the different temperature ranges. With a PI controller designed for each model accordingly, a delay-dependent switching control scheme using the dwell time technique is proposed to ensure the absolute exponential stability of the closed loop. Experiment results demonstrate the effectiveness of the proposed switching technique. PMID:26316283
NASA Astrophysics Data System (ADS)
Wehbe, Ali; Youssef, Wael
2010-10-01
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Wehbe, Ali; Youssef, Wael
2010-10-15
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Robustness for slope stability modelling under deep uncertainty
NASA Astrophysics Data System (ADS)
Almeida, Susana; Holcombe, Liz; Pianosi, Francesca; Wagener, Thorsten
2015-04-01
Landslides can have large negative societal and economic impacts, such as loss of life and damage to infrastructure. However, the ability of slope stability assessment to guide management is limited by high levels of uncertainty in model predictions. Many of these uncertainties cannot be easily quantified, such as those linked to climate change and other future socio-economic conditions, restricting the usefulness of traditional decision analysis tools. Deep uncertainty can be managed more effectively by developing robust, but not necessarily optimal, policies that are expected to perform adequately under a wide range of future conditions. Robust strategies are particularly valuable when the consequences of taking a wrong decision are high as is often the case of when managing natural hazard risks such as landslides. In our work a physically based numerical model of hydrologically induced slope instability (the Combined Hydrology and Stability Model - CHASM) is applied together with robust decision making to evaluate the most important uncertainties (storm events, groundwater conditions, surface cover, slope geometry, material strata and geotechnical properties) affecting slope stability. Specifically, impacts of climate change on long-term slope stability are incorporated, accounting for the deep uncertainty in future climate projections. Our findings highlight the potential of robust decision making to aid decision support for landslide hazard reduction and risk management under conditions of deep uncertainty.
Decentralized adaptive control of robot manipulators with robust stabilization design
NASA Technical Reports Server (NTRS)
Yuan, Bau-San; Book, Wayne J.
1988-01-01
Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.
Robust stability of diamond families of polynomials with complex coefficients
NASA Technical Reports Server (NTRS)
Xu, Zhong Ling
1993-01-01
Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed.
NASA Astrophysics Data System (ADS)
Sun, Jianhua; Wan, Li
2005-08-01
Convergence dynamics of Cohen-Grossberg neural networks (CGNNs) with continuously distributed delays are discussed. Without assuming the differentiability and monotonicity of activation functions, the differentiability of amplification functions and the symmetry of synaptic interconnection weights, by skilfully constructing suitable Lyapunov functionals and employing inequality technique, three sets of easily verifiable delay independent criteria to guarantee the global exponential stability of a unique equilibrium point are given, and moreover, by constructing Poincaré mapping, other three sets of easily verifiable delay independent criteria to assure the existence and globally exponential stability of periodic solutions are obtained. Six examples are given to illustrate the theoretical results.
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results. PMID:25148672
Does a crouched leg posture enhance running stability and robustness?
Blum, Yvonne; Birn-Jeffery, Aleksandra; Daley, Monica A; Seyfarth, Andre
2011-07-21
Humans and birds both walk and run bipedally on compliant legs. However, differences in leg architecture may result in species-specific leg control strategies as indicated by the observed gait patterns. In this work, control strategies for stable running are derived based on a conceptual model and compared with experimental data on running humans and pheasants (Phasianus colchicus). From a model perspective, running with compliant legs can be represented by the planar spring mass model and stabilized by applying swing leg control. Here, linear adaptations of the three leg parameters, leg angle, leg length and leg stiffness during late swing phase are assumed. Experimentally observed kinematic control parameters (leg rotation and leg length change) of human and avian running are compared, and interpreted within the context of this model, with specific focus on stability and robustness characteristics. The results suggest differences in stability characteristics and applied control strategies of human and avian running, which may relate to differences in leg posture (straight leg posture in humans, and crouched leg posture in birds). It has been suggested that crouched leg postures may improve stability. However, as the system of control strategies is overdetermined, our model findings suggest that a crouched leg posture does not necessarily enhance running stability. The model also predicts different leg stiffness adaptation rates for human and avian running, and suggests that a crouched avian leg posture, which is capable of both leg shortening and lengthening, allows for stable running without adjusting leg stiffness. In contrast, in straight-legged human running, the preparation of the ground contact seems to be more critical, requiring leg stiffness adjustment to remain stable. Finally, analysis of a simple robustness measure, the normalized maximum drop, suggests that the crouched leg posture may provide greater robustness to changes in terrain height. PMID
An approximation theorem for entire functions of exponential type and stability of zero sequences
NASA Astrophysics Data System (ADS)
Khabibullin, B. N.
2004-02-01
Let L be an entire function of exponential type in \\mathbb C with indicator function h_L; let \\Lambda=\\{\\lambda_n\\}, n=1,2,\\dots, be a subsequence of zeros of the entire function of exponential type L\
Xi, Qiang
2016-01-01
In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results. PMID:26599709
Impossibility of unconditional stability and robustness of diffusive acceleration schemes
Azmy, Y.Y.
1998-01-01
The authors construct a problem for which exists no preconditioner with a cell-centered diffusion coupling stencil that is unconditionally stable and robust. In particular they consider an asymptotic limit of the Periodic Horizontal Interface (PHI) configuration wherein the cell height in both layers approaches zero like {sigma}{sup 2} while the total cross section varies like a in one layer and like 1/{sigma} in the other layer. In such case they show that the conditions for stability and robustness of the flat eigenmodes of the iteration residual imply instability of the modes flat in the y-dimension and rapidly varying in the x-dimension. This paper is important for radiation transport studies.
Determination of robust stability margin for second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.; Kau, C.-T.; Juang, Jer-Nan
1992-01-01
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
NASA Astrophysics Data System (ADS)
Bao, Haibo; Cao, Jinde
2011-09-01
This paper investigates the problem of the global exponential stability for neutral-type impulsive neural networks with mixed delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays and the jumping parameters are generated from a continuous time discrete state homogenous Markov process. Based on the Lyapunov functional, a sufficient criterion is derived in terms of linear matrix equality (LMI).
Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses
NASA Astrophysics Data System (ADS)
Mohamad, Sannay; Gopalsamy, K.
2009-01-01
This paper demonstrates the reliability of a discrete-time analogue in preserving the exponential convergence of a bidirectional associative memory (BAM) network that is subject to nonlinear impulses. The analogue derived from a semi-discretisation technique with the value of the time-step fixed is treated as a discrete-time dynamical system while its exponential convergence towards an equilibrium state is studied. Thereby, a family of sufficiency conditions governing the network parameters and the impulse magnitude and frequency is obtained for the convergence. As special cases, one can obtain from our results, those corresponding to the non-impulsive discrete-time BAM networks and also those corresponding to continuous-time (impulsive and non-impulsive) systems. A relation between the Lyapunov exponent of the non-impulsive system and that of the impulsive system involving the size of the impulses and the inter-impulse intervals is obtained.
Lack of exponential stability to Timoshenko system with viscoelastic Kelvin-Voigt type
NASA Astrophysics Data System (ADS)
Malacarne, Andréia; Muñoz Rivera, Jaime Edilberto
2016-06-01
We study the Timoshenko systems with a viscoelastic dissipative mechanism of Kelvin-Voigt type. We prove that the model is analytical if and only if the viscoelastic damping is present in both the shear stress and the bending moment. Otherwise, the corresponding semigroup is not exponentially stable no matter the choice of the coefficients. This result is different to all others related to Timoshenko model with partial dissipation, which establish that the system is exponentially stable if and only if the wave speeds are equal. Finally, we show that the solution decays polynomially to zero as {t^{-1/2}} , no matter where the viscoelastic mechanism is effective and that the rate is optimal whenever the initial data are taken on the domain of the infinitesimal operator.
NASA Astrophysics Data System (ADS)
Liao, Xiaofeng; Wong, Kwok-Wo
2003-04-01
In this paper, the dynamical characteristics of hybrid bidirectional associative memory neural networks with constant transmission delays are investigated. Without assuming symmetry of synaptic connection weights and monotonicity and differentiability of activation functions, Halanay-type inequalities (which are different from the approach of constructing Lyapunov functionals) are employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Our results are less conservative and restrictive than previously known results.
NASA Astrophysics Data System (ADS)
Liu, Wenjun
2014-11-01
In this paper, we consider a wave equation with space variable coefficients. Due to physical considerations, a distributed delay damping is acted on the part of the boundary. Under suitable assumptions, we prove the exponential stability of the energy based on the use of Riemannian geometry method, the perturbed energy argument, and some observability inequalities. From the applications point of view, our results may provide some qualitative analysis and intuition for the researchers in fields such as engineering, biophysics, and mechanics. And the method is rather general and can be adapted to other evolution systems with variable coefficients (e. g. elasticity plates) as well.
NASA Astrophysics Data System (ADS)
Mohamad, Sannay
2001-11-01
Convergence dynamics of continuous-time bidirectional neural networks with constant transmission delays are studied. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, Lyapunov functionals and Halanay-type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous-time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks. Discrete-time analogues of the continuous-time networks are formulated and we study their dynamical characteristics. It is shown that the convergence dynamics of the continuous-time networks are preserved by the discrete-time analogues without any restriction on the discretization step-size. Several examples are given to illustrate the advantages of the discrete-time analogues in numerically simulating the continuous-time networks.
Robustness of fuzzy logic power system stabilizers applied to multimachine power system
Hiyama, Takashi . Dept. of Electrical Engineering and Computer Science)
1994-09-01
This paper investigates the robustness of fuzzy logic stabilizers using the information of speed and acceleration states of a study unit. The input signals are the real power output and/or the speed of the study unit. Non-linear simulations show the robustness of the fuzzy logic power system stabilizers. Experiments are also performed by using a micro-machine system. The results show the feasibility of proposed fuzzy logic stabilizer.
Apalara, Tijani A.; Messaoudi, Salim A.
2015-06-15
In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. PMID:26752438
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.
2016-08-01
A (n+1)-dimensional gravitational model with Gauss-Bonnet term and a cosmological constant term is considered. When ansatz with diagonal cosmological metrics is adopted, the solutions with an exponential dependence of the scale factors, a_i ˜ exp { ( v^i t) }, i =1, dots , n , are analyzed for n > 3. We study the stability of the solutions with non-static volume factor, i.e. if K(v) = sum _{k = 1}n v^k ≠ 0. We prove that under a certain restriction R imposed solutions with K(v) > 0 are stable, while solutions with K(v) < 0 are unstable. Certain examples of stable solutions are presented. We show that the solutions with v^1 = v^2 =v^3 = H > 0 and zero variation of the effective gravitational constant are stable if the restriction R is obeyed.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. PMID:24808035
NASA Technical Reports Server (NTRS)
Ryan, R.
1993-01-01
Robustness is a buzz word common to all newly proposed space systems design as well as many new commercial products. The image that one conjures up when the word appears is a 'Paul Bunyon' (lumberjack design), strong and hearty; healthy with margins in all aspects of the design. In actuality, robustness is much broader in scope than margins, including such factors as simplicity, redundancy, desensitization to parameter variations, control of parameter variations (environments flucation), and operational approaches. These must be traded with concepts, materials, and fabrication approaches against the criteria of performance, cost, and reliability. This includes manufacturing, assembly, processing, checkout, and operations. The design engineer or project chief is faced with finding ways and means to inculcate robustness into an operational design. First, however, be sure he understands the definition and goals of robustness. This paper will deal with these issues as well as the need for the requirement for robustness.
Robustness, stability and efficiency of phage lambda genetic switch: dynamical structure analysis.
Zhu, X-M; Yin, L; Hood, L; Ao, P
2004-12-01
Based on the dynamical structure theory for complex networks recently developed by one of us and on the physical-chemical models for gene regulation, developed by Shea and Ackers in the 1980's, we formulate a direct and concise mathematical framework for the genetic switch controlling phage lambda life cycles, which naturally includes the stochastic effect. The dynamical structure theory states that the dynamics of a complex network is determined by its four elementary components: The dissipation (analogous to degradation), the stochastic force, the driving force determined by a potential, and the transverse force. The potential may be interpreted as a landscape for the phage development in terms of attractive basins, saddle points, peaks and valleys. The dissipation gives rise to the adaptivity of the phage in the landscape defined by the potential: The phage always has the tendency to approach the bottom of the nearby attractive basin. The transverse force tends to keep the network on the equal-potential contour of the landscape. The stochastic fluctuation gives the phage the ability to search around the potential landscape by passing through saddle points. With molecular parameters in our model fixed primarily by the experimental data on wild-type phage and supplemented by data on one mutant, our calculated results on mutants agree quantitatively with the available experimental observations on other mutants for protein number, lysogenization frequency, and a lysis frequency in lysogen culture. The calculation reproduces the observed robustness of the phage lambda genetic switch. This is the first mathematical description that successfully represents such a wide variety of major experimental phenomena. Specifically, we find: (1) The explanation for both the stability and the efficiency of phage lambda genetic switch is the exponential dependence of saddle point crossing rate on potential barrier height, a result of the stochastic motion in a landscape; and (2
BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel
2009-03-05
In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.
Liu, Yanbin; Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
NASA Astrophysics Data System (ADS)
Pan, Li-Xin; Jin, Hong-Zhang; Wang, Lin-Lin
2011-06-01
In the case of Autonomous Underwater Vehicle (AUV) navigating with low speed near water surface, a new method for design of roll motion controller is proposed in order to restrain wave disturbance effectively and improve roll stabilizing performance. Robust control is applied, which is based on uncertain nonlinear horizontal motion model of AUV and the principle of zero speed fin stabilizer. Feedback linearization approach is used to transform the complex nonlinear system into a comparatively simple linear system. For parameter uncertainty of motion model, the controller is designed with mixed-sensitivity method based on H-infinity robust control theory. Simulation results show better robustness improved by this control method for roll stabilizing of AUV navigating near water surface.
Robust stabilization of the Space Station in the presence of inertia matrix uncertainty
NASA Technical Reports Server (NTRS)
Wie, Bong; Liu, Qiang; Sunkel, John
1993-01-01
This paper presents a robust H-infinity full-state feedback control synthesis method for uncertain systems with D11 not equal to 0. The method is applied to the robust stabilization problem of the Space Station in the face of inertia matrix uncertainty. The control design objective is to find a robust controller that yields the largest stable hypercube in uncertain parameter space, while satisfying the nominal performance requirements. The significance of employing an uncertain plant model with D11 not equal 0 is demonstrated.
Robust control design with real parameter uncertainty using absolute stability theory. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Hall, Steven R.
1993-01-01
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays.
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Robust H∞ stabilization of a hard disk drive system with a single-stage actuator
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Kiin Woon, Raymond Song
2015-04-01
This paper considers a robust H∞ control problem for a hard disk drive system with a single stage actuator. The hard disk drive system is modeled as a linear time-invariant uncertain system where its uncertain parameters and high-order dynamics are considered as uncertainties satisfying integral quadratic constraints. The robust H∞ control problem is transformed into a nonlinear optimization problem with a pair of parameterized algebraic Riccati equations as nonconvex constraints. The nonlinear optimization problem is then solved using a differential evolution algorithm to find stabilizing solutions to the Riccati equations. These solutions are used for synthesizing an output feedback robust H∞ controller to stabilize the hard disk drive system with a specified disturbance attenuation level.
Control design for robust stability in linear regulators: Application to aerospace flight control
NASA Technical Reports Server (NTRS)
Yedavalli, R. K.
1986-01-01
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Karra, Udayarka; Huang, Guoxian; Umaz, Ridvan; Tenaglier, Christopher; Wang, Lei; Li, Baikun
2013-09-01
A novel and robust distributed benthic microbial fuel cell (DBMFC) was developed to address the energy supply issues for oceanographic sensor network applications, especially under scouring and bioturbation by aquatic life. Multi-anode/cathode configuration was employed in the DBMFC system for enhanced robustness and stability in the harsh ocean environment. The results showed that the DBMFC system achieved peak power and current densities of 190mW/m(2) and 125mA/m(2) respectively. Stability characterization tests indicated the DBMFC with multiple anodes achieved higher power generation over the systems with single anode. A computational model that integrated physical, electrochemical and biological factors of MFCs was developed to validate the overall performance of the DBMFC system. The model simulation well corresponded with the experimental results, and confirmed the hypothesis that using a multi anode/cathode MFC configuration results in reliable and robust power generation. PMID:23890975
Fernández de Cañete, J; Barreiro, A; García-Cerezo, A; García-Moral, I
2001-01-01
A stabilization method based on the input-output conicity criterion is presented. Conventional learning algorithms are applied to adjust the controller dynamics, and robust stability of the closed-loop system is guaranteed by modifying the training patterns which yield unstable behavior. The methodology developed expands the class of nonlinear systems to be controlled using neural control schemes, so that the stabilization of a broad class of neural-network-based control systems, even with unknown dynamics, is assured. Straightforwardness in the application of this method is evident in contrast to the Lyapunov function approach. PMID:18249978
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
NASA Technical Reports Server (NTRS)
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Flight control application of new stability robustness bounds for linear uncertain systems
NASA Technical Reports Server (NTRS)
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
Koh, Yeong Jun; Lee, Chulwoo; Kim, Chang-Su
2015-12-01
We propose a video stabilization algorithm, which extracts a guaranteed number of reliable feature trajectories for robust mesh grid warping. We first estimate feature trajectories through a video sequence and transform the feature positions into rolling-free smoothed positions. When the number of the estimated trajectories is insufficient, we generate virtual trajectories by augmenting incomplete trajectories using a low-rank matrix completion scheme. Next, we detect feature points on a large moving object and exclude them so as to stabilize camera movements, rather than object movements. With the selected feature points, we set a mesh grid on each frame and warp each grid cell by moving the original feature positions to the smoothed ones. For robust warping, we formulate a cost function based on the reliability weights of each feature point and each grid cell. The cost function consists of a data term, a structure-preserving term, and a regularization term. By minimizing the cost function, we determine the robust mesh grid warping and achieve the stabilization. Experimental results demonstrate that the proposed algorithm reconstructs videos more stably than the conventional algorithms. PMID:26394425
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results. PMID:27190502
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results. PMID:26878721
Robust adaptive spin-axis stabilization of a symmetric spacecraft using two bounded torques
NASA Astrophysics Data System (ADS)
Gui, Haichao; Vukovich, George
2015-12-01
The spin-axis stabilization of an axisymmetric spacecraft by two control torques perpendicular to the symmetry axis is addressed. Two control laws are designed to align the symmetry axis along a desired inertial direction despite the revolution around the symmetry axis. The first controller takes a saturated proportional-derivative form and can stabilize the spin-axis to the desired direction with a priori bounded torques in the absence of modeling uncertainties. In order to achieve better robustness, an adaptive controller is then designed to account for the inertia uncertainties and disturbances, in addition to actuator saturation. Numerical examples are presented to demonstrate the advantageous features of the proposed algorithm compared with conventional spin-axis stabilization methods.
High-throughput thermal scanning for protein stability: making a good technique more robust.
Seabrook, Shane A; Newman, Janet
2013-08-12
We present a high-throughput approach to help define experimental formulations that enhance protein stability, which is based on differential scanning fluorimetry (DSF). The method involves defining the thermal stability of a protein against a screen of 13 buffer systems, systematically sampling pH from 5.0 to 9.0 at high and low salt concentrations, using both redundancy and extensive controls to make the method robust. The screen allows rapid determination of a suitable base formulation for protein samples, and is particularly useful for difficult samples: those that are rapidly degraded or cannot be sufficiently concentrated for downstream analyses. Data obtained from three samples in this assay illustrate the vastly different values for thermal stability that can be obtained from different formulations. This approach is simple to interpret and reliable enough that it has been implemented as a service through the Collaborative Crystallisation Centre (C3). PMID:23710551
Redi, M.H.; Diallo, A.; Cooper, W.A.; Fu, G.Y.
2000-01-27
Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic stability is evaluated as well as energetic particle transport. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the non-periodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties.
On the control of elastic vehicles - Model simplification and stability robustness
NASA Technical Reports Server (NTRS)
Schmidt, David K.; Newman, Brett
1989-01-01
Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced-order model will be preserved when controlling the full-order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. A numerical procedure developed previously is shown to lead to results that meet the necessary criteria. The procedure is applied to reduce the model of a flexible aircraft. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. An example is included that demonstrates that an apparently robust control law actually amplifies modest modeling errors in the critical frequency region, and leads to undesirable results. The cause of this problem is identified to be associated with the canceling of lightly-damped transmission zeroes in the plant.
A Robust Method of Vehicle Stability Accurate Measurement Using GPS and INS
NASA Astrophysics Data System (ADS)
Miao, Zhibin; Zhang, Hongtian; Zhang, Jinzhu
2015-12-01
With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.
Wang, Jin; Li, Chunhe; Wang, Erkang
2010-05-01
Studying the cell cycle process is crucial for understanding cell growth, proliferation, development, and death. We uncovered some key factors in determining the global robustness and function of the budding yeast cell cycle by exploring the underlying landscape and flux of this nonequilibrium network. The dynamics of the system is determined by both the landscape which attracts the system down to the oscillation orbit and the curl flux which drives the periodic motion on the ring. This global structure of landscape is crucial for the coherent cell cycle dynamics and function. The topography of the underlying landscape, specifically the barrier height separating basins of attractions, characterizes the capability of changing from one part of the system to another. This quantifies the stability and robustness of the system. We studied how barrier height is influenced by environmental fluctuations and perturbations on specific wirings of the cell cycle network. When the fluctuations increase, the barrier height decreases and the period and amplitude of cell cycle oscillation is more dispersed and less coherent. The corresponding dissipation of the system quantitatively measured by the entropy production rate increases. This implies that the system is less stable under fluctuations. We identified some key structural elements for wirings of the cell cycle network responsible for the change of the barrier height and therefore the global stability of the system through the sensitivity analysis. The results are in agreement with recent experiments and also provide new predictions. PMID:20393126
A novel predictive control algorithm and robust stability criteria for integrating processes.
Zhang, Bin; Yang, Weimin; Zong, Hongyuan; Wu, Zhiyong; Zhang, Weidong
2011-07-01
This paper introduces a novel predictive controller for single-input/single-output (SISO) integrating systems, which can be directly applied without pre-stabilizing the process. The control algorithm is designed on the basis of the tested step response model. To produce a bounded system response along the finite predictive horizon, the effect of the integrating mode must be zeroed while unmeasured disturbances exist. Here, a novel predictive feedback error compensation method is proposed to eliminate the permanent offset between the setpoint and the process output while the integrating system is affected by load disturbance. Also, a rotator factor is introduced in the performance index, which is contributed to the improvement robustness of the closed-loop system. Then on the basis of Jury's dominant coefficient criterion, a robust stability condition of the resulted closed loop system is given. There are only two parameters which need to be tuned for the controller, and each has a clear physical meaning, which is convenient for implementation of the control algorithm. Lastly, simulations are given to illustrate that the proposed algorithm can provide excellent closed loop performance compared with some reported methods. PMID:21353217
Robust flow stability: Theory, computations and experiments in near wall turbulence
NASA Astrophysics Data System (ADS)
Bobba, Kumar Manoj
Helmholtz established the field of hydrodynamic stability with his pioneering work in 1868. From then on, hydrodynamic stability became an important tool in understanding various fundamental fluid flow phenomena in engineering (mechanical, aeronautics, chemical, materials, civil, etc.) and science (astrophysics, geophysics, biophysics, etc.), and turbulence in particular. However, there are many discrepancies between classical hydrodynamic stability theory and experiments. In this thesis, the limitations of traditional hydrodynamic stability theory are shown and a framework for robust flow stability theory is formulated. A host of new techniques like gramians, singular values, operator norms, etc. are introduced to understand the role of various kinds of uncertainty. An interesting feature of this framework is the close interplay between theory and computations. It is shown that a subset of Navier-Stokes equations are globally, non-nonlinearly stable for all Reynolds number. Yet, invoking this new theory, it is shown that these equations produce structures (vortices and streaks) as seen in the experiments. The experiments are done in zero pressure gradient transiting boundary layer on a flat plate in free surface tunnel. Digital particle image velocimetry, and MEMS based laser Doppler velocimeter and shear stress sensors have been used to make quantitative measurements of the flow. Various theoretical and computational predictions are in excellent agreement with the experimental data. A closely related topic of modeling, simulation and complexity reduction of large mechanics problems with multiple spatial and temporal scales is also studied. A nice method that rigorously quantifies the important scales and automatically gives models of the problem to various levels of accuracy is introduced. Computations done using spectral methods are presented.
Anderson, Ericka L.; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K.; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J. Craig; Nelson, Karen E.; Jones, Marcus B.
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
Anderson, Ericka L; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J Craig; Nelson, Karen E; Jones, Marcus B
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
Chen, Bor-Sen; Chang, Yu-Te; Wang, Yu-Chao
2008-02-01
Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering in gene networks is crucial to understand the signal processing in gene networks and to design noise-tolerant gene circuits for synthetic biology. A nonlinear stochastic dynamic model is proposed in describing a gene network under intrinsic molecular fluctuations and extrinsic molecular noises. The stochastic molecular-noise-processing scheme of gene regulatory networks for attenuating these molecular noises is investigated from the nonlinear robust stabilization and filtering perspective. In order to improve the robust stability and noise filtering, a robust gene circuit design for gene networks is proposed based on the nonlinear robust H infinity stochastic stabilization and filtering scheme, which needs to solve a nonlinear Hamilton-Jacobi inequality. However, in order to avoid solving these complicated nonlinear stabilization and filtering problems, a fuzzy approximation method is employed to interpolate several linear stochastic gene networks at different operation points via fuzzy bases to approximate the nonlinear stochastic gene network. In this situation, the method of linear matrix inequality technique could be employed to simplify the gene circuit design problems to improve robust stability and molecular-noise-filtering ability of gene networks to overcome intrinsic molecular fluctuations and extrinsic molecular noises. PMID:18270080
NASA Technical Reports Server (NTRS)
Garg, Sanjay
1989-01-01
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
Li, Ning; Cao, Jinde; Hayat, Tasawar
2014-08-01
This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results. PMID:25009673
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-01-01
The gene regulatory network (GRN) is the central decision‐making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large‐scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation. DOI: http://dx.doi.org/10.7554/eLife.02863.001 PMID:25182846
NASA Astrophysics Data System (ADS)
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
NASA Astrophysics Data System (ADS)
Ratschbacher, Lothar; Gallego, Jose; Ghosh, Sutapa; Alavi, Seyed; Alt, Wolfgang; Martinez-Dorantes, Miguel; Meschede, Dieter
2016-04-01
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal
ERIC Educational Resources Information Center
Ishigami, Yoko; Klein, Raymond M.
2015-01-01
The current study examined the robustness, stability, reliability, and isolability of the attention network scores (alerting, orienting, and executive control) when young children experienced repeated administrations of the child version of the Attention Network Test (ANT; Rueda et al., 2004). Ten test sessions of the ANT were administered to 12…
Robust motion filtering as an enabler to video stabilization for a tele-operated mobile robot
NASA Astrophysics Data System (ADS)
Chereau, Romain; Breckon, Toby P.
2013-10-01
An increasing number of inspection and hazardous environment tasks use mobile robotic vehicles manually tele-operated via a live video feed from an on-board camera. The resulting video imagery frequently suffers from vibration artefacts compromising the accuracy and security of operation in addition to the viable duration for human tele-operation. Here we aim to automatically remove these unwanted visual effects using a novel real-time video stabilization approach. Prior work for hand-held and vehicle mounted cameras is ill-suited to the high-frequency, large magnitude (10-15% of image size) vibration encountered on the short wheelbase, non-suspended robotic platforms typically deployed for such tasks. Without prior knowledge of the robot ego-motion (or vibration characteristics) we develop a novel four stage filtering approach to identify robust Local Motion Vectors (LMV) for Global Motion Vector (GMV) estimation in successive video frames whilst preserving the required real-time responsiveness for tele-operation. Experimental results over a range of tele-operation scenarios show that the method provides both significant qualitative visual improvement and a quantitative reduction in measurable video image displacement (caused by vibration).
NASA Astrophysics Data System (ADS)
Ngamroo, Issarachai
2010-12-01
It is well known that the superconducting magnetic energy storage (SMES) is able to quickly exchange active and reactive power with the power system. The SMES is expected to be the smart storage device for power system stabilization. Although the stabilizing effect of SMES is significant, the SMES is quite costly. Particularly, the superconducting magnetic coil size which is the essence of the SMES, must be carefully selected. On the other hand, various generation and load changes, unpredictable network structure, etc., cause system uncertainties. The power controller of SMES which is designed without considering such uncertainties, may not tolerate and loses stabilizing effect. To overcome these problems, this paper proposes the new design of robust SMES controller taking coil size and system uncertainties into account. The structure of the active and reactive power controllers is the 1st-order lead-lag compensator. No need for the exact mathematical representation, system uncertainties are modeled by the inverse input multiplicative perturbation. Without the difficulty of the trade-off of damping performance and robustness, the optimization problem of control parameters is formulated. The particle swarm optimization is used for solving the optimal parameters at each coil size automatically. Based on the normalized integral square error index and the consideration of coil current constraint, the robust SMES with the smallest coil size which still provides the satisfactory stabilizing effect, can be achieved. Simulation studies in the two-area four-machine interconnected power system show the superior robustness of the proposed robust SMES with the smallest coil size under various operating conditions over the non-robust SMES with large coil size.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Im, Hyeon-Gyun; Jin, Jungho; Ko, Ji-Hoon; Lee, Jaemin; Lee, Jung-Yong; Bae, Byeong-Soo
2014-01-21
We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices. PMID:24284890
Jin, Q B; Liu, Q; Huang, B
2016-03-01
This paper considers the problem of determining all the robust PID (proportional-integral-derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite-Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller. PMID:26708658
NASA Astrophysics Data System (ADS)
Ripamonti, Francesco; Resta, Ferruccio; Vivani, Andrea
2015-04-01
The aim of this paper is to present two control logics and an attitude estimator for UAV stabilization and remote piloting, that are as robust as possible to physical parameters variation and to other external disturbances. Moreover, they need to be implemented on low-cost micro-controllers, in order to be attractive for commercial drones. As an example, possible applications of the two switching control logics could be area surveillance and facial recognition by means of a camera mounted on the drone: the high computational speed logic is used to reach the target, when the high-stability one is activated, in order to complete the recognition tasks.
Jaballi, Ahmed; Sakly, Anis; Hajjaji, Ahmed El
2016-07-01
This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results. PMID:26996925
NASA Astrophysics Data System (ADS)
Im, Hyeon-Gyun; Jin, Jungho; Ko, Ji-Hoon; Lee, Jaemin; Lee, Jung-Yong; Bae, Byeong-Soo
2013-12-01
We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices.We report on the performance of an all-in-one flexible hybrid conducting film employing a monolithically embedded AgNW transparent electrode and a high-performance glass-fabric reinforced composite substrate (AgNW-GFRHybrimer film). Specifically, we perform in-depth investigations on the stability of the AgNW-GFRHybrimer film against heat, thermal oxidation, and wet chemicals to demonstrate the potential of the hybrid conducting film as a robust electrode platform for thin-film optoelectronic devices. With the ease of large-area processability, smooth surface topography, and robust performance stability, the AgNW-GFRHybrimer film can be a promising platform for high-performance optoelectronic devices. Electronic supplementary information (ESI) available: Further characteristics of AgNW-GFRHybrimer films and thermal oxidation of AgNW on glass. See DOI: 10.1039/c3nr05348b
Precup, Radu-Emil; David, Radu-Codrut; Petriu, Emil M; Radac, Mircea-Bogdan; Preitl, Stefan
2014-11-01
This paper suggests a new generation of optimal PI controllers for a class of servo systems characterized by saturation and dead zone static nonlinearities and second-order models with an integral component. The objective functions are expressed as the integral of time multiplied by absolute error plus the weighted sum of the integrals of output sensitivity functions of the state sensitivity models with respect to two process parametric variations. The PI controller tuning conditions applied to a simplified linear process model involve a single design parameter specific to the extended symmetrical optimum (ESO) method which offers the desired tradeoff to several control system performance indices. An original back-calculation and tracking anti-windup scheme is proposed in order to prevent the integrator wind-up and to compensate for the dead zone nonlinearity of the process. The minimization of the objective functions is carried out in the framework of optimization problems with inequality constraints which guarantee the robust stability with respect to the process parametric variations and the controller robustness. An adaptive gravitational search algorithm (GSA) solves the optimization problems focused on the optimal tuning of the design parameter specific to the ESO method and of the anti-windup tracking gain. A tuning method for PI controllers is proposed as an efficient approach to the design of resilient control systems. The tuning method and the PI controllers are experimentally validated by the adaptive GSA-based tuning of PI controllers for the angular position control of a laboratory servo system. PMID:25330468
Robust reliable control design for networked control system with sampling communication
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Santra, Srimanta; Mathiyalagan, K.; Su, Hongye
2015-12-01
In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.
Stabilization and robustness of non-linear unity-feedback system - Factorization approach
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Kabuli, M. G.
1988-01-01
The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.
ERIC Educational Resources Information Center
Huynh, Huynh; Rawls, Anita
2011-01-01
There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests developed by…
Meyer-Baese, A; Theis, F; Emmett, M R
2010-01-01
The tryptophan system present in Escherichia coli represents an important regulatory unit described by multiple feedback loops. The role of these feedback loops is crucial for the analysis of the dynamical behavior of the tryptophan synthesis. We analyze the robust stability of this system which models the dynamics of both fast state, such as transcription and synthesis of free operator, and slow state, such as translation and tryptophan synthesis under consideration of nonlinear uncertainties. In addition, we analyze the role of these feedback loops as key design components of this regulatory unit responsible for its physiological performance. The range of allowed parameter perturbations and the conditions that ensure the existence of asymptotically stable equilibria of the perturbed system are determined. We also analyze two important alternate regulatory designs for the tryptophan synthesis pathway and derive the stability conditions. PMID:20865501
An Exceptional Exponential Function
ERIC Educational Resources Information Center
Curgus, Branko
2006-01-01
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…
Surface Coordination of Black Phosphorus for Robust Air and Water Stability.
Zhao, Yuetao; Wang, Huaiyu; Huang, Hao; Xiao, Quanlan; Xu, Yanhua; Guo, Zhinan; Xie, Hanhan; Shao, Jundong; Sun, Zhengbo; Han, Weijia; Yu, Xue-Feng; Li, Penghui; Chu, Paul K
2016-04-11
A titanium sulfonate ligand is synthesized for surface coordination of black phosphorus (BP). In contrast to serious degradation observed from the bare BP, the BP after surface coordination exhibits excellent stability during dispersion in water and exposure to air for a long period of time, thereby significantly extending the lifetime and spurring broader application of BP. PMID:26968443
NASA Astrophysics Data System (ADS)
Hossain, Jahangir; Mahmud, Apel; Roy, Naruttam K.; Pota, Hemanshu R.
2013-10-01
In stressed power systems with large induction machine component, there exist undamped electromechanical modes and unstable monotonic voltage modes. This article proposes a sequential design of an excitation controller and a power system stabiliser (PSS) to stabilise the system. The operating region, with induction machines in stressed power systems, is often not captured using a linearisation around an operating point, and to alleviate this situation a robust controller is designed which guarantees stable operation in a large region of operation. A minimax linear quadratic Gaussian design is used for the design of the supplementary control to automatic voltage regulators, and a classical PSS structure is used to damp electromechanical oscillations. The novelty of this work is in proposing a method to capture the unmodelled nonlinear dynamics as uncertainty in the design of the robust controller. Tight bounds on the uncertainty are obtained using this method which enables high-performance controllers. An IEEE benchmark test system has been used to demonstrate the performance of the designed controller.
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Dyson, Samuel E.
1996-08-01
A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization
NASA Technical Reports Server (NTRS)
Singh, S. N.; Schy, A. A.
1985-01-01
An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.
Reichert, Malinda D; Lin, Chia-Cheng; Vela, Javier
2014-07-08
Anisotropic II–VI semiconductor nanostructures are important photoactive materials for various energy conversion and optical applications. However, aside from the many available surface chemistry studies and from their ubiquitous photodegradation under continuous illumination, the general chemical reactivity and thermal stability (phase and shape transformations) of these materials are poorly understood. Using CdSe and CdS nanorods as model systems, we have investigated the behavior of II–VI semiconductor nanorods against various conditions of extreme chemical and physical stress (acids, bases, oxidants, reductants, and heat). CdSe nanorods react rapidly with acids, becoming oxidized to Se or SeO2. In contrast, CdSe nanorods remain mostly unreactive when treated with bases or strong oxidants, although bases do partially etch the tips of the nanorods (along their axis). Roasting (heating in air) of CdSe nanorods results in rock-salt CdO, but neither CdSe nor CdO is easily reduced by hydrogen (H2). Another reductant, n-BuLi, reduces CdSe nanorods to metallic Cd. Variable temperature X-ray diffraction experiments show that axial annealing and selective axial melting of the nanorods precede particle coalescence. Furthermore, thermal analysis shows that the axial melting of II–VI nanorods is a ligand-dependent process. In agreement with chemical reactivity and thermal stability observations, silica-coating experiments show that the sharpest (most curved) II–VI surfaces are most active against heterogeneous nucleation of a silica shell. These results provide valuable insights into the fate and possible ways to enhance the stability and improve the use of II–VI semiconductor nanostructures in the fields of optics, magnetism, and energy conversion.
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
Design, stability and robustness analyses of neural networks in control systems
NASA Astrophysics Data System (ADS)
Shen, Jie
1998-12-01
Artificial Neural Network (ANN), also known as connectionist learning and parallel distributed processing, is finding its applications in diverse fields: many branches of engineering, health sciences, cognitive science, archaeology, finance, etc. This research tries to make some efforts to emphasize "design" methodology in ANN, and to explore the structures by which ANN can solve difficult problems by identifying proper ANN architecture. Two classes of ANN--multi-layer neural networks and recurrent networks--are investigated in the context of control of systems and estimation of unknown parameters. The multi-layer neural networks converge to optimal solutions by satisfying mathematical formulations associated with the Hamilton approach and the dynamic programming approach. A benchmark aerospace application is used for illustration. A variant of the Hopfield network, called the Modified Hopfield Neural Network (MHNN), is proposed to show the design approach to the determination of weights in recurrent networks. It is shown how the equilibrium point of this network helps with inversion operations arising in optimal gain determination. Control of dynamic systems using recurrent neural networks are presented. The robustness of the recurrent networks to parameter variation is considered in the context of weights. Analyses are carried out in the frequency domain and the time domain.
NASA Astrophysics Data System (ADS)
Requejo, Rubén J.; Camacho, Juan; Cuesta, José A.; Arenas, Alex
2012-08-01
The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.
Robust design of polyrhythmic neural circuits
NASA Astrophysics Data System (ADS)
Schwabedal, Justus T. C.; Neiman, Alexander B.; Shilnikov, Andrey L.
2014-08-01
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.
A robust method to screen detergents for membrane protein stabilization, revisited.
Champeil, Philippe; Orlowski, Stéphane; Babin, Simon; Lund, Sten; le Maire, Marc; Møller, Jesper; Lenoir, Guillaume; Montigny, Cédric
2016-10-15
This report is a follow up of our previous paper (Lund, Orlowski, de Foresta, Champeil, le Maire and Møller (1989), J Biol Chem 264:4907-4915) showing that solubilization in detergent of a membrane protein may interfere with its long-term stability, and proposing a protocol to reveal the kinetics of such irreversible inactivation. We here clarify the fact that when various detergents are tested for their effects, special attention has of course to be paid to their critical micelle concentration. We also investigate the effects of a few more detergents, some of which have been recently advertised in the literature, and emphasize the role of lipids together with detergents. Among these detergents, lauryl maltose neopentyl glycol (LMNG) exerts a remarkable ability, even higher than that of β-dodecylmaltoside (DDM), to protect our test enzyme, the paradigmatic P-type ATPase SERCA1a from sarcoplasmic reticulum. Performing such experiments for one's favourite protein probably remains useful in pre-screening assays testing various detergents. PMID:27443956
NASA Astrophysics Data System (ADS)
Vachirasricirikul, Sitthidet; Ngamroo, Issarachai; Kaitwanidvilai, Somyot
It is well known that the power system controller designed by H∞ control is complicated, high order and impractical. In power system applications, practical structures such as proportional integral derivative (PID) etc., are widely used, because of their simple structure, less number of tuning parameters and low-order. However, tuning of controller parameters to achieve a good performance and robustness is based on designer's experiences. To overcome this problem, this paper proposes a fixed structure robust H∞ loop shaping control to design Static Var Compensator (SVC) and Automatic Voltage Regulator (AVR) for robust stabilization of voltage fluctuation in an isolated wind-diesel hybrid power system. The structure of the robust controller of SVC and AVR is specified by a PID controller. In the system modeling, a normalized coprime factorization is applied to represent possible unstructured uncertainties in the power system such as variation of system parameters, generating and loading conditions etc. Based on the H∞ loop shaping, the performance and robust stability conditions are formulated as the optimization problem. The particle swarm optimization is applied to solve for PID control parameters of SVC and AVR simultaneously. Simulation studies confirm the control effect and robustness of the proposed control.
Leng, Yan; Wang, Zhifei; Tsai, Li-Kai; Leeds, Peter; Fessler, Emily Bame; Wang, Junyu; Chuang, De-Maw
2013-01-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and dramatically elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment dramatically prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels, and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers, and a potential new therapeutic target for CNS disorders. PMID:24468826
Li, XS; Narayanan, S; Michaelis, VK; Ong, TC; Keeler, EG; Kim, H; Mckay, IS; Griffin, RG; Wang, EN
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg, Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the lab-scale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N-2 sorption, Al-27/Si-29 MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N-2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. (C) 2014 Elsevier Inc. All rights reserved.
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K.; Ong, Ta-Chung; Keeler, Eric G.; Kim, Hyunho; McKay, Ian S.; Griffin, Robert G.; Wang, Evelyn N.
2014-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, 27Al/29Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick’s 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K; Ong, Ta-Chung; Keeler, Eric G; Kim, Hyunho; McKay, Ian S; Griffin, Robert G; Wang, Evelyn N
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg(2+) ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, (27)Al/(29)Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2(nd) law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
Exponentiated power Lindley distribution.
Ashour, Samir K; Eltehiwy, Mahmoud A
2015-11-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
Exponentiated power Lindley distribution
Ashour, Samir K.; Eltehiwy, Mahmoud A.
2014-01-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
The petroleum exponential (again)
NASA Astrophysics Data System (ADS)
Bell, Peter M.
The U.S. production and reserves of liquid and gaseous petroleum have declined since 1960, at least in the lower 48 states. This decline stems from decreased discovery rates, as predicted by M. King Hubbert in the mid-1950's. Hubbert's once unpopular views were based on statistical analysis of the production history of the petroleum industry, and now, even with inclusion of the statistical perturbation caused by the Prudhoe Bay-North Alaskan Slope discovery (the largest oil field ever found in the United States), it seems clear again that production is following the exponential curve to depletion of the resource—to the end of the ultimate yield of petroleum from wells in the United States.In a recent report, C. Hall and C. Cleveland of Cornell University show that large atypical discoveries, such as the Prudhoe Bay find, are but minor influences on what now appears to be the crucial intersection of two exponentials [Science, 211, 576-579, 1981]: the production-per-drilled-foot curve of Hubbert, which crosses zero production no later than the year 2005; the other, a curve that plots the energy cost of drilling and extraction with time; that is, the cost-time rate of how much oil is used to drill and extract oil from the ground. The intersection, if no other discoveries the size of the Prudhoe Bay field are made, could be as early as 1990, the end of the present decade. The inclusion of each Prudhoe-Bay-size find extends the year of intersection by only about 6 years. Beyond that point, more than one barrel of petroleum would be expended for each barrel extracted from the ground. The oil exploration-extraction and refining industry is currently the second most energy-intensive industry in the U.S., and the message seems clear. Either more efficient drilling and production techniques are discovered, or domestic production will cease well before the end of this century if the Hubbert analysis modified by Hall and Cleveland is correct.
OPINION: Safe exponential manufacturing
NASA Astrophysics Data System (ADS)
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
Vaseem, Mohammad; McKerricher, Garret; Shamim, Atif
2016-01-13
Currently, silver-nanoparticle-based inkjet ink is commercially available. This type of ink has several serious problems such as a complex synthesis protocol, high cost, high sintering temperatures (∼200 °C), particle aggregation, nozzle clogging, poor shelf life, and jetting instability. For the emerging field of printed electronics, these shortcomings in conductive inks are barriers for their widespread use in practical applications. Formulating particle-free silver inks has potential to solve these issues and requires careful design of the silver complexation. The ink complex must meet various requirements, such as in situ reduction, optimum viscosity, storage and jetting stability, smooth uniform sintered films, excellent adhesion, and high conductivity. This study presents a robust formulation of silver-organo-complex (SOC) ink, where complexing molecules act as reducing agents. The 17 wt % silver loaded ink was printed and sintered on a wide range of substrates with uniform surface morphology and excellent adhesion. The jetting stability was monitored for 5 months to confirm that the ink was robust and highly stable with consistent jetting performance. Radio frequency inductors, which are highly sensitive to metal quality, were demonstrated as a proof of concept on flexible PEN substrate. This is a major step toward producing high-quality electronic components with a robust inkjet printing process. PMID:26713357
NASA Astrophysics Data System (ADS)
Wang, Yonggang; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Yang, Wenge; Zhao, Yusheng
2016-01-01
The structure stability under high pressure and thermal expansion behavior of Na3OBr and Na4OI2, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na3OBr and Na4OI2, respectively. The cubic Na3OBr structure and tetragonal Na4OI2 with intergrowth K2NiF4 structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na4OI2 exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20-80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
NASA Astrophysics Data System (ADS)
Faure, Guilhem; Koonin, Eugene V.
2015-05-01
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
NASA Astrophysics Data System (ADS)
Ho, D.; Salmonson, J.; Haan, S.; Clark, D.; Lindl, J.; Meezan, N.; Thomas, C.
2015-11-01
We present six ignition designs using W-doped HDC ablators with, respectively, 2, 3, and 4-step increases in Tr. Fuel adiabat α ranges between 1.5 and 4. The 4-step design has the lowest α of 1.5 but has the highest ablation front Rayleigh-Taylor (RT) growth. Consequently, the overall robustness of the 4-step design is inferior to the intermediate- α 3-step design, assuming typical currently measured surface roughness spectrum. As the foot level is increased further and the shocks merge inside the fuel, the fuel adiabat is raised to 4. The RT growth and mix are reduced but the 1D margin is decreased making it overall more susceptible to surface roughness. The 2-step α = 2.5 design turns out to be the most robust against surface roughness and still can deliver very high 1D yield of 14.5 MJ. Systematic evaluation of the robustness of these capsules with respect to low-mode radiation asymmetries, will also be discussed. Different paths to achieve low-convergence-ratio implosions (i.e. high velocity and high α as one option versus low velocity and low α as another option), while still giving respectable neutron yield will be presented. Finally, we discuss how the performance of these doped capsules changes; if the Au wall of the hohlraum is replaced by U. Work performed under auspices of U.S. DOE by LLNL under DE-AC52-07NA27344.
Pandya, Darpan N; Bhatt, Nikunj; An, Gwang Il; Ha, Yeong Su; Soni, Nisarg; Lee, Hochun; Lee, Yong Jin; Kim, Jung Young; Lee, Woonghee; Ahn, Heesu; Yoo, Jeongsoo
2014-09-11
The first macrocyclic bifunctional chelator incorporating propylene cross-bridge was efficiently synthesized from cyclam in seven steps. After the introduction of an extra functional group for facile conjugation onto the propylene cross-bridge, the two carboxylic acid pendants could contribute to strong coordination of Cu(II) ions, leading to a robust Cu complex. The cyclic RGD peptide conjugate of PCB-TE2A-NCS was prepared and successfully radiolabeled with (64)Cu ion. The radiolabeled peptide conjugate was evaluated in vivo through a biodistribution study and animal PET imaging to demonstrate high tumor uptake with low background. PMID:25137619
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth. PMID:25062238
Jiang, Yanjun; Liu, Xinlong; Chen, Yafei; Zhou, Liya; He, Ying; Ma, Li; Gao, Jing
2014-02-01
A novel catalytic system of Pickering emulsion stabilized by lipase-containing periodic mesoporous organosilica was constructed (named LP@PE) and used as biocatalyst for biodiesel production. The reaction parameters were optimized and the optimum conditions were as follows: the water fraction 0.65%, molar ratio of ethanol to oleic acid 2:1, immobilized lipase particles 150mg, phosphate buffer pH 7.0 and temperature 30°C. Under these conditions, the maximum biodiesel yield obtained via esterification of oleic acid with ethanol could reach 95.8%. The biodiesel yield could maintain 88.6% after LP@PE was used 15times. The LP@PE was also used in the synthesis of biodiesel from Jatropha curcas oil. The highest yield could reach 87.1% and the yield was 73.0% after 10 cycles. All these results demonstrated that Pickering emulsion system stabilized by immobilized enzyme may possess much potential in many enzymatic industrial applications. PMID:24368276
Sneppen, Kim; Dodd, Ian B
2015-01-01
How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation. PMID:25830651
Sneppen, Kim; Dodd, Ian B
2015-01-01
How alternative chromatin-based regulatory states can be made stable and heritable in order to provide robust epigenetic memory is poorly understood. Here, we develop a stochastic model of the silencing system in Saccharomyces cerevisiae that incorporates cooperative binding of the repressive SIR complex and antisilencing histone modifications, in addition to positive feedback in Sir2 recruitment. The model was able to reproduce key features of SIR regulation of an HM locus, including heritable bistability, dependence on the silencer elements, and sensitivity to SIR dosage. We found that antisilencing methylation of H3K79 by Dot1 was not needed to generate these features, but acted to reduce spreading of SIR binding, consistent with its proposed role in containment of silencing. In contrast, cooperative inter-nucleosome interactions mediated by the SIR complex were critical for concentrating SIR binding around the silencers in the absence of barriers, and for providing bistability in SIR binding. SIR-SIR interactions magnify the cooperativity in the Sir2-histone deacetylation positive feedback reaction and complete a double-negative feedback circuit involving antisilencing modifications. Thus, our modeling underscores the potential importance of cooperative interactions between nucleosome-bound complexes both in the SIR system and in other chromatin-based complexes in epigenetic regulation. PMID:25830651
Barth, Aline Bergesch; de Oliveira, Gabriela Bolfe; Malesuik, Marcelo Donadel; Paim, Clésio Soldatelli; Volpato, Nadia Maria
2011-08-01
A stability-indicating liquid chromatography method for the determination of the antifungal agent butenafine hydrochloride (BTF) in a cream was developed and validated using the Plackett-Burman experimental design for robustness evaluation. Also, the drug photodegradation kinetics was determined. The analytical column was operated with acetonitrile, methanol and a solution of triethylamine 0.3% adjusted to pH 4.0 (6:3:1) at a flow rate of 1 mL/min and detection at 283 nm. BTF extraction from the cream was done with n-butyl alcohol and methanol in ultrasonic bath. The performed degradation conditions were: acid and basic media with HCl 1M and NaOH 1M, respectively, oxidation with H(2)O(2) 10%, and the exposure to UV-C light. No interference in the BTF elution was verified. Linearity was assessed (r(2) = 0.9999) and ANOVA showed non-significative linearity deviation (p > 0.05). Adequate results were obtained for repeatability, intra-day precision, and accuracy. Critical factors were selected to examine the method robustness with the two-level Plackett-Burman experimental design and no significant factors were detected (p > 0.05). The BTF photodegradation kinetics was determined for the standard and for the cream, both in methanolic solution, under UV light at 254 nm. The degradation process can be described by first-order kinetics in both cases. PMID:21801482
Real-Time Exponential Curve Fits Using Discrete Calculus
NASA Technical Reports Server (NTRS)
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Punctuated evolution and robustness in morphogenesis
Grigoriev, D.; Reinitz, J.; Vakulenko, S.; Weber, A.
2014-01-01
This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. PMID:24996115
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-01-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA. PMID:26516290
Vasantha, Vivek Arjunan; Junhui, Chen; Ying, Tay Boon; Parthiban, Anbanandam
2015-10-13
Metal nanoparticles (MNps) tend to be influenced by environmental factors such as pH, ionic strength, and temperature, thereby leading to aggregation. Forming stable aqueous dispersions could be one way of addressing the environmental toxicity of MNps. In contrast to the electrolyte-induced aggregation of MNps, novel zwitterionic sulfabetaine polymers reported here act as stabilizers of MNps even under high salinity. Polysulfabetaines exhibited unique solubility and swelling tendencies in brine and deionized water, respectively. The polysulfabetaines derived from methacrylate (PSBMA) and methacrylamide (PSBMAm) also showed reversible salt-responsive and thermoresponsive behaviors as confirmed by cloud-point titration, transmittance, and dynamic light scattering studies. The brine soluble nature was explored for its ability to be used as a capping agents to form metal nanoparticles using formic acid as a reducing agent. Thus, silver and noble metal (gold and palladium) nanoparticles were synthesized. The nanoparticles formed were characterized by UV-vis, XRD, TEM, EDX, and DLS studies. The size of the nanoparticles remained more or less the same even after 2 months of storage in 2 M sodium chloride solution under ambient conditions and also at elevated temperatures as confirmed by light-scattering measurements. The tunable, stimuli-responsive polysulfabetaine-capped stable MNp formed under low (hyposalinity) and hypersalinity could find potential applications in a variety of areas. PMID:26394088
Exponential Finite-Difference Technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1989-01-01
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…
Exponential tilting in Bayesian asymptotics
Kharroubi, S. A.; Sweeting, T. J.
2016-01-01
We use exponential tilting to obtain versions of asymptotic formulae for Bayesian computation that do not involve conditional maxima of the likelihood function, yielding a more stable computational procedure and significantly reducing computational time. In particular we present an alternative version of the Laplace approximation for a marginal posterior density. Implementation of the asymptotic formulae and a modified signed root based importance sampler are illustrated with an example. PMID:27279661
Exponential estimates of symplectic slow manifolds
NASA Astrophysics Data System (ADS)
Kristiansen, K. U.; Wulff, C.
2016-07-01
In this paper we prove the existence of an almost invariant symplectic slow manifold for analytic Hamiltonian slow-fast systems with finitely many slow degrees of freedom for which the error field is exponentially small. We allow for infinitely many fast degrees of freedom. The method we use is motivated by a paper of MacKay from 2004. The method does not notice resonances, and therefore we do not pose any restrictions on the motion normal to the slow manifold other than it being fast and analytic. We also present a stability result and obtain a generalization of a result of Gelfreich and Lerman on an invariant slow manifold to (finitely) many fast degrees of freedom.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Saad, Ahmed S; Ismail, Nahla S; Soliman, Marwa; Zaazaa, Hala E
2016-03-01
A sensitive and highly selective stability-indicating gradient HPLC method was developed and validated for simultaneous determination of clorsulon (CLO) and ivermectin (IVM) in the presence of their degradation products. The drugs were subjected to different stress conditions, including acid and alkaline hydrolysis, oxidative, thermal, and photolytic forced degradation. The robustness of the proposed method was assessed using the Plackett-Burman experimental design, the factors affecting system performance were defined, and nonsignificant intervals for the significant factors were determined. The separation was carried out on a ZORBAX SB phenyl analytical column (250 × 4.6 mm id, 5 μm particle size), with gradient elution utilizing 10 mM sodium dihydrogen phosphate and acetonitrile as mobile phase. UV detection was performed for CLO and IVM at 254 nm over a concentration range of 4-140 and 5-50 μg/mL, respectively, with mean percentage recoveries of 99.90 ± 1.30 and 98.59 ± 1.16%, respectively. The proposed method was successfully applied to a pharmaceutical dosage form containing the investigated drugs. The results were statistically compared with the official HPLC methods, and no significant differences were found. PMID:26997479
NASA Astrophysics Data System (ADS)
Tulsi, Avatar
2016-07-01
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers significant robustness to certain systematic errors. To search N items, our recursive algorithm can tolerate errors of size O(1{/}√{ln N}) which is exponentially better than quantum walk algorithms for which tolerable error size is only O(ln N{/}√{N}). Also, our algorithm does not need any ancilla qubit. Thus our algorithm is much easier to implement experimentally compared to quantum walk algorithms.
NASA Astrophysics Data System (ADS)
Tulsi, Avatar
2016-04-01
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers significant robustness to certain systematic errors. To search N items, our recursive algorithm can tolerate errors of size O(1{/}√{N}) which is exponentially better than quantum walk algorithms for which tolerable error size is only O(ln N{/}√{N}) . Also, our algorithm does not need any ancilla qubit. Thus our algorithm is much easier to implement experimentally compared to quantum walk algorithms.
Robust stability under additive perturbations
NASA Technical Reports Server (NTRS)
Bhaya, A.; Desoer, C. A.
1985-01-01
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
Derivatives of Siegel modular forms and exponential functions
NASA Astrophysics Data System (ADS)
Bertrand, D.; Zudilin, W. W.
2001-08-01
We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over \\mathbb C. Combined with our previous work [3], this provides a complete multidimensional extension of Mahler's theorem on the transcendence degree of the field generated by the exponential function and the derivatives of a modular function. We give two proofs of our result, one purely algebraic, the other analytic, but both based on arguments from differential algebra and on the stability under the action of the symplectic group of the differential field generated by rational and modular functions.
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Robust controls with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1993-01-01
This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here.
Fully exponentially correlated wavefunctions for small atoms
Harris, Frank E.
2015-01-22
Fully exponentially correlated atomic wavefunctions are constructed from exponentials in all the interparticle coordinates, in contrast to correlated wavefunctions of the Hylleraas form, in which only the electron-nuclear distances occur exponentially, with electron-electron distances entering only as integer powers. The full exponential correlation causes many-configuration wavefunctions to converge with expansion length more rapidly than either orbital formulations or correlated wavefunctions of the Hylleraas type. The present contribution surveys the effectiveness of fully exponentially correlated functions for the three-body system (the He isoelectronic series) and reports their application to a four-body system (the Li atom)
Simple robust control laws for robot manipulators. Part 1: Non-adaptive case
NASA Technical Reports Server (NTRS)
Wen, J. T.; Bayard, D. S.
1987-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
NASA Technical Reports Server (NTRS)
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
EXPONENTIAL GALAXY DISKS FROM STELLAR SCATTERING
Elmegreen, Bruce G.; Struck, Curtis E-mail: curt@iastate.edu
2013-10-01
Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly flat rotation curves and near-solid-body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.
Giving Exponential Functions a Fair Shake
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2005-01-01
This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)
The matrix exponential in transient structural analysis
NASA Technical Reports Server (NTRS)
Minnetyan, Levon
1987-01-01
The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Huang, Dong; Cabral, Ricardo; De la Torre, Fernando
2016-02-01
Discriminative methods (e.g., kernel regression, SVM) have been extensively used to solve problems such as object recognition, image alignment and pose estimation from images. These methods typically map image features ( X) to continuous (e.g., pose) or discrete (e.g., object category) values. A major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion, specular reflections or noise. It is important to notice that existing discriminative approaches assume the input variables X to be noise free. Thus, discriminative methods experience significant performance degradation when gross outliers are present. Despite its obvious importance, the problem of robust discriminative learning has been relatively unexplored in computer vision. This paper develops the theory of robust regression (RR) and presents an effective convex approach that uses recent advances on rank minimization. The framework applies to a variety of problems in computer vision including robust linear discriminant analysis, regression with missing data, and multi-label classification. Several synthetic and real examples with applications to head pose estimation from images, image and video classification and facial attribute classification with missing data are used to illustrate the benefits of RR. PMID:26761740
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Exponential fitting quadrature rule for functional equations
NASA Astrophysics Data System (ADS)
Cardone, A.; Paternoster, B.; Santomauro, G.
2012-09-01
A Gaussian quadrature rule for periodic integrand function is presented. The weights and nodes depend on the frequency of the problem and they are constructed by following the exponential fitting theory. The composite rule based on this formula is derived. The analysis of the error is carried out and it proves that the exponentially fitted Gaussian rule is more accurate than the classical Gauss-Legendre rule when oscillatory functions are treated. Some numerical tests are presented.
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; Chueh, Chu-Chen; Yang, Shihe; Jen, Alex K-Y
2016-08-01
Highly crystalline SnO2 is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO2 electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity. PMID:27168338
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view. PMID:23515240
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Finite Higher Spin Transformations from Exponentiation
NASA Astrophysics Data System (ADS)
Monnier, Samuel
2015-05-01
We study the exponentiation of elements of the gauge Lie algebras hs(λ) of three-dimensional higher spin theories. Exponentiable elements generate one-parameter groups of finite higher spin symmetries. We show that elements of hs(λ) in a dense set are exponentiable, when pictured in certain representations of hs(λ), induced from representations of in the complementary series. We also provide a geometric picture of higher spin gauge transformations clarifying the physical origin of these representations. This allows us to construct an infinite-dimensional topological group HS(λ) of finite higher spin symmetries. Interestingly, this construction is possible only for 0 ≤ λ ≤ 1, which are the values for which the higher spin theory is believed to be unitary and for which the Gaberdiel-Gopakumar duality holds. We exponentiate explicitly various commutative subalgebras of hs(λ). Among those, we identify families of elements of hs(λ) exponentiating to the unit of HS(λ), generalizing the logarithms of the holonomies of BTZ black hole connections. Our techniques are generalizable to the Lie algebras relevant to higher spin theories in dimensions above three.
Sniedovich, Moshe
2012-10-01
One would have expected the considerable public debate created by Nassim Taleb's two best selling books on uncertainty, Fooled by Randomness and The Black Swan, to inspire greater caution to the fundamental difficulties posed by severe uncertainty. Yet, methodologies exhibiting an incautious approach to uncertainty have been proposed recently in a range of publications. So, the objective of this short note is to call attention to a prime example of an incautious approach to severe uncertainty that is manifested in the proposition to use the concept radius of stability as a measure of robustness against severe uncertainty. The central proposition of this approach, which is exemplified in info-gap decision theory, is this: use a simple radius of stability model to analyze and manage a severe uncertainty that is characterized by a vast uncertainty space, a poor point estimate, and a likelihood-free quantification of uncertainty. This short discussion serves then as a reminder that the generic radius of stability model is a model of local robustness. It is, therefore, utterly unsuitable for the treatment of severe uncertainty when the latter is characterized by a poor estimate of the parameter of interest, a vast uncertainty space, and a likelihood-free quantification of uncertainty. PMID:22384828
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
Why does human culture increase exponentially?
Enquist, M; Ghirlanda, S; Jarrick, A; Wachtmeister, C-A
2008-08-01
Historical records show that culture can increase exponentially in time, e.g., in number of poems, musical works, scientific discoveries. We model how human capacities for creativity and cultural transmission may make such an increase possible, suggesting that: (1) creativity played a major role at the origin of human culture and for its accumulation throughout history, because cultural transmission cannot, on its own, generate exponentially increasing amounts of culture; (2) exponential increase in amount of culture can only occur if creativity is positively influenced by culture. The evolution of cultural transmission is often considered the main genetic bottleneck for the origin of culture, because natural selection cannot favor cultural transmission without any culture to transmit. Our models suggest that an increase in individual creativity may have been the first step toward human culture, because in a population of creative individuals there may be enough non-genetic information to favor the evolution of cultural transmission. PMID:18571686
Modeling aftershocks as a stretched exponential relaxation
NASA Astrophysics Data System (ADS)
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Method for exponentiating in cryptographic systems
Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.
1994-01-01
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Exponential Growth of Nonlinear Ballooning Instability
Zhu, P.; Hegna, C. C.; Sovinec, C. R.
2009-06-12
Recent ideal magnetohydrodynamic (MHD) theory predicts that a perturbation evolving from a linear ballooning instability will continue to grow exponentially in the intermediate nonlinear phase at the same linear growth rate. This prediction is confirmed in ideal MHD simulations. When the Lagrangian compression, a measure of the ballooning nonlinearity, becomes of the order of unity, the intermediate nonlinear phase is entered, during which the maximum plasma displacement amplitude as well as the total kinetic energy continues to grow exponentially at the rate of the corresponding linear phase.
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Hayes, Roger; LeLacheur, Richard; Dumont, Isabelle; Couerbe, Philippe; Safavi, Afshin; Islam, Rafiq; Pattison, Colin; Cape, Stephanie; Rocci, Mario; Briscoe, Chad; Cojocaru, Laura; Groeber, Elizabeth; Silvestro, Luigi; Bravo, Jennifer; Shoup, Ron; Verville, Manon; Zimmer, Jennifer; Caturla, Maria Cruz; Khadang, Ardeshir; Bourdage, James; Hughes, Nicola; Fatmi, Saadya; Di Donato, Lorella; Sheldon, Curtis; Keyhani, Anahita; Satterwhite, Christina; Yu, Mathilde; Fiscella, Michele; Hulse, James; Lin, Zhongping John; Garofolo, Wei; Savoie, Natasha; Xiao, Yi Qun; Kurylak, Kai; Harris, Sarah; Saxena, Manju; Buonarati, Mike; Lévesque, Ann; Boudreau, Nadine; Lin, Jenny; Khan, Masood U; Ray, Gene; Liu, Yansheng; Xu, Allan; Soni, Gunjan; Ward, Ian; Kingsley, Clare; Ritzén, Hanna; Tabler, Edward; Nicholson, Bob; Bennett, Patrick; van de Merbel, Nico; Karnik, Shane; Bouhajib, Mohammed; Wieling, Jaap; Mulvana, Daniel; Ingelse, Benno; Allen, Mike; Malone, Michele; Fang, Xinping
2016-03-01
The 9th GCCClosed Forum was held just prior to the 2015 Workshop on Recent Issues in Bioanalysis (WRIB) in Miami, FL, USA on 13 April 2015. In attendance were 58 senior-level participants, from eight countries, representing 38 CRO companies offering bioanalytical services. The objective of this meeting was for CRO bioanalytical representatives to meet and discuss scientific and regulatory issues specific to bioanalysis. The issues selected at this year's closed forum include CAPA, biosimilars, preclinical method validation, endogenous biomarkers, whole blood stability, and ELNs. A summary of the industry's best practices and the conclusions from the discussion of these topics is included in this meeting report. PMID:26916197
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Intersection of the Exponential and Logarithmic Curves
ERIC Educational Resources Information Center
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Graphical Models via Univariate Exponential Family Distributions
Yang, Eunho; Ravikumar, Pradeep; Allen, Genevera I.; Liu, Zhandong
2016-01-01
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions. PMID:27570498
Exponential asymptotics of the Voigt functions
NASA Astrophysics Data System (ADS)
Paris, R. B.
2015-06-01
We obtain the asymptotic expansion of the Voigt functionss K( x, y) and L( x, y) for large (real) values of the variables x and y, paying particular attention to the exponentially small contributions. A Stokes phenomenon is encountered as with x > 0 fixed. Numerical examples are presented to demonstrate the accuracy of these new expansions.
Kovalevskaya exponents of systems with exponential interaction
Emel'yanov, K V; Tsygvintsev, A V
2000-10-31
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
Kovalevskaya exponents of systems with exponential interaction
NASA Astrophysics Data System (ADS)
Emel'yanov, K. V.; Tsygvintsev, A. V.
2000-10-01
The Kovalevskaya exponents are calculated for a class of systems generalizing Toda chains: systems with exponential interaction. It is shown that the known cases of algebraic integrability have no direct analogues in the case of spaces with pseudo-Euclidean metrics because the full-parameter expansions of the general solution contain complex powers of the independent variable.
Robust impedance shaping telemanipulation
Colgate, J.E.
1993-08-01
When a human operator performs a task via a bilateral manipulator, the feel of the task is embodied in the mechanical impedance of the manipulator. Traditionally, a bilateral manipulator is designed for transparency; i.e., so that the impedance reflected through the manipulator closely approximates that of the task. Impedance shaping bilateral control, introduced here, differs in that it treats the bilateral manipulator as a means of constructively altering the impedance of a task. This concept is particularly valuable if the characteristic dimensions (e.g., force, length, time) of the task impedance are very different from those of the human limb. It is shown that a general form of impedance shaping control consists of a conventional power-scaling bilateral controller augmented with a real-time interactive task simulation (i.e., a virtual environment). An approach to impedance shaping based on kinematic similarity between tasks of different scale is introduced and illustrated with an example. It is shown that an important consideration in impedance shaping controller design is robustness; i.e., guaranteeing the stability of the operator/manipulator/task system. A general condition for the robustness of a bilateral manipulator is derived. This condition is based on the structured singular value ({mu}). An example of robust impedance shaping bilateral control is presented and discussed.
Robustness analysis applied to substructure controller synthesis
NASA Technical Reports Server (NTRS)
Gonzalez-Oberdoerffer, Marcelo F.; Craig, Roy R., Jr.
1993-01-01
The stability and robustness of the controlled system obtained via the substructure control synthesis (SCS) method of Su et al. (1990) were examined using a six-bay truss model, and employing an LQG control design method to obtain controllers for two separate structures. It is found that the assembled controller provides a stability in this instance. A qualitative assessment of the stability robustness of the system with controller designed with the SCS method is provided by obtaining a controller using the complete truss model and comparing the robustness of the corresponding closed-loop systems.
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation. PMID:26924600
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-01-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm−2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability. PMID:24504344
Photocounting distributions for exponentially decaying sources.
Teich, M C; Card, H C
1979-05-01
Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model. PMID:19687829
Exponential integration algorithms applied to viscoplasticity
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Walker, Kevin P.
1991-01-01
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
Exponential Decay of Correlations Implies Area Law
NASA Astrophysics Data System (ADS)
Brandão, Fernando G. S. L.; Horodecki, Michał
2015-01-01
We prove that a finite correlation length, i.e., exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the state, thus reproducing as a particular case Hastings's proof of an area law for groundstates of 1D gapped Hamiltonians. As a consequence, we show that 1D quantum states with exponential decay of correlations have an efficient classical approximate description as a matrix product state of polynomial bond dimension, thus giving an equivalence between injective matrix product states and states with a finite correlation length. The result can be seen as a rigorous justification, in one dimension, of the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe. It also has implications for quantum computing: it shows that unless a pure state quantum computation involves states with long-range correlations, decaying at most algebraically with the distance, it can be efficiently simulated classically. The proof relies on several previous tools from quantum information theory—including entanglement distillation protocols achieving the hashing bound, properties of single-shot smooth entropies, and the quantum substate theorem—and also on some newly developed ones. In particular we derive a new bound on correlations established by local random measurements, and we give a generalization to the max-entropy of a result of Hastings concerning the saturation of mutual information in multiparticle systems. The proof can also be interpreted as providing a limitation on the phenomenon of data hiding in quantum states.
Wang, Le; Zhang, Hong; Wang, Xiao-Jun; Dierre, Benjamin; Suehiro, Takayuki; Takeda, Takahashi; Hirosaki, Naoto; Xie, Rong-Jun
2015-06-28
Knowing the physicochemical properties of a material is of great importance to design and utilize it in a suitable way. In this paper, we conduct a comprehensive survey of photoluminescence spectra, localized cathodoluminescence, temperature-dependent luminescence efficiency, and applications of Eu(2+)-doped Sr0.5Ba0.5Si2O2N2 in solid-state lighting. This phosphor exhibits a broad emission band with a maximum at 560-580 nm and a full-width at half maximum of 92-103 nm upon blue light excitation, whereas a dual-band emission (i.e., 470 nm and 550 nm) is observed under electron beam irradiation due to perhaps the intergrowth of BaSi2O2N2:Eu(2+) and Sr0.5+σBa0.5-σSi2O2N2:Eu(2+) in each phosphor particle. Under 450 nm blue light irradiation, this yellow phosphor exhibits excellent luminescence properties with absorption, internal and external efficiencies of 83.2, 87.7 and 72.6%, respectively. Furthermore, it also possesses high thermal stability, with the quantum efficiency being decreased by only 4.2% at 150 °C and a high quenching temperature of 450 °C. High-efficiency white LEDs using the title phosphor have a luminous efficacy, color temperature and color rendition of ∼120 lm W(-1), 6000 K and 61, respectively, validating its suitability for use in solid-state white lighting. PMID:26016417
Method for exponentiating in cryptographic systems
Brickell, E.F.; Gordon, D.M.; McCurley, K.S.
1992-12-31
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a pre-approved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g{sup e}; transmitting the value g{sup e} to a remote facility by a communications network; receiving the value g{sup e} at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g{sup xi}, computing a{sub i} representations for a integer base b, where a{sub i} represents the weighing factor of the ith digit of the integer e; computing the individual values of c{sub d} according to the rule: c{sub d}={product}a{sub i}=d g{sup x {sub i}}; and computing the product of {product}{sup h}/{sub d=1} c{sub d}{sup d} from the stored values of from the plurality of memory locations so as to determine a value for g{sup e}.
On Using Exponential Parameter Estimators with an Adaptive Controller
NASA Technical Reports Server (NTRS)
Patre, Parag; Joshi, Suresh M.
2011-01-01
Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.
Twofold PT symmetry in doubly exponential optical lattices
NASA Astrophysics Data System (ADS)
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-01-01
We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT -symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted PT -symmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.
Exponential sensor array geometry and simulation
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1988-01-01
The polar exponential arrays whose geometric parameters are presently analyzed have proven superior to X-Y raster imaging sensors when wide FOV, high central resolution, and rotation- and zoom-invariance are required; attractive applications for such arrays are in spacecraft docking/tracking/stationkeeping and mobile robot navigation. Attention is given to optimal designs minimizing sensor configuration and computation requirements, and the relation of geometric parameters to the three-dimensional sensing precision requirements driving sensor design. A method for smooth patching of the 'blind-spot' singularity in the sensor with a uniformly high-resolution 'fovea' is also presented.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
Robust control with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1988-01-01
Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.
Exponential gradient maker using a disposable syringe.
Domingo, A
1990-08-15
With a simple modification, any disposable syringe can become a reliable and easy to use exponential gradient maker. The modification consists of two notches, made with a razor blade, in the borders of the rubber sealing tip of the plunger. A clamp in the tube connected to the syringe allows control over solution flow. With the clamp prohibiting drainage, the body of the syringe is filled with the desired volume of starting solution I. A magnetic stir bar, small enough to spin inside the syringe is included. The notched plunger is introduced until no air space remains. This forms the fixed volume, closed mixing chamber, while the rest of the volume of the syringe forms the open chamber. The two chambers are connected through the notches in the plunger. The ending solution II is poured after the introduction of the plunger. Opening the clamp allows solution I in the closed chamber to flow out, and the solution II in the open chamber flows through the notches and mixes with solution I. This exponential gradient maker can be reused many times, but the low cost of the components makes it potentially disposable. This feature is especially useful when using toxic chemicals, or when pouring polyacrylamide gradient gels, since the apparatus may be disposed of after contamination or eventual polymerization. PMID:2278394
The Matrix Exponential Approach To Elementary Operations
NASA Astrophysics Data System (ADS)
Delosme, Jean-Marc
1986-04-01
In 1971, J.S. Walther generalized and unified J.E. Volder's coordinate rotation (CORDIC) algorithms. Using Walther's algorithms a few commonly used functions such as divide, multiply-and-accumulate, arctan, plane rotation, arctanh, hyperbolic rotation can be implemented on the same simple hardware (shifters and adders, elementary controller) and computed in approximately the same time. Can other useful functions be computed on the same hardware by further generalizing these algorithms? Our positive answer lies in a deeper understanding of Walther's unification: the key to the CORDIC algorithms is that all of them effect the multiplication of a vector by the exponential of a 2 X 2 matrix. The importance of this observation is readily demonstrated as it easily yields the convergence conditions for the CORDIC algorithms and an efficient way of extending the domain of convergence for the hyperbolic functions. A correspondence may be established between elementary functions such as square-root, √(x2+y) , inverse square-root or cubic root and exponentials of simple matrices. Whenever such a correspondence is found, a CORDIC-like algorithm for computing the function can be synthesized in a very straightforward manner. The algorithms thus derived have a simple structure and exhibit uniform convergence inside an adjustable, precisely defined, domain.
A natural spline interpolation and exponential parameterization
NASA Astrophysics Data System (ADS)
Kozera, R.; Wilkołazka, M.
2016-06-01
We consider here a natural spline interpolation based on reduced data and the so-called exponential parameterization (depending on parameter λ ∈ [0, 1]). In particular, the latter is studied in the context of the trajectory approximation in arbitrary euclidean space. The term reduced data refers to an ordered collection of interpolation points without provision of the corresponding knots. The numerical verification of the intrinsic asymptotics α(λ) in γ approximation by natural spline γ^3'N is conducted here for regular and sufficiently smooth curve γ sampled more-or-less uniformly. We select in this paper the substitutes for the missing knots according to the exponential parameterization. The outcomes of the numerical tests manifest sharp linear convergence orders α(λ) = 1, for all λ ∈ [0, 1). In addition, the latter results in unexpected left-hand side dis-continuity at λ = 1, since as shown again here a sharp quadratic order α(1) = 2 prevails. Remarkably, the case of α(1)=2 (derived for reduced data) coincides with the well-known asymptotics established for a natural spline to fit non-reduced data determined by the sequence of interpolation points supplemented with the corresponding knots (see e.g. [1]).
Exponential Size Distribution of von Willebrand Factor
Lippok, Svenja; Obser, Tobias; Müller, Jochen P.; Stierle, Valentin K.; Benoit, Martin; Budde, Ulrich; Schneppenheim, Reinhard; Rädler, Joachim O.
2013-01-01
Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications. PMID:24010664
Exponential evolution: implications for intelligent extraterrestrial life.
Russell, D A
1983-01-01
Some measures of biologic complexity, including maximal levels of brain development, are exponential functions of time through intervals of 10(6) to 10(9) yrs. Biological interactions apparently stimulate evolution but physical conditions determine the time required to achieve a given level of complexity. Trends in brain evolution suggest that other organisms could attain human levels within approximately 10(7) yrs. The number (N) and longevity (L) terms in appropriate modifications of the Drake Equation, together with trends in the evolution of biological complexity on Earth, could provide rough estimates of the prevalence of life forms at specified levels of complexity within the Galaxy. If life occurs throughout the cosmos, exponential evolutionary processes imply that higher intelligence will soon (10(9) yrs) become more prevalent than it now is. Changes in the physical universe become less rapid as time increases from the Big Bang. Changes in biological complexity may be most rapid at such later times. This lends a unique and symmetrical importance to early and late universal times. PMID:11542467
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Aston, Elizabeth; Channon, Alastair; Day, Charles; Knight, Christopher G.
2013-01-01
Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has
Human-chimpanzee alignment: ortholog exponentials and paralog power laws.
Gao, Kun; Miller, Jonathan
2014-12-01
Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences. PMID:25443749
Duan, Lian; Huang, Lihong; Guo, Zhenyuan
2016-07-01
In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations. PMID:27475061
NASA Astrophysics Data System (ADS)
Duan, Lian; Huang, Lihong; Guo, Zhenyuan
2016-07-01
In this paper, the problems of robust dissipativity and robust exponential dissipativity are discussed for a class of recurrent neural networks with time-varying delay and discontinuous activations. We extend an invariance principle for the study of the dissipativity problem of delay systems to the discontinuous case. Based on the developed theory, some novel criteria for checking the global robust dissipativity and global robust exponential dissipativity of the addressed neural network model are established by constructing appropriate Lyapunov functionals and employing the theory of Filippov systems and matrix inequality techniques. The effectiveness of the theoretical results is shown by two examples with numerical simulations.
Robust nonlinear control of vectored thrust aircraft
NASA Technical Reports Server (NTRS)
Doyle, John C.; Murray, Richard; Morris, John
1993-01-01
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
A Robustly Stabilizing Model Predictive Control Algorithm
NASA Technical Reports Server (NTRS)
Ackmece, A. Behcet; Carson, John M., III
2007-01-01
A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation.
Robust fuzzy logic control of mechanical systems
NASA Astrophysics Data System (ADS)
Kohn-Rich, Sylvia
An approach for the design of robust fuzzy control laws for a large class of mechanical systems was developed. The approach applies Lyapunov's Stability Theory to ensure closed loop stability in the presence of plant perturbations and bounded disturbances. It uses inherent properties of an important class of mechanical and aerospace systems, such as robotic manipulators and large spacecraft, to derive closed-loop stability conditions. Based on these conditions, a methodology for the design of robust fuzzy control systems with guaranteed closed-loop stability was developed. Two classes of control laws for mechanical systems were considered. First, a methodology for point-to-point control was formulated. It combines an energy-type approach with Lyapunov's Stability Theory and its extensions, to obtain robust stability conditions for the closed-loop system. A procedure for control system development based on the above conditions is presented. Finally, a procedure for the implementation of the fuzzy control system with guaranteed performance and closed-loop stability characteristics is formulated. In the second part of the dissertation, the problem of robust tracking for mechanical systems was considered. Based on Lyapunov's Stability Theory and its extensions due to Leitmann and Corless, conditions were developed to prove robust stability and performance in the presence of plant uncertainties, bounded disturbances and control saturation. These conditions involve a large number of parameters and functional dependencies that can be chosen by the designer, therefore are well suited for Fuzzy Logic Control implementation. Three different fuzzy implementation methods for the proposed controls system were analyzed and their relative advantages were discussed. An extensive simulation study of the proposed approach was conducted. It demonstrated the excellent performance of the proposed control systems. The proposed method showed superior performance compared to other robust
Universal stretched exponential relaxation in nanoconfined water
NASA Astrophysics Data System (ADS)
Shekhar, Adarsh; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya; Alm, Camilla K.; Malthe-Sørenssen, Anders
2014-10-01
Understanding the behavior of water confined at the nanometer scale is a fundamental problem not only in physics but also in life sciences, geosciences, and atmospheric sciences. Here, we examine spatial and dynamic heterogeneities in water confined in nanoporous silica using molecular dynamics (MD) simulations. The simulations reveal intermixed low-density water and high-density water with distinct local structures in nanopores of silica. The MD simulations also show dynamic heterogeneities in nanoconfined water. The temporal decay of cage correlation functions for room temperature and supercooled, nanoconfined water is very well described by stretched exponential relaxation, exp(-(t/τ)β). The exponent β has a unique value, d/(d + 2), which agrees with an exact result for diffusion in systems with static, random traps in d = 3 dimensions.
Fluctuation Bounds in the Exponential Bricklayers Process
NASA Astrophysics Data System (ADS)
Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo
2012-04-01
This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.
An Exponentiation Method for XML Element Retrieval
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP. PMID:24696643
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP. PMID:24696643
Radiating stars with exponential Lie symmetries
NASA Astrophysics Data System (ADS)
Mohanlal, R.; Maharaj, S. D.; Tiwari, Ajey K.; Narain, R.
2016-07-01
We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.
Random walk with an exponentially varying step
NASA Astrophysics Data System (ADS)
de La Torre, A. C.; Maltz, A.; Mártin, H. O.; Catuogno, P.; García-Mata, I.
2000-12-01
A random walk with exponentially varying step, modeling damped or amplified diffusion, is studied. Each step is equal to the previous one multiplied by a step factor s (01/s relating different processes. For s<1/2 and s>2, the process is retrodictive (i.e., every final position can be reached by a unique path) and the set of all possible final points after infinite steps is fractal. For step factors in the interval [1/2,2], some cases result in smooth density distributions, other cases present overlapping self-similarity and there are values of the step factor for which the distribution is singular without a density function.
Arsenic for the fool: an exponential connection.
Dani, Sergio U
2010-03-15
Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS(2)) - nicknamed "fool's gold". Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils - in the 7-18ppm range - is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils. PMID:20123147
Modified OMP Algorithm for Exponentially Decaying Signals
Kazimierczuk, Krzysztof; Kasprzak, Paweł
2015-01-01
A group of signal reconstruction methods, referred to as compressed sensing (CS), has recently found a variety of applications in numerous branches of science and technology. However, the condition of the applicability of standard CS algorithms (e.g., orthogonal matching pursuit, OMP), i.e., the existence of the strictly sparse representation of a signal, is rarely met. Thus, dedicated algorithms for solving particular problems have to be developed. In this paper, we introduce a modification of OMP motivated by nuclear magnetic resonance (NMR) application of CS. The algorithm is based on the fact that the NMR spectrum consists of Lorentzian peaks and matches a single Lorentzian peak in each of its iterations. Thus, we propose the name Lorentzian peak matching pursuit (LPMP). We also consider certain modification of the algorithm by introducing the allowed positions of the Lorentzian peaks' centers. Our results show that the LPMP algorithm outperforms other CS algorithms when applied to exponentially decaying signals. PMID:25609044
Exponential family models and statistical genetics.
Palmgren, J
2000-02-01
This article describes the evolution of applied exponential family models, starting at 1972, the year of publication of the seminal papers on generalized linear models and on Cox regression, and leading to multivariate (i) marginal models and inference based on estimating equations and (ii) random effects models and Bayesian simulation-based posterior inference. By referring to recent work in genetic epidemiology, on semiparametric methods for linkage analysis and on transmission/disequilibrium tests for haplotype transmission this paper illustrates the potential for the recent advances in applied probability and statistics to contribute to new and unified tools for statistical genetics. Finally, it is emphasized that there is a need for well-defined postgraduate education paths in medical statistics in the year 2000 and thereafter. PMID:10826159
Cascade DNA nanomachine and exponential amplification biosensing.
Xu, Jianguo; Wu, Zai-Sheng; Shen, Weiyu; Xu, Huo; Li, Hongling; Jia, Lee
2015-11-15
DNA is a versatile scaffold for the assembly of multifunctional nanostructures, and potential applications of various DNA nanodevices have been recently demonstrated for disease diagnosis and treatment. In the current study, a powerful cascade DNA nanomachine was developed that can execute the exponential amplification of p53 tumor suppressor gene. During the operation of the newly-proposed DNA nanomachine, dual-cyclical nucleic acid strand-displacement polymerization (dual-CNDP) was ingeniously introduced, where the target trigger is repeatedly used as the fuel molecule and the nicked fragments are dramatically accumulated. Moreover, each displaced nicked fragment is able to activate the another type of cyclical strand-displacement amplification, increasing exponentially the value of fluorescence intensity. Essentially, one target binding event can induce considerable number of subsequent reactions, and the nanodevice was called cascade DNA nanomachine. It can implement several functions, including recognition element, signaling probe, polymerization primer and template. Using the developed autonomous operation of DNA nanomachine, the p53 gene can be quantified in the wide concentration range from 0.05 to 150 nM with the detection limit of 50 pM. If taking into account the final volume of mixture, the detection limit is calculated as lower as 6.2 pM, achieving an desirable assay ability. More strikingly, the mutant gene can be easily distinguished from the wild-type one. The proof-of-concept demonstrations reported herein is expected to promote the development and application of DNA nanomachine, showing great potential value in basic biology and medical diagnosis. PMID:26042874
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz, Kenneth; Bayard, David S.
1988-01-01
A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.
Robust Inflation from fibrous strings
NASA Astrophysics Data System (ADS)
Burgess, C. P.; Cicoli, M.; de Alwis, S.; Quevedo, F.
2016-05-01
Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models—including the key (though often ignored) issue of modulus stabilisation—to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio r and the spectral index ns of the form r propto (ns‑1)2 where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order r lesssim 0.01. We contrast this general picture with specific popular models, such as the Starobinsky scenario and α-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.
NASA Astrophysics Data System (ADS)
Carmele, Alexander; Heyl, Markus; Kraus, Christina; Dalmonte, Marcello
2015-11-01
We investigate the resilience of symmetry-protected topological edge states at the boundaries of Kitaev chains in the presence of a bath which explicitly introduces symmetry-breaking terms. Specifically, we focus on single-particle losses and gains, violating the protecting parity symmetry, which could generically occur in realistic scenarios. For homogeneous systems we show that the Majorana mode decays exponentially fast. By the inclusion of strong disorder, where the closed system enters a many-body localized phase, we find that the Majorana mode can be stabilized substantially. The decay of the Majorana converts into a stretched exponential form for particle losses or gains occurring in the bulk. In particular, for pure loss dynamics we find a universal exponent α ≃2 /3 . We show that this holds both in the Anderson and many-body localized regimes. Our results thus provide a first step to stabilize edge states even in the presence of symmetry-breaking environments.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Mechanisms for Robust Cognition.
Walsh, Matthew M; Gluck, Kevin A
2015-08-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within variable environments. This raises the question, how do cognitive systems achieve similarly high degrees of robustness? The aim of this study was to identify a set of mechanisms that enhance robustness in cognitive systems. We identify three mechanisms that enhance robustness in biological and engineered systems: system control, redundancy, and adaptability. After surveying the psychological literature for evidence of these mechanisms, we provide simulations illustrating how each contributes to robust cognition in a different psychological domain: psychomotor vigilance, semantic memory, and strategy selection. These simulations highlight features of a mathematical approach for quantifying robustness, and they provide concrete examples of mechanisms for robust cognition. PMID:25352094
Stretched Exponential relaxation in pure Se glass
NASA Astrophysics Data System (ADS)
Dash, S.; Ravindren, S.; Boolchand, P.
A universal feature of glasses is the stretched exponential relaxation, f (t) = exp[ - t / τ ] β . The model of diffusion of excitations to randomly distributed traps in a glass by Phillips1 yields the stretched exponent β = d[d +2] where d, the effective dimensionality. We have measured the enthalpy of relaxation ΔHnr (tw) at Tg of Se glass in modulated DSC experiments as glasses age at 300K and find β = 0.43(2) for tw in the 0
Rearranging the exponential wall for large N-body systems.
Watson, Deborah K; Dunn, Martin
2010-07-01
The work required to solve for the fully interacting N boson wave function, which is widely believed to scale exponentially with N, is rearranged so the problem scales order by order in a perturbation series as N0. The exponential complexity reappears in an exponential scaling with the order of our perturbation series allowing exact analytical calculations for very large N systems through low order. PMID:20867687
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
An exponential filter model predicts lightness illusions.
Zeman, Astrid; Brooks, Kevin R; Ghebreab, Sennay
2015-01-01
Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects
An exponential filter model predicts lightness illusions
Zeman, Astrid; Brooks, Kevin R.; Ghebreab, Sennay
2015-01-01
Lightness, or perceived reflectance of a surface, is influenced by surrounding context. This is demonstrated by the Simultaneous Contrast Illusion (SCI), where a gray patch is perceived lighter against a black background and vice versa. Conversely, assimilation is where the lightness of the target patch moves toward that of the bounding areas and can be demonstrated in White's effect. Blakeslee and McCourt (1999) introduced an oriented difference-of-Gaussian (ODOG) model that is able to account for both contrast and assimilation in a number of lightness illusions and that has been subsequently improved using localized normalization techniques. We introduce a model inspired by image statistics that is based on a family of exponential filters, with kernels spanning across multiple sizes and shapes. We include an optional second stage of normalization based on contrast gain control. Our model was tested on a well-known set of lightness illusions that have previously been used to evaluate ODOG and its variants, and model lightness values were compared with typical human data. We investigate whether predictive success depends on filters of a particular size or shape and whether pooling information across filters can improve performance. The best single filter correctly predicted the direction of lightness effects for 21 out of 27 illusions. Combining two filters together increased the best performance to 23, with asymptotic performance at 24 for an arbitrarily large combination of filter outputs. While normalization improved prediction magnitudes, it only slightly improved overall scores in direction predictions. The prediction performance of 24 out of 27 illusions equals that of the best performing ODOG variant, with greater parsimony. Our model shows that V1-style orientation-selectivity is not necessary to account for lightness illusions and that a low-level model based on image statistics is able to account for a wide range of both contrast and assimilation effects
101 Ways to Teach About Exponential Growth and Its Consequences.
ERIC Educational Resources Information Center
Allen, Rodney F., Ed.
Exponential growth is a mega-concept which has many applications. It is fundamental to understanding how and why systems work and fail, be they natural or man-made systems. Lessons/activities in this booklet are designed for Florida teachers to help provide their students with an understanding of the nature and implications of exponential growth.…
Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
Review of "Going Exponential: Growing the Charter School Sector's Best"
ERIC Educational Resources Information Center
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
Kaneko, Kunihiko
2011-06-01
Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells. PMID:21538414
NASA Technical Reports Server (NTRS)
Narendra, K. S.; Annaswamy, A. M.
1985-01-01
Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known.
NASA Astrophysics Data System (ADS)
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Caraballo, Tomas Kloeden, Peter E. Schmalfuss, Bjoern
2004-10-15
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.
Robust flight control of rotorcraft
NASA Astrophysics Data System (ADS)
Pechner, Adam Daniel
With recent design improvement in fixed wing aircraft, there has been a considerable interest in the design of robust flight control systems to compensate for the inherent instability necessary to achieve desired performance. Such systems are designed for maximum available retention of stability and performance in the presence of significant vehicle damage or system failure. The rotorcraft industry has shown similar interest in adopting these reconfigurable flight control schemes specifically because of their ability to reject disturbance inputs and provide a significant amount of robustness for all but the most catastrophic of situations. The research summarized herein focuses on the extension of the pseudo-sliding mode control design procedure interpreted in the frequency domain. Application of the technique is employed and simulated on two well known helicopters, a simplified model of a hovering Sikorsky S-61 and the military's Black Hawk UH-60A also produced by Sikorsky. The Sikorsky helicopter model details are readily available and was chosen because it can be limited to pitch and roll motion reducing the number of degrees of freedom and yet contains two degrees of freedom, which is the minimum requirement in proving the validity of the pseudo-sliding control technique. The full order model of a hovering Black Hawk system was included both as a comparison to the S-61 helicopter design system and as a means to demonstrate the scaleability and effectiveness of the control technique on sophisticated systems where design robustness is of critical concern.
Mechanisms for Robust Cognition
ERIC Educational Resources Information Center
Walsh, Matthew M.; Gluck, Kevin A.
2015-01-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within…
Comparison of Multi Disk Exponential Gas Distribution vs. Single Disk
NASA Astrophysics Data System (ADS)
Rao, Erica; O'Brien, James
2013-04-01
In fitting galactic rotation curves to data, most standard theories make use of a single exponential disk approximation of the gas distribution to account for the HI synthesis data observed at various radio telescope facilities. We take a sample of surface brightness profiles from The HI Nearby Galaxy Survey (THINGS), and apply both single disk exponentials and Multi-Disk exponentials, and use these various models to see how the modelling procedure changes the Newtonian prediction of the mass of the galaxy. Since the missing mass problem has not been fully explained in large spiral galaxies, different modelling procedures could account for some of the missing matter.
Average-cost based robust structural control
NASA Technical Reports Server (NTRS)
Hagood, Nesbitt W.
1993-01-01
A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed.
NASA Astrophysics Data System (ADS)
Johnson, Y.; Dasgupta, S.
2014-07-01
Multiple unmanned aerial vehicle (UAV) control in formation flight is comparatively a new research area in the field of aerospace engineering. In the proposed work, robust control techniques are implemented to maintain a fixed relative distance in horizontal and vertical direction with uniform pitch orientation in an uncertain leader-follower pattern of close formation flight platform. The forward velocity dynamics is of focal interest in this paper. H-infinity controllers are designed for leader control and its tracking. The robustness of the H-infinity controller is validated with Kharitonov related bounded phase conditions by forming interval polynomials.
Robust Decentralized Controller Design: Subsystem Approach
NASA Astrophysics Data System (ADS)
Rosinová, Danica; Thuan, Nguyen Quang; Veselý, Vojtech; Marko, L'ubomír
2012-01-01
The paper addresses the problem of the robust output feedback PI controller design for complex large-scale stable systems with a state decentralized control structure. A decentralized control design procedure is proposed for static output feedback control which is based on solving robust control design problems of subsystems' size. The presented approach is based
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks. PMID:19520639
Biological robustness: paradigms, mechanisms, and systems principles.
Whitacre, James Michael
2012-01-01
Robustness has been studied through the analysis of data sets, simulations, and a variety of experimental techniques that each have their own limitations but together confirm the ubiquity of biological robustness. Recent trends suggest that different types of perturbation (e.g., mutational, environmental) are commonly stabilized by similar mechanisms, and system sensitivities often display a long-tailed distribution with relatively few perturbations representing the majority of sensitivities. Conceptual paradigms from network theory, control theory, complexity science, and natural selection have been used to understand robustness, however each paradigm has a limited scope of applicability and there has been little discussion of the conditions that determine this scope or the relationships between paradigms. Systems properties such as modularity, bow-tie architectures, degeneracy, and other topological features are often positively associated with robust traits, however common underlying mechanisms are rarely mentioned. For instance, many system properties support robustness through functional redundancy or through response diversity with responses regulated by competitive exclusion and cooperative facilitation. Moreover, few studies compare and contrast alternative strategies for achieving robustness such as homeostasis, adaptive plasticity, environment shaping, and environment tracking. These strategies share similarities in their utilization of adaptive and self-organization processes that are not well appreciated yet might be suggestive of reusable building blocks for generating robust behavior. PMID:22593762
Biological Robustness: Paradigms, Mechanisms, and Systems Principles
Whitacre, James Michael
2012-01-01
Robustness has been studied through the analysis of data sets, simulations, and a variety of experimental techniques that each have their own limitations but together confirm the ubiquity of biological robustness. Recent trends suggest that different types of perturbation (e.g., mutational, environmental) are commonly stabilized by similar mechanisms, and system sensitivities often display a long-tailed distribution with relatively few perturbations representing the majority of sensitivities. Conceptual paradigms from network theory, control theory, complexity science, and natural selection have been used to understand robustness, however each paradigm has a limited scope of applicability and there has been little discussion of the conditions that determine this scope or the relationships between paradigms. Systems properties such as modularity, bow-tie architectures, degeneracy, and other topological features are often positively associated with robust traits, however common underlying mechanisms are rarely mentioned. For instance, many system properties support robustness through functional redundancy or through response diversity with responses regulated by competitive exclusion and cooperative facilitation. Moreover, few studies compare and contrast alternative strategies for achieving robustness such as homeostasis, adaptive plasticity, environment shaping, and environment tracking. These strategies share similarities in their utilization of adaptive and self-organization processes that are not well appreciated yet might be suggestive of reusable building blocks for generating robust behavior. PMID:22593762
FAST TRACK COMMUNICATION: Central limit theorem and deformed exponentials
NASA Astrophysics Data System (ADS)
Vignat, C.; Plastino, A.
2007-11-01
The central limit theorem (CLT) can be ranked among the most important ones in probability theory and statistics and plays an essential role in several basic and applied disciplines, notably in statistical thermodynamics. We show that there exists a natural extension of the CLT from exponentials to so-called deformed exponentials (also denoted as q-Gaussians). Our proposal applies exactly in the usual conditions in which the classical CLT is used.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1985-01-01
Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Exponential increases of RNA virus fitness during large population transmissions.
Novella, I S; Duarte, E A; Elena, S F; Moya, A; Domingo, E; Holland, J J
1995-01-01
The great adaptability shown by RNA viruses is a consequence of their high mutation rates. Here we investigate the kinetics of virus fitness gains during repeated transfers of large virus populations in cell culture. Results always show that fitness increases exponentially. Low fitness clones exhibit regular increases observed as biphasic periods of exponential evolutionary improvement, while neutral clones show monophasic kinetics. These results are significant for RNA virus epidemiology, optimal handling of attenuated live virus vaccines, and routine laboratory procedures. PMID:7597039
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Ruggedness and robustness testing.
Dejaegher, Bieke; Heyden, Yvan Vander
2007-07-27
Due to the strict regulatory requirements, especially in pharmaceutical analysis, analysis results with an acceptable quality should be reported. Thus, a proper validation of the measurement method is required. In this context, ruggedness and robustness testing becomes increasingly more important. In this review, the definitions of ruggedness and robustness are given, followed by a short explanation of the different approaches applied to examine the ruggedness or the robustness of an analytical method. Then, case studies, describing ruggedness or robustness tests of high-performance liquid chromatographic (HPLC), capillary electrophoretic (CE), gas chromatographic (GC), supercritical fluid chromatographic (SFC), and ultra-performance liquid chromatographic (UPLC) assay methods, are critically reviewed and discussed. Mainly publications of the last 10 years are considered. PMID:17379230
Stability of algebraically unstable dispersive flows
NASA Astrophysics Data System (ADS)
King, Kristina; Zaretzky, Paula; Weinstein, Steven; Cromer, Michael; Barlow, Nathaniel
2015-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to a class of partial differential equations describing wave propagation in dispersive media. There are several morphological differences between algebraically growing disturbances and the exponentially growing wave packets inherent to classical linear stability analysis, and these are elucidated in this study.
NASA Astrophysics Data System (ADS)
Cox, Henry; Heaney, Kevin D.
2003-04-01
The term robustness in signal processing applications usually refers to approaches that are not degraded significantly when the assumptions that were invoked in defining the processing algorithm are no longer valid. Highly tuned algorithms that fall apart in real-world conditions are useless. The classic example is super-directive arrays of closely spaced elements. The very narrow beams and high directivity could be predicted under ideal conditions, could not be achieved under realistic conditions of amplitude, phase and position errors. The robust design tries to take into account the real environment as part of the optimization problem. This problem led to the introduction of the white noise gain constraint and diagonal loading in adaptive beam forming. Multiple linear constraints have been introduced in pursuit of robustness. Sonar systems such as towed arrays operate in less than ideal conditions, making robustness a concern. A special problem in sonar systems is failed array elements. This leads to severe degradation in beam patterns and bearing response patterns. Another robustness issue arises in matched field processing that uses an acoustic propagation model in the beamforming. Knowledge of the environmental parameters is usually limited. This paper reviews the various approaches to achieving robustness in sonar systems.
Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised
NASA Technical Reports Server (NTRS)
Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.
1995-01-01
The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
Exponential H∞ filtering for discrete-time switched neural networks with random delays.
Mathiyalagan, Kalidass; Su, Hongye; Shi, Peng; Sakthivel, Rathinasamy
2015-04-01
This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design. PMID:25020225
Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles
Warshaw, S I
2001-07-15
In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.
NASA Technical Reports Server (NTRS)
Pratt, D. T.
1984-01-01
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Robust control of accelerators
Johnson, W.J.D. ); Abdallah, C.T. )
1990-01-01
The problem of controlling the variations in the rf power system can be effectively cast as an application of modern control theory. Two components of this theory are obtaining a model and a feedback structure. The model inaccuracies influence the choice of a particular controller structure. Because of the modeling uncertainty, one has to design either a variable, adaptive controller or a fixed, robust controller to achieve the desired objective. The adaptive control scheme usually results in very complex hardware; and, therefore, shall not be pursued in this research. In contrast, the robust control methods leads to simpler hardware. However, robust control requires a more accurate mathematical model of the physical process than is required by adaptive control. Our research at the Los Alamos National Laboratory (LANL) and the University of New Mexico (UNM) has led to the development and implementation of a new robust rf power feedback system. In this paper, we report on our research progress. In section one, the robust control problem for the rf power system and the philosophy adopted for the beginning phase of our research is presented. In section two, the results of our proof-of-principle experiments are presented. In section three, we describe the actual controller configuration that is used in LANL FEL physics experiments. The novelty of our approach is that the control hardware is implemented directly in rf without demodulating, compensating, and then remodulating.
Robust control of accelerators
NASA Astrophysics Data System (ADS)
Joel, W.; Johnson, D.; Chaouki, Abdallah T.
1991-07-01
The problem of controlling the variations in the rf power system can be effectively cast as an application of modern control theory. Two components of this theory are obtaining a model and a feedback structure. The model inaccuracies influence the choice of a particular controller structure. Because of the modelling uncertainty, one has to design either a variable, adaptive controller or a fixed, robust controller to achieve the desired objective. The adaptive control scheme usually results in very complex hardware; and, therefore, shall not be pursued in this research. In contrast, the robust control method leads to simpler hardware. However, robust control requires a more accurate mathematical model of the physical process than is required by adaptive control. Our research at the Los Alamos National Laboratory (LANL) and the University of New Mexico (UNM) has led to the development and implementation of a new robust rf power feedback system. In this article, we report on our research progress. In section 1, the robust control problem for the rf power system and the philosophy adopted for the beginning phase of our research is presented. In section 2, the results of our proof-of-principle experiments are presented. In section 3, we describe the actual controller configuration that is used in LANL FEL physics experiments. The novelty of our approach is that the control hardware is implemented directly in rf. without demodulating, compensating, and then remodulating.
Engineering robust intelligent robots
NASA Astrophysics Data System (ADS)
Hall, E. L.; Ali, S. M. Alhaj; Ghaffari, M.; Liao, X.; Cao, M.
2010-01-01
The purpose of this paper is to discuss the challenge of engineering robust intelligent robots. Robust intelligent robots may be considered as ones that not only work in one environment but rather in all types of situations and conditions. Our past work has described sensors for intelligent robots that permit adaptation to changes in the environment. We have also described the combination of these sensors with a "creative controller" that permits adaptive critic, neural network learning, and a dynamic database that permits task selection and criteria adjustment. However, the emphasis of this paper is on engineering solutions which are designed for robust operations and worst case situations such as day night cameras or rain and snow solutions. This ideal model may be compared to various approaches that have been implemented on "production vehicles and equipment" using Ethernet, CAN Bus and JAUS architectures and to modern, embedded, mobile computing architectures. Many prototype intelligent robots have been developed and demonstrated in terms of scientific feasibility but few have reached the stage of a robust engineering solution. Continual innovation and improvement are still required. The significance of this comparison is that it provides some insights that may be useful in designing future robots for various manufacturing, medical, and defense applications where robust and reliable performance is essential.
Exponential Sensitivity and its Cost in Quantum Physics.
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-01-01
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076
Exponential rise of dynamical complexity in quantum computing through projections
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-01-01
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692
Rotational stretched exponential relaxation in random trap-barrier model
NASA Astrophysics Data System (ADS)
Aydiner, Ekrem
2015-07-01
The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature. Project supported by Istanbul University (Grant Nos. 28432 and 45662).
Exponential Sensitivity and its Cost in Quantum Physics
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-01-01
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076
Design of a 9-loop quasi-exponential waveform generator.
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output. PMID:26724051
Design of a 9-loop quasi-exponential waveform generator
NASA Astrophysics Data System (ADS)
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
Kullback-Leibler divergence and the Pareto-Exponential approximation.
Weinberg, G V
2016-01-01
Recent radar research interests in the Pareto distribution as a model for X-band maritime surveillance radar clutter returns have resulted in analysis of the asymptotic behaviour of this clutter model. In particular, it is of interest to understand when the Pareto distribution is well approximated by an Exponential distribution. The justification for this is that under the latter clutter model assumption, simpler radar detection schemes can be applied. An information theory approach is introduced to investigate the Pareto-Exponential approximation. By analysing the Kullback-Leibler divergence between the two distributions it is possible to not only assess when the approximation is valid, but to determine, for a given Pareto model, the optimal Exponential approximation. PMID:27247900
Exponential filtering of singular values improves photoacoustic image reconstruction.
Bhatt, Manish; Gutta, Sreedevi; Yalavarthy, Phaneendra K
2016-09-01
Model-based image reconstruction techniques yield better quantitative accuracy in photoacoustic image reconstruction. In this work, an exponential filtering of singular values was proposed for carrying out the image reconstruction in photoacoustic tomography. The results were compared with widely popular Tikhonov regularization, time reversal, and the state of the art least-squares QR-based reconstruction algorithms for three digital phantom cases with varying signal-to-noise ratios of data. It was shown that exponential filtering provides superior photoacoustic images of better quantitative accuracy. Moreover, the proposed filtering approach was observed to be less biased toward the regularization parameter and did not come with any additional computational burden as it was implemented within the Tikhonov filtering framework. It was also shown that the standard Tikhonov filtering becomes an approximation to the proposed exponential filtering. PMID:27607501
Exponential time-differencing with embedded Runge–Kutta adaptive step control
Whalen, P.; Brio, M.; Moloney, J.V.
2015-01-01
We have presented the first embedded Runge–Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In our stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations: the shock-fronts of Burgers equation, interacting KdV solitons, KS controlled chaos, and critical collapse of two-dimensional NLS.
NASA Astrophysics Data System (ADS)
Yang, Dong-Sheng; Liu, Zhen-Wei; Zhao, Yan; Liu, Zhao-Bing
2012-04-01
The networked synchronization problem of a class of master-slave chaotic systems with time-varying communication topologies is investigated in this paper. Based on algebraic graph theory and matrix theory, a simple linear state feedback controller is designed to synchronize the master chaotic system and the slave chaotic systems with a time-varying communication topology connection. The exponential stability of the closed-loop networked synchronization error system is guaranteed by applying Lyapunov stability theory. The derived novel criteria are in the form of linear matrix inequalities (LMIs), which are easy to examine and tremendously reduce the computation burden from the feedback matrices. This paper provides an alternative networked secure communication scheme which can be extended conveniently. An illustrative example is given to demonstrate the effectiveness of the proposed networked synchronization method.
Exponential growth of codimensions of identities of algebras with unity
NASA Astrophysics Data System (ADS)
Zaicev, M. V.; Repovš, D.
2015-10-01
The asymptotic behaviour is studied of exponentially bounded sequences of codimensions of identities of algebras with unity. A series of algebras is constructed for which the base of the exponential increases by exactly 1 when an outer unity is adjoined to the original algebra. It is shown that the PI-exponents of unital algebras can take any value greater than 2, and the exponents of finite-dimensional unital algebras form a dense subset in the domain \\lbrack 2,∞). Bibliography: 34 titles.
Suppression of Exponential Electronic Decay in a Charged Environment
Averbukh, Vitali; Saalmann, Ulf; Rost, Jan Michael
2010-06-11
Inner-shell ionization of atoms and molecules leads to the creation of highly excited ionic states that often decay by electron emission. The dynamics of the decay is usually assumed to be exponential and the process is characterized by a decay rate. Here we show that in a multiply ionized cluster created by interaction with a high-intensity free-electron laser (FEL) radiation, trapping of the emitted electron by the neighboring ions changes the character of the decay dynamics qualitatively to the extent that it can become oscillatory instead of exponential. Implications of the predicted effect on Coster-Kronig and interatomic Coulombic decay processes induced by FELs are investigated.
Expansivity properties and rigidity for non-recurrent exponential maps
NASA Astrophysics Data System (ADS)
Benini, Anna Miriam
2015-07-01
We show that an exponential map fc(z) = ez + c whose singular value c is combinatorially non-recurrent and non-escaping is uniquely determined by its combinatorics, i.e. the pattern in which its periodic dynamic rays land together. We do this by constructing puzzles and parapuzzles in the exponential family. We also prove that f is expanding on the postsingular set with respect to the Euclidean metric in the case that the singular value is non-recurrent. Finally, we show that boundedness of the postsingular set implies combinatorial non-recurrence if c is in the Julia set.
Exponential velocity profile of granular flows down a confined heap
NASA Astrophysics Data System (ADS)
Martínez, E.; González-Lezcano, A.; Batista-Leyva, A. J.; Altshuler, E.
2016-06-01
Thick granular flows are essential to many natural and industrial phenomena. Experimentally, it has been well established that the grain velocity profile is linear from the free surface to a certain depth, after which it decreases exponentially in the so-called "creep region". In this paper we obtain an exponential velocity profile based on the force balance of a grain near a wall, where the Janssen effect and the non-locality of interactions between grains are considered. When experimental parameters such as flow angles and friction coefficients are introduced in our model, it is able to reproduce experimental creep velocity profiles previously reported in the literature.
Exponential model for option prices: Application to the Brazilian market
NASA Astrophysics Data System (ADS)
Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.
2016-03-01
In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
Excitation of a single atom with exponentially rising light pulses.
Aljunid, Syed Abdullah; Maslennikov, Gleb; Wang, Yimin; Dao, Hoang Lan; Scarani, Valerio; Kurtsiefer, Christian
2013-09-01
We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique. PMID:25166660
Excitation of a Single Atom with Exponentially Rising Light Pulses
NASA Astrophysics Data System (ADS)
Aljunid, Syed Abdullah; Maslennikov, Gleb; Wang, Yimin; Dao, Hoang Lan; Scarani, Valerio; Kurtsiefer, Christian
2013-09-01
We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique.
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Dehyadegari, A.; Sheykhi, A.; Dehghani, M. H.
2016-03-01
In this paper, we construct a new class of topological black hole Lifshitz solutions in the presence of nonlinear exponential electrodynamics for Einstein-dilaton gravity. We show that the reality of Lifshitz supporting Maxwell matter fields exclude the negative horizon curvature solutions except for the asymptotic AdS case. Calculating the conserved and thermodynamical quantities, we obtain a Smarr type formula for the mass and confirm that thermodynamics first law is satisfied on the black hole horizon. Afterward, we study the thermal stability of our solutions and figure out the effects of different parameters on the stability of solutions under thermal perturbations. Next, we apply the gauge/gravity duality in order to calculate the ratio of shear viscosity to entropy for a three-dimensional hydrodynamic system by using the pole method. Furthermore, we study the behavior of holographic conductivity for two-dimensional systems such as graphene. We consider linear Maxwell and nonlinear exponential electrodynamics separately and disclose the effect of nonlinearity on holographic conductivity. We indicate that holographic conductivity vanishes for z > 3 in the case of nonlinear electrodynamics while it does not in the linear Maxwell case. Finally, we solve perturbative additional field equations numerically and plot the behaviors of real and imaginary parts of conductivity for asymptotic AdS and Lifshitz cases. We present experimental results match with our numerical ones.
Mathews, K.A.; Brennan, C.R.
1997-07-01
The exponential characteristic (EC) method is one of a family of nonlinear spatial quadratures for discrete ordinates radiation transport that are positive and at least second-order accurate and provide accurate results for deep-penetration problems using coarse meshes. The authors use a split-cell methodology to adapt the method to unstructured grids of arbitrarily shaped and oriented triangular cells that provide efficient representation of curved surfaces. Exponential representations of the flux entering through a cell edge and of the scattering source within a cell are constructed to match average values and first moments passed from the adjacent cell (or from the boundary conditions) or obtained from the angular quadrature of the directional flux spatial moments in the previous iteration (or from an initial guess). The resulting one- and two-dimensional nonlinear rootsolving problems are efficiently solved using Newton`s method with an accurate starting approximation. Improved algorithms, presented here, have increased the efficiency of the method by a factor of 10 as compared to an initial report. The EC method now costs only twice as much per cell as does the linear characteristic method but can be accurate with many fewer cells. Numerical testing shows the EC method to be robust and effective.
Robust controller design for a skid to turn missile
NASA Astrophysics Data System (ADS)
Sreenatha, A. G.; Rajhans, Vivek; Bhardwaj, Neeraj
1999-11-01
The design and analysis of Robust Autopilot for skid-to-turn missile is presented. Two of the popular Robust Controller design approaches, The Loop Shaping Design Procedure (LSDP) and The Robust Eigenstructure Assignment are considered. The missile model considered in the present work is having lightly damped modes and non-minimum phase zeros, with stringent performance requirements. Numerical results are presented to evaluate the Robustness of stability and performance of the controller. Merits and demerits of the above said methodologies are brought out clearly as applied to this specific plant.
Learning robust plans for mobile robots from a single trial
Engelson, S.P.
1996-12-31
We address the problem of learning robust plans for robot navigation by observing particular robot behaviors. In this Paper we present a method which can learn a robust reactive example of a desired behavior. The translating a sequence of events arising system into a plan which represents among such events. This method allows us to rely or the underlying stability properties of low-level behavior processes in order to produce robust plans. Since the resultant plan reproduces the original behavior of the robot at a high level, it generalizes over small environmental changes and is robust to sensor and effector noise.
Robustness of spatial micronetworks
NASA Astrophysics Data System (ADS)
McAndrew, Thomas C.; Danforth, Christopher M.; Bagrow, James P.
2015-04-01
Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure.
Robustness of spatial micronetworks.
McAndrew, Thomas C; Danforth, Christopher M; Bagrow, James P
2015-04-01
Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure. PMID:25974553
Mutational robustness emerges in a microscopic model of protein evolution
NASA Astrophysics Data System (ADS)
Zeldovich, Konstantin; Shakhnovich, Eugene
2009-03-01
The ability to absorb mutations while retaining structure and function, or mutational robustness, is a remarkable property of natural proteins. We use a computational model of organismic evolution [Zeldovich et al, PLOS Comp Biol 3(7):e139 (2007)], which explicitly couples protein physics and population dynamics, to study mutational robustness of evolved model proteins. We compare evolved sequences with the ones designed to fold into the same native structures and having the same thermodynamic stability, and find that evolved sequences are more robust against point mutations, being less likely to be destabilized, and more likely to increase stability upon a point mutation. These results point to sequence evolution as an important method of protein engineering if mutational robustness of the artificially developed proteins is desired. On the biological side, mutational robustness of proteins appears to be a natural consequence of the divergence-mutation- selection evolutionary process.
Identification and robust control of an experimental servo motor.
Adam, E J; Guestrin, E D
2002-04-01
In this work, the design of a robust controller for an experimental laboratory-scale position control system based on a dc motor drive as well as the corresponding identification and robust stability analysis are presented. In order to carry out the robust design procedure, first, a classic closed-loop identification technique is applied and then, the parametrization by internal model control is used. The model uncertainty is evaluated under both parametric and global representation. For the latter case, an interesting discussion about the conservativeness of this description is presented by means of a comparison between the uncertainty disk and the critical perturbation radius approaches. Finally, conclusions about the performance of the experimental system with the robust controller are discussed using comparative graphics of the controlled variable and the Nyquist stability margin as a robustness measurement. PMID:12071255
Matlab as a robust control design tool
NASA Technical Reports Server (NTRS)
Gregory, Irene M.
1994-01-01
This presentation introduces Matlab as a tool used in flight control research. The example used to illustrate some of the capabilities of this software is a robust controller designed for a single stage to orbit air breathing vehicles's ascent to orbit. The global requirements of the controller are to stabilize the vehicle and follow a trajectory in the presence of atmospheric disturbances and strong dynamic coupling between airframe and propulsion.
Exponentially Fitted Variants of Euler's Method for ODEs
ERIC Educational Resources Information Center
Kanwar, V.; Tomar, S. K.
2008-01-01
A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…
Weight Factor Selection in Double Exponential Smoothing Enrollment Forecasts.
ERIC Educational Resources Information Center
Gardner, Don E.
1981-01-01
The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The basic assumptions and formulas for its use are outlined. The difficulties associated with selecting an appropriate weight factor are discussed, and the potential effect on prediction results is illustrated.…
Looking for Connections between Linear and Exponential Functions
ERIC Educational Resources Information Center
Lo, Jane-Jane; Kratky, James L.
2012-01-01
Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…
Exponential energy growth in adiabatically changing Hamiltonian systems
NASA Astrophysics Data System (ADS)
Pereira, Tiago; Turaev, Dmitry
2015-01-01
We show that the mixed phase space dynamics of a typical smooth Hamiltonian system universally leads to a sustained exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of geometric Brownian motion with a positive drift, and relate it to the steady entropy increase after each period of the parameters variation.
Using Logarithms to Explore Power and Exponential Functions.
ERIC Educational Resources Information Center
Rahn, James R.; Berndes, Barry A.
1994-01-01
Discusses activities to help students make visual generalizations about power and exponential functions, methods to determine an approximate function represented by data using logarithms, hands-on activities, and student activity sheets. Includes a Pascal Turbo computer program which generates random numbers. (MKR)
Teaching Exponential Growth and Decay: Examples from Medicine
ERIC Educational Resources Information Center
Hobbie, Russell K.
1973-01-01
A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)
Exponentiation of eikonal cross sections in nonabelian gauge theories
NASA Astrophysics Data System (ADS)
Gatheral, J. G. M.
1983-12-01
A theorem is presented which generalises the well-known exponentiation property of eikonal cross sections in abelian gauge theories to the nonabelian case. Address after September 1, 1983: Bank of America, 25 Cannon Street, London EC4P 4HN, UK.
Double Exponential Relativity Theory Coupled Theoretically with Quantum Theory?
Montero Garcia, Jose de la Luz; Novoa Blanco, Jesus Francisco
2007-04-28
Here the problem of special relativity is analyzed into the context of a new theoretical formulation: the Double Exponential Theory of Special Relativity with respect to which the current Special or Restricted Theory of Relativity (STR) turns to be a particular case only.
Concept of the Exponential Law Prior to 1900
ERIC Educational Resources Information Center
Curtis, Lorenzo J.
1978-01-01
Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)
On exponential sums of digital sums related to Gelfond's theorem
NASA Astrophysics Data System (ADS)
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
Robust Control Design for Systems With Probabilistic Uncertainty
NASA Technical Reports Server (NTRS)
Crespo, Luis G.; Kenny, Sean P.
2005-01-01
This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.
Robust multivariable controller design for flexible spacecraft
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Armstrong, Ernest S.
1986-01-01
Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.
Exponentially localized Wannier functions in periodic zero flux magnetic fields
NASA Astrophysics Data System (ADS)
De Nittis, G.; Lein, M.
2011-11-01
In this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results [Panati, G., Ann. Henri Poincare 8, 995-1011 (2007), 10.1007/s00023-007-0326-8] to include periodic zero flux magnetic fields which is the setting also investigated by Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. The new notion of magnetic symmetry plays a crucial rôle; to a large class of symmetries for a non-magnetic system, one can associate "magnetic" symmetries of the related magnetic system. Observing that the existence of an exponentially localized Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic time-reversal symmetry is sufficient to ensure the triviality of the Bloch bundle in spatial dimension d = 1, 2, 3. For d = 4, an exponentially localized Wannier basis exists provided that the trace per unit volume of a suitable function of the Fermi projection vanishes. For d > 4 and d ⩽ 2m (stable rank regime) only the exponential localization of a subset of Wannier functions is shown; this improves part of the analysis of Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. Finally, for d > 4 and d > 2m (unstable rank regime) we show that the mere analysis of Chern classes does not suffice in order to prove triviality and thus exponential localization.
Guidance laws with input saturation and nonlinear robust H∞ observers.
Liao, Fei; Luo, Qiang; Ji, Haibo; Gai, Wen
2016-07-01
A novel three-dimensional law based on input-to-state stability (ISS) and nonlinear robust H∞ filtering is proposed for interception of maneuvering targets in the presence of input saturation. A dead zone operator model is introduced to design an ISS-based guidance law to guarantee robust tracking of a maneuvering target. Input saturation and system stability are considered simultaneously, and the globally input-to-state stability have been ensured in theory. Since in practice line-of-sight (LOS) rate is difficult for a pursuer to measure accurately, the nonlinear robust H∞ filtering method is utilized to estimate it. The stability analyses and performed simulation results show that the presented approach is effective. PMID:27018143
Steingrimsson, Jon Arni; Diao, Liqun; Molinaro, Annette M; Strawderman, Robert L
2016-09-10
Estimating a patient's mortality risk is important in making treatment decisions. Survival trees are a useful tool and employ recursive partitioning to separate patients into different risk groups. Existing 'loss based' recursive partitioning procedures that would be used in the absence of censoring have previously been extended to the setting of right censored outcomes using inverse probability censoring weighted estimators of loss functions. In this paper, we propose new 'doubly robust' extensions of these loss estimators motivated by semiparametric efficiency theory for missing data that better utilize available data. Simulations and a data analysis demonstrate strong performance of the doubly robust survival trees compared with previously used methods. Copyright © 2016 John Wiley & Sons, Ltd. PMID:27037609
NASA Astrophysics Data System (ADS)
Rider, William; Witkowski, Walt; Kamm, James R.; Wildey, Tim
2016-02-01
We introduce a new methodology for inferring the accuracy of computational simulations through the practice of solution verification. We demonstrate this methodology on examples from computational heat transfer, fluid dynamics and radiation transport. Our methodology is suited to both well- and ill-behaved sequences of simulations. Our approach to the analysis of these sequences of simulations incorporates expert judgment into the process directly via a flexible optimization framework, and the application of robust statistics. The expert judgment is systematically applied as constraints to the analysis, and together with the robust statistics guards against over-emphasis on anomalous analysis results. We have named our methodology Robust Verification. Our methodology is based on utilizing multiple constrained optimization problems to solve the verification model in a manner that varies the analysis' underlying assumptions. Constraints applied in the analysis can include expert judgment regarding convergence rates (bounds and expectations) as well as bounding values for physical quantities (e.g., positivity of energy or density). This approach then produces a number of error models, which are then analyzed through robust statistical techniques (median instead of mean statistics). This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations.
Robust Collaborative Recommendation
NASA Astrophysics Data System (ADS)
Burke, Robin; O'Mahony, Michael P.; Hurley, Neil J.
Collaborative recommender systems are vulnerable to malicious users who seek to bias their output, causing them to recommend (or not recommend) particular items. This problem has been an active research topic since 2002. Researchers have found that the most widely-studied memory-based algorithms have significant vulnerabilities to attacks that can be fairly easily mounted. This chapter discusses these findings and the responses that have been investigated, especially detection of attack profiles and the implementation of robust recommendation algorithms.
Robust quantitative scratch assay
Vargas, Andrea; Angeli, Marc; Pastrello, Chiara; McQuaid, Rosanne; Li, Han; Jurisicova, Andrea; Jurisica, Igor
2016-01-01
The wound healing assay (or scratch assay) is a technique frequently used to quantify the dependence of cell motility—a central process in tissue repair and evolution of disease—subject to various treatments conditions. However processing the resulting data is a laborious task due its high throughput and variability across images. This Robust Quantitative Scratch Assay algorithm introduced statistical outputs where migration rates are estimated, cellular behaviour is distinguished and outliers are identified among groups of unique experimental conditions. Furthermore, the RQSA decreased measurement errors and increased accuracy in the wound boundary at comparable processing times compared to previously developed method (TScratch). Availability and implementation: The RQSA is freely available at: http://ophid.utoronto.ca/RQSA/RQSA_Scripts.zip. The image sets used for training and validation and results are available at: (http://ophid.utoronto.ca/RQSA/trainingSet.zip, http://ophid.utoronto.ca/RQSA/validationSet.zip, http://ophid.utoronto.ca/RQSA/ValidationSetResults.zip, http://ophid.utoronto.ca/RQSA/ValidationSet_H1975.zip, http://ophid.utoronto.ca/RQSA/ValidationSet_H1975Results.zip, http://ophid.utoronto.ca/RQSA/RobustnessSet.zip, http://ophid.utoronto.ca/RQSA/RobustnessSet.zip). Supplementary Material is provided for detailed description of the development of the RQSA. Contact: juris@ai.utoronto.ca Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26722119
Robustness of metabolic networks
NASA Astrophysics Data System (ADS)
Jeong, Hawoong
2009-03-01
We investigated the robustness of cellular metabolism by simulating the system-level computational models, and also performed the corresponding experiments to validate our predictions. We address the cellular robustness from the ``metabolite''-framework by using the novel concept of ``flux-sum,'' which is the sum of all incoming or outgoing fluxes (they are the same under the pseudo-steady state assumption). By estimating the changes of the flux-sum under various genetic and environmental perturbations, we were able to clearly decipher the metabolic robustness; the flux-sum around an essential metabolite does not change much under various perturbations. We also identified the list of the metabolites essential to cell survival, and then ``acclimator'' metabolites that can control the cell growth were discovered. Furthermore, this concept of ``metabolite essentiality'' should be useful in developing new metabolic engineering strategies for improved production of various bioproducts and designing new drugs that can fight against multi-antibiotic resistant superbacteria by knocking-down the enzyme activities around an essential metabolite. Finally, we combined a regulatory network with the metabolic network to investigate its effect on dynamic properties of cellular metabolism.
Robustness of Interdependent Networks
NASA Astrophysics Data System (ADS)
Havlin, Shlomo
2011-03-01
In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of many interdependent networks. We will present a framework for understanding the robustness of interacting networks subject to such cascading failures and provide a basic analytic approach that may be useful in future studies. We present exact analytical solutions for the critical fraction of nodes that upon removal will lead to a failure cascade and to a complete fragmentation of two interdependent networks in a first order transition. Surprisingly, analyzing complex systems as a set of interdependent networks may alter a basic assumption that network theory has relied on: while for a single network a broader degree distribution of the network nodes results in the network being more robust to random failures, for interdependent networks, the broader the distribution is, the more vulnerable the networks become to random failure. We also show that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. These findings pose a significant challenge to the future design of robust networks that need to consider the unique properties of interdependent networks.
NASA Astrophysics Data System (ADS)
Chowdhary, Girish; Mühlegg, Maximilian; Johnson, Eric
2014-08-01
In model reference adaptive control (MRAC) the modelling uncertainty is often assumed to be parameterised with time-invariant unknown ideal parameters. The convergence of parameters of the adaptive element to these ideal parameters is beneficial, as it guarantees exponential stability, and makes an online learned model of the system available. Most MRAC methods, however, require persistent excitation of the states to guarantee that the adaptive parameters converge to the ideal values. Enforcing PE may be resource intensive and often infeasible in practice. This paper presents theoretical analysis and illustrative examples of an adaptive control method that leverages the increasing ability to record and process data online by using specifically selected and online recorded data concurrently with instantaneous data for adaptation. It is shown that when the system uncertainty can be modelled as a combination of known nonlinear bases, simultaneous exponential tracking and parameter error convergence can be guaranteed if the system states are exciting over finite intervals such that rich data can be recorded online; PE is not required. Furthermore, the rate of convergence is directly proportional to the minimum singular value of the matrix containing online recorded data. Consequently, an online algorithm to record and forget data is presented and its effects on the resulting switched closed-loop dynamics are analysed. It is also shown that when radial basis function neural networks (NNs) are used as adaptive elements, the method guarantees exponential convergence of the NN parameters to a compact neighbourhood of their ideal values without requiring PE. Flight test results on a fixed-wing unmanned aerial vehicle demonstrate the effectiveness of the method.
Historical remarks on exponential product and quantum analysis
Suzuki, Masuo
2015-03-10
The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and a general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].
Rare events and the convergence of exponentially averaged work values
NASA Astrophysics Data System (ADS)
Jarzynski, Christopher
2006-04-01
Equilibrium free energy differences are given by exponential averages of nonequilibrium work values; such averages, however, often converge poorly, as they are dominated by rare realizations. I show that there is a simple and intuitively appealing description of these rare but dominant realizations. This description is expressed as a duality between “forward” and “reverse” processes, and provides both heuristic insights and quantitative estimates regarding the number of realizations needed for convergence of the exponential average. Analogous results apply to the equilibrium perturbation method of estimating free energy differences. The pedagogical example of a piston and gas [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005)] is used to illustrate the general discussion.
Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems.
Cai, Zi; Barthel, Thomas
2013-10-11
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence. PMID:24160582
The scaling of human mobility by taxis is exponential
NASA Astrophysics Data System (ADS)
Liang, Xiao; Zheng, Xudong; Lv, Weifeng; Zhu, Tongyu; Xu, Ke
2012-03-01
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users' locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis' traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.
Exponential growth of bacteria: Constant multiplication through division
NASA Astrophysics Data System (ADS)
Hagen, Stephen J.
2010-12-01
The growth of a bacterial culture is one of the most familiar examples of exponential growth, with important consequences in biology and medicine. Bacterial growth involves more than just a rate constant. To sustain exponential growth, the cell must carefully coordinate the accumulation of mass, constant replication of the chromosome, and physical division. Hence, the growth rate is centrally important in any physical and chemical description of a bacterial cell. These aspects of bacterial growth can be described by empirical laws that suggest simple and intuitive models. Therefore, a quantitative discussion of bacterial growth could be a part of any undergraduate biophysics course. We present a general overview of some classic experimental studies and mathematical models of bacterial growth from a mostly physical perspective.
l-State Solutions of Multiparameter Exponential-type Potentials
NASA Astrophysics Data System (ADS)
Peña, J. J.; García-Martínez, J.; García-Ravelo, J.; Morales, J.
2014-03-01
In the present work, bound state solutions for a class of multiparameter exponential-type potential are obtained in the frame of the Greene and Aldrich approximation for the centrifugal term. The proposal is general and their usefulness is exemplified with the treatment of the Eckart, Manning-Rosen, Hulthen and Deng Fan potentials that are obtained straightforwardly without resorting to specialized methods of solution for each specific potential, as usually is done. Furthermore, the proposal admits other approximations for the centrifugal term indicating an improvement to procedures developed with the same objective. So, our proposal can be considered as an unified treatment of the l-state solutions for exponential-type potentials and can be used to find new solvable potentials.
Steady, Near-exponential Galaxy Disks Produced by Scattering Processes
NASA Astrophysics Data System (ADS)
Struck, Curtis; Elmegreen, Bruce
2016-05-01
Exponential surface brightness profiles are ubiquitous in galaxy disks over a wide range of Hubble types and masses. Radial migration and scattering via bars, waves, clumps and satellites have been discussed as causes, but most of these cannot account for the full range of the phenomenon. Numerical models of clump scattering show that this process can produce near-exponential or core-Sérsic profiles in a variety of circumstances, also suggesting a connection to bulge and elliptical galaxy profiles. Density profile forms do not depend on the specifics of the scattering processes, but stellar kinematics and profile evolution rates do. Analytic models, with a power-law times a Sérsic profile form, can satisfy Jeans equations in cases dominated by either halo potentials (outer disk) or self-gravity (inner disk).
Interactive Visualization Applets for Modular Exponentiation Using Addition Chains
NASA Astrophysics Data System (ADS)
Bahig, Hatem M.; Kotb, Yasser
Online visualization systems have come to be heavily used in education, particularly for online learning. Most e-learning systems, including interactive learning systems, have been designed to simplify understanding the ideas of some main problems or in general overall course materials. This paper presents a novel interactive visualization system for one of the most important operation in public-key cryptosystems. This operation is modular exponentiation using addition chains. An addition chain for a natural number e is a sequence 1 = a 0 < a 1 < ... < a r = e of numbers such that for each 0 < i ≤ r, a i = a j + a k for some 0 ≤ k ≤ j < i. Finding an addition chain with minimal length is NP-hard problem. The proposed system visualizes how to generate addition chains with minimal length using depth-first branch and bound technique and how to compute the modular exponentiation using addition chains.
Least Squ Fit of Lin Combination of Exponential Decay
2001-07-06
This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k) ).
Pricing turbo warrants under mixed-exponential jump diffusion model
NASA Astrophysics Data System (ADS)
Yu, Jianfeng; Xu, Weidong
2016-06-01
Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrant under the mixed-exponential jump diffusion model, which is able to approximate any jump size distribution. The numerical Laplace inversion examples verify that the analytical solutions are accurate. The results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants.
On the Linear Combination of Exponential and Gamma Random Variables
NASA Astrophysics Data System (ADS)
Nadarajah, Saralees; Kotz, Samuel
2005-06-01
The exact distribution of the linear combination α X + β Y is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing and other areas of computer science.
Exponential sums with continuous arguments, interference and factorization
NASA Astrophysics Data System (ADS)
Tamma, V.; Garuccio, A.; Shih, Y.
2011-10-01
We take advantage of the interesting connection between truncated exponential sums with continuous arguments (CTES) in number theory and interference in Physics in order to investigate the challenging problem of factoring large numbers. In particular we develop a novel method of factorization based on the use of an optical computer able to reproduce "CTES interferograms" by exploiting polychromatic interference. The scaling properties at the core of such "factoring" interferograms allows, in principle, the prime number decomposition of several large integers.
An exponentially fitted quadrature rule over unbounded intervals
NASA Astrophysics Data System (ADS)
Conte, D.; Paternoster, B.; Santomauro, G.
2012-09-01
A new class of quadrature formulae for the computation of integrals over unbounded intervals with oscillating integrand is illustrated. Such formulae are a generalization of the gaussian quadrature formulae by exploiting the Exponential Fitting theory. The coefficients depend on the frequency of oscillation, in order to improve the accuracy of the solution. The construction of the methods with 1, 2 and 3 nodes is described, together with the comparison of the order of accuracy with respect to classical formulae.
Exponential growth of publications on carbon nanodots by Chinese authors
Wang, Junqing; Choi, Hak Soo
2015-01-01
Publication statistics was retrieved on carbon nanodots (C-dots) from 2004 up till 2014 using the web of ScienceTM search engine. The number of publications from Chinese authors increased exponentially during this period. Till 2014 China mainland authors contributed 47% of the total publications. Publications on pharmacology and toxicology lagged far behind the publications on chemistry and material science, indicating that research is not solidly moving toward the direction of application. PMID:26380753
Practical robustness measures in multivariable control system analysis. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.
1981-01-01
The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.
Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares
NASA Technical Reports Server (NTRS)
Dorobantu, Andrei; Crespo, Luis G.; Seiler, Peter J.
2012-01-01
A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.
Bayer, T.; Wollenhaupt, M.; Sarpe-Tudoran, C.; Baumert, T.
2009-01-16
We experimentally demonstrate a strong-field coherent control mechanism that combines the advantages of photon locking (PL) and rapid adiabatic passage (RAP). Unlike earlier implementations of PL and RAP by pulse sequences or chirped pulses, we use shaped pulses generated by phase modulation of the spectrum of a femtosecond laser pulse with a generalized phase discontinuity. The novel control scenario is characterized by a high degree of robustness achieved via adiabatic preparation of a state of maximum coherence. Subsequent phase control allows for efficient switching among different target states. We investigate both properties by photoelectron spectroscopy on potassium atoms interacting with the intense shaped light field.
Carlson, J. M.; Doyle, John
2002-01-01
Highly optimized tolerance (HOT) was recently introduced as a conceptual framework to study fundamental aspects of complexity. HOT is motivated primarily by systems from biology and engineering and emphasizes, (i) highly structured, nongeneric, self-dissimilar internal configurations, and (ii) robust yet fragile external behavior. HOT claims these are the most important features of complexity and not accidents of evolution or artifices of engineering design but are inevitably intertwined and mutually reinforcing. In the spirit of this collection, our paper contrasts HOT with alternative perspectives on complexity, drawing on real-world examples and also model systems, particularly those from self-organized criticality. PMID:11875207
Ballance, Robert A.
2003-01-01
The Robust Systems Test Framework (RSTF) provides a means of specifying and running test programs on various computation platforms. RSTF provides a level of specification above standard scripting languages. During a set of runs, standard timing information is collected. The RSTF specification can also gather job-specific information, and can include ways to classify test outcomes. All results and scripts can be stored into and retrieved from an SQL database for later data analysis. RSTF also provides operations for managing the script and result files, and for compiling applications and gathering compilation information such as optimization flags.
2003-01-01
The Robust Systems Test Framework (RSTF) provides a means of specifying and running test programs on various computation platforms. RSTF provides a level of specification above standard scripting languages. During a set of runs, standard timing information is collected. The RSTF specification can also gather job-specific information, and can include ways to classify test outcomes. All results and scripts can be stored into and retrieved from an SQL database for later data analysis. RSTF alsomore » provides operations for managing the script and result files, and for compiling applications and gathering compilation information such as optimization flags.« less
Robust Kriged Kalman Filtering
Baingana, Brian; Dall'Anese, Emiliano; Mateos, Gonzalo; Giannakis, Georgios B.
2015-11-11
Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.
Robust control for uncertain structures
NASA Technical Reports Server (NTRS)
Douglas, Joel; Athans, Michael
1991-01-01
Viewgraphs on robust control for uncertain structures are presented. Topics covered include: robust linear quadratic regulator (RLQR) formulas; mismatched LQR design; RLQR design; interpretations of RLQR design; disturbance rejection; and performance comparisons: RLQR vs. mismatched LQR.
A nearly analytic exponential time difference method for solving 2D seismic wave equations
NASA Astrophysics Data System (ADS)
Zhang, Xiao; Yang, Dinghui; Song, Guojie
2014-02-01
In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in multilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Marmousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
Sliding mode control of continuous time systems with reaching law based on exponential function
NASA Astrophysics Data System (ADS)
Gamorski, Piotr
2015-11-01
In this paper a pseudo-sliding mode control is proposed by introducing a continuous and smooth input signal in order to guarantee both chattering elimination and boundedness of sliding variable derivative in the presence of non-zero external disturbance. For this purpose, having fixed a suitable sliding manifold, a homogeneous differential equation describing the sliding variable evolution is considered. It is discussed later in this paper that the input signal formed on the basis of this equation provides asymptotic convergence of the sliding variable and its derivative to zero as well as the asymptotic stability of the non-linear system in the absence of external disturbance. The dynamics of the system affected by non-zero external disturbance make the state vector converge to domains in a vicinity of the origin at the exponential rate, as the norm of arbitrary trajectory is limited to decreasing exponential function. In order to expand the variety of controllers based on a reaching law and providing the above-mentioned properties, a certain class of functions is presented.
Synthesis Methods for Robust Passification and Control
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M. (Technical Monitor)
2000-01-01
The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.
Robustness and modeling error characterization
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.; Castanon, D. A.; Sandell, N. R., Jr.; Levy, B. C.; Athans, M.; Stein, G.
1984-01-01
The results on robustness theory presented here are extensions of those given in Lehtomaki et al., (1981). The basic innovation in these new results is that they utilize minimal additional information about the structure of the modeling error, as well as its magnitude, to assess the robustness of feedback systems for which robustness tests based on the magnitude of modeling error alone are inconclusive.
Robustness in multicellular systems
NASA Astrophysics Data System (ADS)
Xavier, Joao
2011-03-01
Cells and organisms cope with the task of maintaining their phenotypes in the face of numerous challenges. Much attention has recently been paid to questions of how cells control molecular processes to ensure robustness. However, many biological functions are multicellular and depend on interactions, both physical and chemical, between cells. We use a combination of mathematical modeling and molecular biology experiments to investigate the features that convey robustness to multicellular systems. Cell populations must react to external perturbations by sensing environmental cues and acting coordinately in response. At the same time, they face a major challenge: the emergence of conflict from within. Multicellular traits are prone to cells with exploitative phenotypes that do not contribute to shared resources yet benefit from them. This is true in populations of single-cell organisms that have social lifestyles, where conflict can lead to the emergence of social ``cheaters,'' as well as in multicellular organisms, where conflict can lead to the evolution of cancer. I will describe features that diverse multicellular systems can have to eliminate potential conflicts as well as external perturbations.
Tuteja, Anish; Choi, Wonjae; Mabry, Joseph M.; McKinley, Gareth H.; Cohen, Robert E.
2008-01-01
Superhydrophobic surfaces display water contact angles greater than 150° in conjunction with low contact angle hysteresis. Microscopic pockets of air trapped beneath the water droplets placed on these surfaces lead to a composite solid-liquid-air interface in thermodynamic equilibrium. Previous experimental and theoretical studies suggest that it may not be possible to form similar fully-equilibrated, composite interfaces with drops of liquids, such as alkanes or alcohols, that possess significantly lower surface tension than water (γlv = 72.1 mN/m). In this work we develop surfaces possessing re-entrant texture that can support strongly metastable composite solid-liquid-air interfaces, even with very low surface tension liquids such as pentane (γlv = 15.7 mN/m). Furthermore, we propose four design parameters that predict the measured contact angles for a liquid droplet on a textured surface, as well as the robustness of the composite interface, based on the properties of the solid surface and the contacting liquid. These design parameters allow us to produce two different families of re-entrant surfaces— randomly-deposited electrospun fiber mats and precisely fabricated microhoodoo surfaces—that can each support a robust composite interface with essentially any liquid. These omniphobic surfaces display contact angles greater than 150° and low contact angle hysteresis with both polar and nonpolar liquids possessing a wide range of surface tensions. PMID:19001270
Robust efficient video fingerprinting
NASA Astrophysics Data System (ADS)
Puri, Manika; Lubin, Jeffrey
2009-02-01
We have developed a video fingerprinting system with robustness and efficiency as the primary and secondary design criteria. In extensive testing, the system has shown robustness to cropping, letter-boxing, sub-titling, blur, drastic compression, frame rate changes, size changes and color changes, as well as to the geometric distortions often associated with camcorder capture in cinema settings. Efficiency is afforded by a novel two-stage detection process in which a fast matching process first computes a number of likely candidates, which are then passed to a second slower process that computes the overall best match with minimal false alarm probability. One key component of the algorithm is a maximally stable volume computation - a three-dimensional generalization of maximally stable extremal regions - that provides a content-centric coordinate system for subsequent hash function computation, independent of any affine transformation or extensive cropping. Other key features include an efficient bin-based polling strategy for initial candidate selection, and a final SIFT feature-based computation for final verification. We describe the algorithm and its performance, and then discuss additional modifications that can provide further improvement to efficiency and accuracy.
Robust disturbance rejection for flexible mechanical structures
NASA Astrophysics Data System (ADS)
Enzmann, Marc R.; Doeschner, Christian
2000-06-01
Topic of the presentation is a procedure to determine controller parameters using principles from Internal Model Control (IMC) in combination with Quantitative Feedback Theory (QFT) for robust vibration control of flexible mechanical structures. IMC design is based on a parameterization of all controllers that stabilize a given nominal plant, called the Q-parameter or Youla-parameter. It will be shown that it is possible to choose the controller structure and the Q- parameter in a very straightforward manner, so that a low order controller results, which stabilizes the given nominal model. Additional constraints can be implemented, so that the method allows for a direct and transparent trade-off between control performance and controller complexity and facilitates the inclusion of low-pass filters. In order to test (and if necessary augment) the inherent robust performance of the resulting controllers, boundaries based on the work of Kidron and Yaniv are calculated in the Nichols-Charts of the open loop and the complementary sensitivity function. The application of these boundaries is presented. Very simple uncertainty models for resonant modes are used to assess the robustness of the design. Using a simply structured plant as illustrative example we will demonstrate the design process. This will illuminate several important features of the design process, e.g. trade-off between conflicting objectives, trade- off between controller complexity and achievable performance.
Species interactions differ in their genetic robustness
Chubiz, Lon M.; Granger, Brian R.; Segre, Daniel; Harcombe, William R.
2015-04-14
Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S.more » enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.« less
Z-type control of populations for Lotka-Volterra model with exponential convergence.
Zhang, Yunong; Yan, Xiaogang; Liao, Bolin; Zhang, Yinyan; Ding, Yaqiong
2016-02-01
The population control of the Lotka-Volterra model is one of the most important and widely investigated issues in mathematical ecology. In this study, assuming that birth rate is controllable and using the Z-type dynamic method, we develop Z-type control laws to drive the prey population and/or predator population to a desired state to keep species away from extinction and to improve ecosystem stability. A direct controller group is initially designed to control the prey and predator populations simultaneously. Two indirect controllers are then proposed for prey population control and predator population control by exerting exogenous measure on another species. All three control laws possess exponential convergence performances. Finally, the corresponding numerical simulations are performed. Results substantiate the theoretical analysis and effectiveness of such Z-type control laws for the population control of the Lotka-Volterra model. PMID:26644036
Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm
Hsiao, Feng-Hsiag
2015-01-01
This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432
Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm.
Hsiao, Feng-Hsiag
2015-01-01
This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432
Vehicle active steering control research based on two-DOF robust internal model control
NASA Astrophysics Data System (ADS)
Wu, Jian; Liu, Yahui; Wang, Fengbo; Bao, Chunjiang; Sun, Qun; Zhao, Youqun
2016-03-01
Because of vehicle's external disturbances and model uncertainties, robust control algorithms have obtained popularity in vehicle stability control. The robust control usually gives up performance in order to guarantee the robustness of the control algorithm, therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness. The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties. In order to separate the design process of model tracking from the robustness design process, the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization. Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm, on the basis of a nonlinear vehicle simulation model with a magic tyre model. Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance, which can enhance the vehicle stability and handling, regardless of variations of the vehicle model parameters and the external crosswind interferences. Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.
A robust fuzzy logic controller for robot manipulators with uncertainties.
Yi, S Y; Chung, M J
1997-01-01
Owing to load variation and unmodeled dynamics, a robot manipulator can be classified as a nonlinear dynamic system with structured and unstructured uncertainties. In this paper, the stability and robustness of a class of the fuzzy logic control (FLC) is investigated and a robust FLC is proposed for a robot manipulator with uncertainties. In order to show the performance of the proposed control algorithm, computer simulations are carried out on a simple two-link robot manipulator. PMID:18255910
Robust Flutter Margin Analysis that Incorporates Flight Data
NASA Technical Reports Server (NTRS)
Lind, Rick; Brenner, Martin J.
1998-01-01
An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.
Exponential Stability of Slowly Decaying Solutions to the Kinetic-Fokker-Planck Equation
NASA Astrophysics Data System (ADS)
Mischler, S.; Mouhot, C.
2016-08-01
The aim of the present paper is twofold: 1. We carry on with developing an abstract method for deriving decay estimates on the semigroup associated to non-symmetric operators in Banach spaces as introduced in [10]. We extend the method so as to consider the shrinkage of the functional space. Roughly speaking, we consider a class of operators written as a dissipative part plus a mild perturbation, and we prove that if the associated semigroup satisfies a decay estimate in some reference space then it satisfies the same decay estimate in another—smaller or larger—Banach space under the condition that a certain iterate of the "mild perturbation" part of the operator combined with the dissipative part of the semigroup maps the larger space to the smaller space in a bounded way. The cornerstone of our approach is a factorization argument, reminiscent of the Dyson series.
Evolving Robust Gene Regulatory Networks
Noman, Nasimul; Monjo, Taku; Moscato, Pablo; Iba, Hitoshi
2015-01-01
Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems. PMID:25616055
Robust automated knowledge capture.
Stevens-Adams, Susan Marie; Abbott, Robert G.; Forsythe, James Chris; Trumbo, Michael Christopher Stefan; Haass, Michael Joseph; Hendrickson, Stacey M. Langfitt
2011-10-01
This report summarizes research conducted through the Sandia National Laboratories Robust Automated Knowledge Capture Laboratory Directed Research and Development project. The objective of this project was to advance scientific understanding of the influence of individual cognitive attributes on decision making. The project has developed a quantitative model known as RumRunner that has proven effective in predicting the propensity of an individual to shift strategies on the basis of task and experience related parameters. Three separate studies are described which have validated the basic RumRunner model. This work provides a basis for better understanding human decision making in high consequent national security applications, and in particular, the individual characteristics that underlie adaptive thinking.
Robustness in Digital Hardware
NASA Astrophysics Data System (ADS)
Woods, Roger; Lightbody, Gaye
The growth in electronics has probably been the equivalent of the Industrial Revolution in the past century in terms of how much it has transformed our daily lives. There is a great dependency on technology whether it is in the devices that control travel (e.g., in aircraft or cars), our entertainment and communication systems, or our interaction with money, which has been empowered by the onset of Internet shopping and banking. Despite this reliance, there is still a danger that at some stage devices will fail within the equipment's lifetime. The purpose of this chapter is to look at the factors causing failure and address possible measures to improve robustness in digital hardware technology and specifically chip technology, giving a long-term forecast that will not reassure the reader!
Robust snapshot interferometric spectropolarimetry.
Kim, Daesuk; Seo, Yoonho; Yoon, Yonghee; Dembele, Vamara; Yoon, Jae Woong; Lee, Kyu Jin; Magnusson, Robert
2016-05-15
This Letter describes a Stokes vector measurement method based on a snapshot interferometric common-path spectropolarimeter. The proposed scheme, which employs an interferometric polarization-modulation module, can extract the spectral polarimetric parameters Ψ(k) and Δ(k) of a transmissive anisotropic object by which an accurate Stokes vector can be calculated in the spectral domain. It is inherently strongly robust to the object 3D pose variation, since it is designed distinctly so that the measured object can be placed outside of the interferometric module. Experiments are conducted to verify the feasibility of the proposed system. The proposed snapshot scheme enables us to extract the spectral Stokes vector of a transmissive anisotropic object within tens of msec with high accuracy. PMID:27176992
Robust springback compensation
NASA Astrophysics Data System (ADS)
Carleer, Bart; Grimm, Peter
2013-12-01
Springback simulation and springback compensation are more and more applied in productive use of die engineering. In order to successfully compensate a tool accurate springback results are needed as well as an effective compensation approach. In this paper a methodology has been introduce in order to effectively compensate tools. First step is the full process simulation meaning that not only the drawing operation will be simulated but also all secondary operations like trimming and flanging. Second will be the verification whether the process is robust meaning that it obtains repeatable results. In order to effectively compensate a minimum clamping concept will be defined. Once these preconditions are fulfilled the tools can be compensated effectively.
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.
1995-01-01
The potential for a revolutionary step in the durability of reusable rocket engines is made possible by the combination of several emerging technologies. The recent creation and analytical demonstration of life extending (or damage mitigating) control technology enables rapid rocket engine transients with minimum fatigue and creep damage. This technology has been further enhanced by the formulation of very simple but conservative continuum damage models. These new ideas when combined with recent advances in multidisciplinary optimization provide the potential for a large (revolutionary) step in reusable rocket engine durability. This concept has been named the robust rocket engine concept (RREC) and is the basic contribution of this paper. The concept also includes consideration of design innovations to minimize critical point damage.
Chen, Li; Shen, Cencheng; Vogelstein, Joshua T; Priebe, Carey E
2016-03-01
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, we propose a sparse representation vertex classifier which does not require information about the model dimension. This classifier represents a test vertex as a sparse combination of the vertices in the training set and uses the recovered coefficients to classify the test vertex. We prove consistency of our proposed classifier for stochastic blockmodels, and demonstrate that the sparse representation classifier can predict vertex labels with higher accuracy than adjacency spectral embedding approaches via both simulation studies and real data experiments. Our results demonstrate the robustness and effectiveness of our proposed vertex classifier when the model dimension is unknown. PMID:26340770
Exponential frequency spectrum and Lorentzian pulses in magnetized plasmas
Pace, D. C.; Shi, M.; Maggs, J. E.; Morales, G. J.; Carter, T. A.
2008-12-15
Two different experiments involving pressure gradients across the confinement magnetic field in a large plasma column are found to exhibit a broadband turbulence that displays an exponential frequency spectrum for frequencies below the ion cyclotron frequency. The exponential feature has been traced to the presence of solitary pulses having a Lorentzian temporal signature. These pulses arise from nonlinear interactions of drift-Alfven waves driven by the pressure gradients. In both experiments the width of the pulses is narrowly distributed resulting in exponential spectra with a single characteristic time scale. The temporal width of the pulses is measured to be a fraction of a period of the drift-Alfven waves. The experiments are performed in the Large Plasma Device (LAPD-U) [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] operated by the Basic Plasma Science Facility at the University of California, Los Angeles. One experiment involves a controlled, pure electron temperature gradient associated with a microscopic (6 mm gradient length) hot electron temperature filament created by the injection a small electron beam embedded in the center of a large, cold magnetized plasma. The other experiment is a macroscopic (3.5 cm gradient length) limiter-edge experiment in which a density gradient is established by inserting a metallic plate at the edge of the nominal plasma column of the LAPD-U. The temperature filament experiment permits a detailed study of the transition from coherent to turbulent behavior and the concomitant change from classical to anomalous transport. In the limiter experiment the turbulence sampled is always fully developed. The similarity of the results in the two experiments strongly suggests a universal feature of pressure-gradient driven turbulence in magnetized plasmas that results in nondiffusive cross-field transport. This may explain previous observations in helical confinement devices, research tokamaks, and arc plasmas.
Polar exponential sensor arrays unify iconic and Hough space representation
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1990-01-01
The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.
Exponential Methods for the Time Integration of Schroedinger Equation
Cano, B.; Gonzalez-Pachon, A.
2010-09-30
We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.
Boundary layer flow of nanofluid over an exponentially stretching surface
2012-01-01
The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt. PMID:22289390
Green's function evaluation for three-dimensional exponentially graded elasticity
Criado Portero, Rafael M; Gray, Leonard J; Mantic, Vladislav; Paris, Federico
2008-01-01
The numerical implementation of the Green's function for an isotropic exponentially graded three dimensional elastic solid is reported. The formulas for the nonsingular {\\lq}grading term{\\rq} in this Green's function, originally deduced by Martin et al., \\emph{Proc. R. Soc. Lond. A, 458, 1931-1947, 2000}, are quite complicated, and a small error in one of the formulas is corrected. The evaluation of the fundamental solution is tested by employing indirect boundary integral formulation using a Galerkin approximation to solve several problems having analytic solutions. The numerical results indicate that the Green's function formulas, and their evaluation, are correct.
Stretched Exponential Relaxation of Glasses at Low Temperature
NASA Astrophysics Data System (ADS)
Yu, Yingtian; Wang, Mengyi; Zhang, Dawei; Wang, Bu; Sant, Gaurav; Bauchy, Mathieu
2015-10-01
The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent β =3 /5 , as predicted by Phillips's diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but it is rather a manifestation of the mixed alkali effect.
Distribution of Periods of Closed Trajectories in Exponentially Shrinking Intervals
NASA Astrophysics Data System (ADS)
Petkov, Vesselin; Stoyanov, Luchezar
2012-03-01
For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods T γ lying in exponentially shrinking intervals {(x - e^{-δ x}, x + e^{-δ x}), δ > 0, x to + infty.} A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hyperbolic flows on basic sets, in particular to geodesic flows on manifolds of constant negative curvature and to open billiard flows.
A Detailed Investigation into Near Degenerate Exponential Random Graphs
NASA Astrophysics Data System (ADS)
Yin, Mei
2016-07-01
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.
Kicked Bose-Einstein Condensates: in Search of Exponential Instability
NASA Astrophysics Data System (ADS)
Monteiro, T. S.; Rancon, A.; Ruostekoski, J.
Bose-Einstein condensates subject to short pulses ("kicks") from standing waves of light represent a nonlinear analogue of the well-known chaos paradigm, the quantum kicked rotor. We review briefly our current understanding of dynamical or exponential instability in weakly kicked BECs. Previous studies of the onset of dynamical instability associated it with some form of classical chaos. We show it is due to parametric instability: resonant driving of certain collective modes. We map the zones of instability and calculate the Liapunov exponents.
A Detailed Investigation into Near Degenerate Exponential Random Graphs
NASA Astrophysics Data System (ADS)
Yin, Mei
2016-05-01
The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.
3-D sensing with polar exponential sensor arrays
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1988-01-01
The present computations for three-dimensional vision involve, in such cases as those of scaling for perspective and optic flow, their reduction to additive operations by the implicit logarithmic transformation of image coordinates. Expressions for such computations are derived and applied to illustrative examples of sensor design. The advantages of polar exponential arrays over X-Y rasters for binocular vision are noted to encompass the inference of range and three-dimensional position from local image velocity without knowledge of pixel location, provided that the relative velocity of the target and sensor are known by some other means.
Exponentially Slow Heating in Periodically Driven Many-Body Systems
NASA Astrophysics Data System (ADS)
Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François
2015-12-01
We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that, for systems with local interactions, the energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including the decay of highly energetic excitations in cold atomic and solid-state systems.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Improving Convergence of Backpropagation Learning using Exponential Cost Function
NASA Astrophysics Data System (ADS)
Kamruzzaman, Joarder
Backpropagation, one of the most popular learning algorithms in multi-layered feedforward neural networks, suffers from the drawback of slow convergence. Several modifications have been proposed to accelerate the learning process using different techniques. In this paper, a new cost function expressed as exponential of sum-squared or Log-likelihood is proposed. Weight update using this modification varies the learning rate parameter dynamically during training as opposed to constant learning rate parameter used in standard Backpropagation. Simulation results with different problems demonstrate significant improvement in the learning speed of Backpropagation algorithm.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
Curve fitting of aeroelastic transient response data with exponential functions
NASA Technical Reports Server (NTRS)
Bennett, R. M.; Desmarais, R. N.
1976-01-01
The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.
Comparison of confidence procedures for type I censored exponential lifetimes.
Sundberg, R
2001-12-01
In the model of type I censored exponential lifetimes, coverage probabilities are compared for a number of confidence interval constructions proposed in literature. The coverage probabilities are calculated exactly for sample sizes up to 50 and for different degrees of censoring and different degrees of intended confidence. If not only a fair two-sided coverage is desired, but also fair one-sided coverages, only few methods are quite satisfactory. A likelihood-based interval and a third root transformation to normality work almost perfectly, but the chi 2-based method that is perfect under no censoring and under type II censoring can also be advocated. PMID:11763546
On Ideal Stability of Cylindrical Localized Interchange Modes
Umansky, M V
2007-05-15
Stability of cylindrical localized ideal pressure-driven interchange plasma modes is revisited. Converting the underlying eigenvalue problem into the form of the Schroedinger equation gives a new simple way of deriving the Suydam stability criterion and calculating the growth rates of unstable modes. Near the marginal stability limit the growth rate is exponentially small and the mode has a double-peak structure.
Inherent robustness of discrete-time adaptive control systems
NASA Technical Reports Server (NTRS)
Ma, C. C. H.
1986-01-01
Global stability robustness with respect to unmodeled dynamics, arbitrary bounded internal noise, as well as external disturbance is shown to exist for a class of discrete-time adaptive control systems when the regressor vectors of these systems are persistently exciting. Although fast adaptation is definitely undesirable, so far as attaining the greatest amount of global stability robustness is concerned, slow adaptation is shown to be not necessarily beneficial. The entire analysis in this paper holds for systems with slowly varying return difference matrices; the plants in these systems need not be slowly varying.
Influence of annular boundaries on Thomson's vortex polygon stability
Kurakin, L. G.
2014-06-15
The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle inside an annulus is presented. The problem is reduced to one of the equilibrium stability of the Hamiltonian system with a cyclic variable. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The stability of the stationary motion is interpreted as a Routh stability. The exponential instability is shown always to take place if N ≥ 7. For N = 2, 4, and 6, the parameter space is divided in two: a Routh stability domain in an exact nonlinear setting and an exponential instability domain. For N = 3 and 5, the parameter space consists of three domains. The stability of the third in an exact nonlinear setting is sandwiched between the Routh and exponential domains. Its analysis remains an open problem with its solution requiring nonlinear analysis.
Robust technique allowing manufacturing superoleophobic surfaces
NASA Astrophysics Data System (ADS)
Bormashenko, Edward; Grynyov, Roman; Chaniel, Gilad; Taitelbaum, Haim; Bormashenko, Yelena
2013-04-01
We report the robust technique allowing manufacturing of superhydrophobic and oleophobic (omniphobic) surfaces with industrial grade low density polyethylene. The reported process includes two stages: (1) hot embossing of polyethylene with micro-scaled steel gauzes; (2) treatment of embossed surfaces with cold radiofrequency plasma of tetrafluoromethane. The reported surfaces demonstrate not only pronounced superhydrophobicity but also superoleophobicity. Superoleophobicity results from the hierarchical nano-scaled topography of fluorinated polyethylene surface. The observed superoleophobicity is strengthened by the hydrophobic recovery. The stability of the Cassie wetting regime was studied.
Arima model and exponential smoothing method: A comparison
NASA Astrophysics Data System (ADS)
Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri
2013-04-01
This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
A stochastic evolutionary model generating a mixture of exponential distributions
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2016-02-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Truncated γ-exponential models for tidal stellar systems
NASA Astrophysics Data System (ADS)
Gomez-Leyton, Y. J.; Velazquez, L.
2016-05-01
We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution fγ (q, p|β,ɛs) that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature β, in particular, a power-law truncation at the scape energy ɛs with exponent γ > 0. This deformation is implemented using a generalized γ-exponential function obtained from the fractional integration of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with isothermal cores and polytropic haloes, e.g.: Michie-King models. We perform the analysis of thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and polytropic haloes are only obtained for low energies whenever deformation parameter γ < γc ≃ 2.13. This study is a first approximation to characterize a self- gravitating system, so we consider equal to all the particles that constitute the system.
Exponentially more precise quantum simulation of fermions in second quantization
NASA Astrophysics Data System (ADS)
Babbush, Ryan; Berry, Dominic W.; Kivlichan, Ian D.; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán
2016-03-01
We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie-Trotter-Suzuki decomposition. We present the first application of a general technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. We solve this problem with a novel quantum algorithm for on-the-fly computation of integrals that is exponentially faster than classical sampling. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most studied application of Hamiltonian simulation. Our central result is an algorithm for simulating an N spin-orbital system that requires \\tilde{{ O }}({N}5t) gates. This approach is exponentially faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature.
Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design
NASA Technical Reports Server (NTRS)
Whorton, Mark
2003-01-01
Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.
NASA Astrophysics Data System (ADS)
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Exponential Sum-Fitting of Dwell-Time Distributions without Specifying Starting Parameters
Landowne, David; Yuan, Bin; Magleby, Karl L.
2013-01-01
Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems. PMID:23746510
Facilitating Understanding of a Catch-22 Concept: Teaching Exponential Change with Logo.
ERIC Educational Resources Information Center
Weller, Herman G.; Johnson, Vivian
1992-01-01
Describes a unit for teaching exponential change in a noncalculus physics course by having students write recursive procedures in LOGO to graphically represent linear and exponential change. Summarizes the experience of implementing the unit in a segment on radioactive decay. Modifications to the unit are suggested for teaching exponential change…
Mitigation of Remedial Action Schemes by Decentralized Robust Governor Control
Elizondo, Marcelo A.; Marinovici, Laurentiu D.; Lian, Jianming; Kalsi, Karanjit; Du, Pengwei
2014-04-15
This paper presents transient stability improvement by a new distributed hierarchical control architecture (DHC). The integration of remedial action schemes (RAS) to the distributed hierarchical control architecture is studied. RAS in power systems are designed to maintain stability and avoid undesired system conditions by rapidly switching equipment and/or changing operating points according to predetermined rules. The acceleration trend relay currently in use in the US western interconnection is an example of RAS that trips generators to maintain transient stability. The link between RAS and DHC is through fast acting robust turbine/governor control that can also improve transient stability. In this paper, the influence of the decentralized robust turbine/governor control on the design of RAS is studied. Benefits of combining these two schemes are increasing power transfer capability and mitigation of RAS generator tripping actions; the later benefit is shown through simulations.
Robustness of disturbance attenuation with respect to disturbance model uncertainty
NASA Astrophysics Data System (ADS)
Davison, Daniel Edward
In contrast to the case of robustness with respect to plant model uncertainty, the control systems community has paid relatively little attention to the issue of robustness with respect to disturbance model uncertainty. However, disturbance model uncertainty is of significance in many practical problems, including, for example, aircraft control (where the disturbance is turbulence), ship control (where the disturbances are wind and waves), and active suspension problems (where the disturbance is road roughness). Motivated, in particular, by turbulence model uncertainty, this dissertation considers the analysis and design of linear time-invariant controllers that are robust with respect to uncertainty in the disturbance intensity and bandwidth, where disturbance attenuation is measured by the output variance. Five aspects of the robust disturbance attenuation problem are considered. First, an expression for the output variance in terms of the uncertain disturbance parameters is derived. This expression is written in terms of an operator called the V-transform. Second, the notions of disturbance gain margin and disturbance bandwidth margin are introduced as quantitative measures of robustness with respect to uncertainty in the disturbance gain and disturbance bandwidth, respectively. Third, lower bounds on the achievable output variance are found under constraints of practical importance, e.g., constraints on bandwidth and stability robustness. The lower bounds are used to show that, in almost every practical situation, there is a limitation on both the achievable nominal performance and the achievable robustness margins. Fourth, tradeoffs between nominal performance and robust performance are investigated. The main result is that good nominal and good robust performance are neither incompatible nor equivalent. Fifth, a design procedure to achieve a prespecified level of robustness is proposed; the principal idea is to reduce the robust performance design problem to
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-03-15
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Long-wave theory for a new convective instability with exponential growth normal to the wall.
Healey, J J
2005-05-15
A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems. PMID:16105773
Robust stochastic resonance for simple threshold neurons
NASA Astrophysics Data System (ADS)
Kosko, Bart; Mitaim, Sanya
2004-09-01
Simulation and theoretical results show that memoryless threshold neurons benefit from small amounts of almost all types of additive noise and so produce the stochastic-resonance or SR effect. Input-output mutual information measures the performance of such threshold systems that use subthreshold signals. The SR result holds for all possible noise probability density functions with finite variance. The only constraint is that the noise mean must fall outside a “forbidden” threshold-related interval that the user can control—a new theorem shows that this condition is also necessary. A corollary and simulations show that the SR effect occurs for right-sided beta and Weibull noise as well. These SR results further hold for the entire uncountably infinite class of alpha-stable probability density functions. Alpha-stable noise densities have infinite variance and infinite higher-order moments and often model impulsive noise environments. The stable noise densities include the special case of symmetric bell-curve densities with thick tails such as the Cauchy probability density. The SR result for alpha-stable noise densities shows that the SR effect in threshold and thresholdlike systems is robust against occasional or even frequent violent fluctuations in noise. Regression analysis reveals both an exponential relationship for the optimal noise dispersion as a function of the alpha bell-curve tail thickness and an approximate linear relationship for the SR-maximal mutual information as a function of the alpha bell-curve tail thickness.
Transient superdiffusion in random walks with a q-exponentially decaying memory profile
NASA Astrophysics Data System (ADS)
Moura, Thiago R. S.; Viswanathan, G. M.; da Silva, M. A. A.; Cressoni, J. C.; da Silva, L. R.
2016-07-01
We propose a random walk model with q-exponentially decaying memory profile. The q-exponential function is a generalization of the ordinary exponential function. In the limit q → 1, the q-exponential becomes the ordinary exponential function. This model presents a Markovian diffusive regime that is characterized by finite memory correlations. It is well known, that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. In this problem we report the outcome of a transient superdiffusion for finite sized walks.
Iterative exponential growth of stereo- and sequence-controlled polymers
NASA Astrophysics Data System (ADS)
Barnes, Jonathan C.; Ehrlich, Deborah J. C.; Gao, Angela X.; Leibfarth, Frank A.; Jiang, Yivan; Zhou, Erica; Jamison, Timothy F.; Johnson, Jeremiah A.
2015-10-01
Chemists have long sought sequence-controlled synthetic polymers that mimic nature's biopolymers, but a practical synthetic route that enables absolute control over polymer sequence and structure remains a key challenge. Here, we report an iterative exponential growth plus side-chain functionalization (IEG+) strategy that begins with enantiopure epoxides and facilitates the efficient synthesis of a family of uniform >3 kDa macromolecules of varying sequence and stereoconfiguration that are coupled to produce unimolecular polymers (>6 kDa) with sequences and structures that cannot be obtained using traditional polymerization techniques. Selective side-chain deprotection of three hexadecamers is also demonstrated, which imbues each compound with the ability to dissolve in water. We anticipate that these new macromolecules and the general IEG+ strategy will find broad application as a versatile platform for the scalable synthesis of sequence-controlled polymers.
Modular exponentiation via the explicit Chinese remainder theorem
NASA Astrophysics Data System (ADS)
Bernstein, Daniel J.; Sorenson, Jonathan P.
2007-03-01
Fix pairwise coprime positive integers p_1,p_2,dots,p_s . We propose representing integers u modulo m , where m is any positive integer up to roughly sqrt{p_1p_2\\cdots p_s} , as vectors (ubmod p_1,ubmod p_2,dots,ubmod p_s) . We use this representation to obtain a new result on the parallel complexity of modular exponentiation: there is an algorithm for the Common CRCW PRAM that, given positive integers x , e , and m in binary, of total bit length n , computes x^ebmod m in time O(n/{lglg n}) using n^{O(1)} processors. For comparison, a parallelization of the standard binary algorithm takes superlinear time; Adleman and Kompella gave an O((lg n)^3) expected time algorithm using exp( O(sqrt{nlg n})) processors; von zur Gathen gave an NC algorithm for the highly special case that m is polynomially smooth.
Control of a heterogeneous two-server exponential queueing system
NASA Technical Reports Server (NTRS)
Larsen, R. L.; Agrawala, A. K.
1983-01-01
A dynamic control policy known as 'threshold queueing' is defined for scheduling customers from a Poisson source on a set of two exponential servers with dissimilar service rates. The slower server is invoked in response to instantaneous system loading as measured by the length of the queue of waiting customers. In a threshold queueing policy, a specific queue length is identified as a 'threshold,' beyond which the slower server is invoked. The slower server remains busy until it completes service on a customer and the queue length is less than its invocation threshold. Markov chain analysis is employed to analyze the performance of the threshold queueing policy and to develop optimality criteria. It is shown that probabilistic control is suboptimal to minimize the mean number of customers in the system. An approximation to the optimum policy is analyzed which is computationally simple and suffices for most operational applications.
Rational approximations to linear forms of exponentials and binomials
Chudnovsky, G. V.
1983-01-01
Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: ǀΣi=0nCieriǀ > H-n-ε for any distinct rational numbers r0,r1,..., rn and rational integers C0,C1,...,Cn with H = max0≤i≤n ǀCiǀ. We improve Mahler's estimate by replacing exponentials eri by linearly independent linear forms Li = Σ Lijesij with rational Lij,siji = 0,1,...,n. Similar results are obtained for binomials (a/b)ri or Σ Lij(a/b)sij with integers a,b and logǀbǀ/logǀaǀ > 1 - ε. The simplest examples of new numbers with the irrationality exponent “2 + ε” are sinh 1 or sin 1. PMID:16593320
Statistical modelling of agrometeorological time series by exponential smoothing
NASA Astrophysics Data System (ADS)
Murat, Małgorzata; Malinowska, Iwona; Hoffmann, Holger; Baranowski, Piotr
2016-01-01
Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, long-term meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
Stretched exponential distribution of recurrent time of wars in China
NASA Astrophysics Data System (ADS)
Tang, Da-Hai; Han, Xiao-Pu; Wang, Bing-Hong
2010-07-01
As a killing machine and a decisive factor of history, wars play an important role in social system. In this paper, we present an empirical exploration of the distribution of recurrent time of wars in ancient China and find that it obeys a stretched exponential form. The pattern we found implies that there are undetected mechanisms that underlie the dynamics of wars. In order to explain the origin of this form, a model mainly based on the correlation between two consecutive wars is constructed, which is somewhat similar to the Bak-Sneppen model. The simulation results of the model are in agreement with the empirical statistics and suggest that the dynamics of wars could relate with self-organized criticality.
Type II Hermite-Pade approximation to the exponential function
NASA Astrophysics Data System (ADS)
Kuijlaars, A. B. J.; Stahl, H.; van Assche, W.; Wielonsky, F.
2007-10-01
We obtain strong and uniform asymptotics in every domain of the complex plane for the scaled polynomials a(3nz), b(3nz), and c(3nz) where a, b, and c are the type II Hermite-Pade approximants to the exponential function of respective degrees 2n+2, 2n and 2n, defined by and as z-->0. Our analysis relies on a characterization of these polynomials in terms of a 3x3 matrix Riemann-Hilbert problem which, as a consequence of the famous Mahler relations, corresponds by a simple transformation to a similar Riemann-Hilbert problem for type I Hermite-Pade approximants. Due to this relation, the study that was performed in previous work, based on the Deift-Zhou steepest descent method for Riemann-Hilbert problems, can be reused to establish our present results.
Exponential generating functions for the associated Bessel functions
NASA Astrophysics Data System (ADS)
Fakhri, H.; Mojaveri, B.; Gomshi Nobary, M. A.
2008-09-01
Similar to the associated Legendre functions, the differential equation for the associated Bessel functions Bl,m(x) is introduced so that its form remains invariant under the transformation l → -l - 1. A Rodrigues formula for the associated Bessel functions as squared integrable solutions in both regions l < 0 and l >= 0 is presented. The functions with the same m but with different positive and negative values of l are not independent of each other, while the functions with the same l + m (l - m) but with different values of l and m are independent of each other. So, all the functions Bl,m(x) may be taken into account as the union of the increasing (decreasing) infinite sequences with respect to l. It is shown that two new different types of exponential generating functions are attributed to the associated Bessel functions corresponding to these rearranged sequences.
Piecewise-quartics and exponential parameterization for interpolating reduced data
NASA Astrophysics Data System (ADS)
Kozera, R.
2016-06-01
We examine the asymptotics of a piecewise-quartic Lagrange interpolation used to fit reduced data in arbitrary Euclidean space which are sampled more-or-less uniformly. The unknown interpolation knots are guessed here according to the so-called exponential parameterization which depends on a single parameter λ ∈ [0, 1]. In this work we demonstrate numerically an abrupt discontinuity in the quality of the discussed interpolation scheme yielding a slow linear convergence order for all λ ∈ [0, 1). On the other hand, as well-known the quality of the curve approximation for λ = 1 sharply increases to the fast sharp quartic order which can be further accelerated for special subfamilies of more-or-less uniform samplings.
The Unreasonable Effectiveness of Exponentially Suppressed Corrections in Preserving Information
NASA Astrophysics Data System (ADS)
Papadodimas, Kyriakos; Raju, Suvrat
2013-11-01
We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.
Exponential random graph models for networks with community structure
NASA Astrophysics Data System (ADS)
Fronczak, Piotr; Fronczak, Agata; Bujok, Maksymilian
2013-09-01
Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.
Exponential and power laws in public procurement markets
NASA Astrophysics Data System (ADS)
Kristoufek, Ladislav; Skuhrovec, Jiri
2012-07-01
We analyze for the first time a unique public procurement database, which includes information about a number of bidders for a contract, a final price, an identification of a winner and an identification of a contracting authority for each of more than 40000 public procurements in the Czech Republic between 2006 and 2011, focusing on the distributional properties of the variables of interest. We uncover several scaling laws —the exponential law for the number of bidders, and the power laws for the total revenues and total spendings of the participating companies, which even follows Zipf's law for the 100 most spending institutions. We propose an analogy between extensive and non-extensive systems in physics and the public procurement market situations. Through an entropy maximization, such analogy yields some interesting results and policy implications with respect to the Maxwell-Boltzmann and Pareto distributions in the analyzed quantities.
Approximation of nonnegative functions by means of exponentiated trigonometric polynomials
NASA Astrophysics Data System (ADS)
Fasino, Dario
2002-03-01
We consider the problem of approximating a nonnegative function from the knowledge of its first Fourier coefficients. Here, we analyze a method introduced heuristically in a paper by Borwein and Huang (SIAM J. Opt. 5 (1995) 68-99), where it is shown how to construct cheaply a trigonometric or algebraic polynomial whose exponential is close in some sense to the considered function. In this note, we prove that approximations given by Borwein and Huang's method, in the trigonometric case, can be related to a nonlinear constrained optimization problem, and their convergence can be easily proved under mild hypotheses as a consequence of known results in approximation theory and spectral properties of Toeplitz matrices. Moreover, they allow to obtain an improved convergence theorem for best entropy approximations.
Exponential-family random graph models for valued networks
Krivitsky, Pavel N.
2013-01-01
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions. PMID:24678374
Exponential Clogging Time for a One Dimensional DLA
NASA Astrophysics Data System (ADS)
Benjamini, Itai; Hoffman, Christopher
2008-06-01
In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187-223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686-5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.
Heavy quark-antiquark systems from exponential moments in QCD
NASA Astrophysics Data System (ADS)
Bertlmann, R. A.
1982-09-01
We present a detailed analysis for heavy QQ¯ systems, of how they emerge from the moment procedure of Shifman, Vainshtein and Zakharov. We work with exponential moments which we calculate as limits of power moments presented by Reinders, Rubinstein and Yazaki. Application to charmonium reproduces the results of these authors very well. We are able to treat bottonium states too, and predict the centre-of-mass of the p-states at 9.80 GeV with a bottom on-shell quark mass of m¯b = 4.71 GeV. Finally, we show that non-relativistic approximations to the moments, which provide extremely simple formulae, yield results very close to the relativistic moments, for both s- and p-waves.
Exponential protection of zero modes in Majorana islands.
Albrecht, S M; Higginbotham, A P; Madsen, M; Kuemmeth, F; Jespersen, T S; Nygård, J; Krogstrup, P; Marcus, C M
2016-03-10
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a 'Majorana island') that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation. PMID:26961654
Exponential protection of zero modes in Majorana islands
NASA Astrophysics Data System (ADS)
Albrecht, S. M.; Higginbotham, A. P.; Madsen, M.; Kuemmeth, F.; Jespersen, T. S.; Nygård, J.; Krogstrup, P.; Marcus, C. M.
2016-03-01
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a ‘Majorana island’) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Robust Understanding of Statistical Variation
ERIC Educational Resources Information Center
Peters, Susan A.
2011-01-01
This paper presents a framework that captures the complexity of reasoning about variation in ways that are indicative of robust understanding and describes reasoning as a blend of design, data-centric, and modeling perspectives. Robust understanding is indicated by integrated reasoning about variation within each perspective and across…
Robust, Optimal Subsonic Airfoil Shapes
NASA Technical Reports Server (NTRS)
Rai, Man Mohan
2014-01-01
A method has been developed to create an airfoil robust enough to operate satisfactorily in different environments. This method determines a robust, optimal, subsonic airfoil shape, beginning with an arbitrary initial airfoil shape, and imposes the necessary constraints on the design. Also, this method is flexible and extendible to a larger class of requirements and changes in constraints imposed.
NASA Technical Reports Server (NTRS)
Westall, F.; Steele, A.; Toporski, J.; Walsh, M. M.; Allen, C. C.; Guidry, S.; McKay, D. S.; Gibson, E. K.; Chafetz, H. S.
2000-01-01
containing fossil biofilm, including the 3.5 b.y..-old carbonaceous cherts from South Africa and Australia. As a result of the unique compositional, structural and "mineralisable" properties of bacterial polymer and biofilms, we conclude that bacterial polymers and biofilms constitute a robust and reliable biomarker for life on Earth and could be a potential biomarker for extraterrestrial life.
Robust Neural Sliding Mode Control of Robot Manipulators
Nguyen Tran Hiep; Pham Thuong Cat
2009-03-05
This paper proposes a robust neural sliding mode control method for robot tracking problem to overcome the noises and large uncertainties in robot dynamics. The Lyapunov direct method has been used to prove the stability of the overall system. Simulation results are given to illustrate the applicability of the proposed method.
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David Albert; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Robust adaptive tracking control for nonholonomic mobile manipulator with uncertainties.
Peng, Jinzhu; Yu, Jie; Wang, Jie
2014-07-01
In this paper, mobile manipulator is divided into two subsystems, that is, nonholonomic mobile platform subsystem and holonomic manipulator subsystem. First, the kinematic controller of the mobile platform is derived to obtain a desired velocity. Second, regarding the coupling between the two subsystems as disturbances, Lyapunov functions of the two subsystems are designed respectively. Third, a robust adaptive tracking controller is proposed to deal with the unknown upper bounds of parameter uncertainties and disturbances. According to the Lyapunov stability theory, the derived robust adaptive controller guarantees global stability of the closed-loop system, and the tracking errors and adaptive coefficient errors are all bounded. Finally, simulation results show that the proposed robust adaptive tracking controller for nonholonomic mobile manipulator is effective and has good tracking capacity. PMID:24917071
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David A.; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the causality recovery methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Species interactions differ in their genetic robustness
Chubiz, Lon M.; Granger, Brian R.; Segre, Daniel; Harcombe, William R.
2015-04-14
Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S. enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.
Generalized internal model robust control for active front steering intervention
NASA Astrophysics Data System (ADS)
Wu, Jian; Zhao, Youqun; Ji, Xuewu; Liu, Yahui; Zhang, Lipeng
2015-03-01
Because of the tire nonlinearity and vehicle's parameters' uncertainties, robust control methods based on the worst cases, such as H ∞, µ synthesis, have been widely used in active front steering control, however, in order to guarantee the stability of active front steering system (AFS) controller, the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control. In this paper, a generalized internal model robust control (GIMC) that can overcome the contradiction between performance and stability is used in the AFS control. In GIMC, the Youla parameterization is used in an improved way. And GIMC controller includes two sections: a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters' uncertainties and some external disturbances. Simulations of double lane change (DLC) maneuver and that of braking on split- µ road are conducted to compare the performance and stability of the GIMC control, the nominal performance PID controller and the H ∞ controller. Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle's parameters variations, H ∞ controller is conservative so that the performance is a little low, and only the GIMC controller overcomes the contradiction between performance and robustness, which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller. Therefore, the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system, that is, can solve the instability of PID or LQP control methods and the low performance of the standard H ∞ controller.
Robust feature selection for microarray data based on multicriterion fusion.
Yang, Feng; Mao, K Z
2011-01-01
Feature selection often aims to select a compact feature subset to build a pattern classifier with reduced complexity, so as to achieve improved classification performance. From the perspective of pattern analysis, producing stable or robust solution is also a desired property of a feature selection algorithm. However, the issue of robustness is often overlooked in feature selection. In this study, we analyze the robustness issue existing in feature selection for high-dimensional and small-sized gene-expression data, and propose to improve robustness of feature selection algorithm by using multiple feature selection evaluation criteria. Based on this idea, a multicriterion fusion-based recursive feature elimination (MCF-RFE) algorithm is developed with the goal of improving both classification performance and stability of feature selection results. Experimental studies on five gene-expression data sets show that the MCF-RFE algorithm outperforms the commonly used benchmark feature selection algorithm SVM-RFE. PMID:21566255
Robust adaptive vibration control of a flexible structure.
Khoshnood, A M; Moradi, H M
2014-07-01
Different types of L1 adaptive control systems show that using robust theories with adaptive control approaches has produced high performance controllers. In this study, a model reference adaptive control scheme considering robust theories is used to propose a practical control system for vibration suppression of a flexible launch vehicle (FLV). In this method, control input of the system is shaped from the dynamic model of the vehicle and components of the control input are adaptively constructed by estimating the undesirable vibration frequencies. Robust stability of the adaptive vibration control system is guaranteed by using the L1 small gain theorem. Simulation results of the robust adaptive vibration control strategy confirm that the effects of vibration on the vehicle performance considerably decrease without the loss of the phase margin of the system. PMID:24703188
Robustness of solutions to a benchmark control problem
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Marrison, Christopher I.
1992-01-01
The robustness of 10 solutions to a benchmark control design problem presented at the 1990 American Control Conference has been evaluated. The 10 controllers have second-to-eighth-order transfer functions and have been designed using several different methods, including H-infinity optimization, loop-transfer recovery, imaginary-axis shifting, constrained optimization, structured covariance, game theory, and the internal model principle. Stochastic robustness analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights into system response that are not readily derived from other robustness criteria and provides a common ground for judging controllers produced by alternative methods. One important conclusion is that gain and phase margins are not reliable indicators of the probability of instability. Furthermore, parameter variations actually may improve the likelihood of achieving selected performance metrics, as demonstrated by results for the probability of settling-time exceedance.
Vikulina, Anna S; Anissimov, Yuri G; Singh, Prateek; Prokopović, Vladimir Z; Uhlig, Katja; Jaeger, Magnus S; von Klitzing, Regine; Duschl, Claus; Volodkin, Dmitry
2016-03-21
In this study, the effect of temperature on the build-up of exponentially growing polyelectrolyte multilayer films was investigated. It aims at understanding the multilayer growth mechanism as crucially important for the fabrication of tailor-made multilayer films. Model poly(L-lysine)/hyaluronic acid (PLL/HA) multilayers were assembled in the temperature range of 25-85 °C by layer-by-layer deposition using a dipping method. The film growth switches from the exponential to the linear regime at the transition point as a result of limited polymer diffusion into the film. With the increase of the build-up temperature the film growth rate is enhanced in both regimes; the position of the transition point shifts to a higher number of deposition steps confirming the diffusion-mediated growth mechanism. Not only the faster polymer diffusion into the film but also more porous/permeable film structure are responsible for faster film growth at higher preparation temperature. The latter mechanism is assumed from analysis of the film growth rate upon switching of the preparation temperature during the film growth. Interestingly, the as-prepared films are equilibrated and remain intact (no swelling or shrinking) during temperature variation in the range of 25-45 °C. The average activation energy for complexation between PLL and HA in the multilayers calculated from the Arrhenius plot has been found to be about 0.3 kJ mol(-1) for monomers of PLL. Finally, the following processes known to be dependent on temperature are discussed with respect to the multilayer growth: (i) polymer diffusion, (ii) polymer conformational changes, and (iii) inter-polymer interactions. PMID:26911320
RSRE: RNA structural robustness evaluator.
Shu, Wenjie; Bo, Xiaochen; Zheng, Zhiqiang; Wang, Shengqi
2007-07-01
Biological robustness, defined as the ability to maintain stable functioning in the face of various perturbations, is an important and fundamental topic in current biology, and has become a focus of numerous studies in recent years. Although structural robustness has been explored in several types of RNA molecules, the origins of robustness are still controversial. Computational analysis results are needed to make up for the lack of evidence of robustness in natural biological systems. The RNA structural robustness evaluator (RSRE) web server presented here provides a freely available online tool to quantitatively evaluate the structural robustness of RNA based on the widely accepted definition of neutrality. Several classical structure comparison methods are employed; five randomization methods are implemented to generate control sequences; sub-optimal predicted structures can be optionally utilized to mitigate the uncertainty of secondary structure prediction. With a user-friendly interface, the web application is easy to use. Intuitive illustrations are provided along with the original computational results to facilitate analysis. The RSRE will be helpful in the wide exploration of RNA structural robustness and will catalyze our understanding of RNA evolution. The RSRE web server is freely available at http://biosrv1.bmi.ac.cn/RSRE/ or http://biotech.bmi.ac.cn/RSRE/. PMID:17567615
Robust stability of linear systems: Some computational considerations
NASA Technical Reports Server (NTRS)
Laub, A. J.
1979-01-01
The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.
NASA Astrophysics Data System (ADS)
Wang, Xiaoqiang; Ju, Lili; Du, Qiang
2016-07-01
The Willmore flow formulated by phase field dynamics based on the elastic bending energy model has been widely used to describe the shape transformation of biological lipid vesicles. In this paper, we develop and investigate some efficient and stable numerical methods for simulating the unconstrained phase field Willmore dynamics and the phase field Willmore dynamics with fixed volume and surface area constraints. The proposed methods can be high-order accurate and are completely explicit in nature, by combining exponential time differencing Runge-Kutta approximations for time integration with spectral discretizations for spatial operators on regular meshes. We also incorporate novel linear operator splitting techniques into the numerical schemes to improve the discrete energy stability. In order to avoid extra numerical instability brought by use of large penalty parameters in solving the constrained phase field Willmore dynamics problem, a modified augmented Lagrange multiplier approach is proposed and adopted. Various numerical experiments are performed to demonstrate accuracy and stability of the proposed methods.
Bishai, David; Opuni, Marjorie
2009-01-01
Background Time trends in infant mortality for the 20th century show a curvilinear pattern that most demographers have assumed to be approximately exponential. Virtually all cross-country comparisons and time series analyses of infant mortality have studied the logarithm of infant mortality to account for the curvilinear time trend. However, there is no evidence that the log transform is the best fit for infant mortality time trends. Methods We use maximum likelihood methods to determine the best transformation to fit time trends in infant mortality reduction in the 20th century and to assess the importance of the proper transformation in identifying the relationship between infant mortality and gross domestic product (GDP) per capita. We apply the Box Cox transform to infant mortality rate (IMR) time series from 18 countries to identify the best fitting value of lambda for each country and for the pooled sample. For each country, we test the value of λ against the null that λ = 0 (logarithmic model) and against the null that λ = 1 (linear model). We then demonstrate the importance of selecting the proper transformation by comparing regressions of ln(IMR) on same year GDP per capita against Box Cox transformed models. Results Based on chi-squared test statistics, infant mortality decline is best described as an exponential decline only for the United States. For the remaining 17 countries we study, IMR decline is neither best modelled as logarithmic nor as a linear process. Imposing a logarithmic transform on IMR can lead to bias in fitting the relationship between IMR and GDP per capita. Conclusion The assumption that IMR declines are exponential is enshrined in the Preston curve and in nearly all cross-country as well as time series analyses of IMR data since Preston's 1975 paper, but this assumption is seldom correct. Statistical analyses of IMR trends should assess the robustness of findings to transformations other than the log transform. PMID:19698144
Robustness of airline route networks
NASA Astrophysics Data System (ADS)
Lordan, Oriol; Sallan, Jose M.; Escorihuela, Nuria; Gonzalez-Prieto, David
2016-03-01
Airlines shape their route network by defining their routes through supply and demand considerations, paying little attention to network performance indicators, such as network robustness. However, the collapse of an airline network can produce high financial costs for the airline and all its geographical area of influence. The aim of this study is to analyze the topology and robustness of the network route of airlines following Low Cost Carriers (LCCs) and Full Service Carriers (FSCs) business models. Results show that FSC hubs are more central than LCC bases in their route network. As a result, LCC route networks are more robust than FSC networks.
Pervasive robustness in biological systems.
Félix, Marie-Anne; Barkoulas, Michalis
2015-08-01
Robustness is characterized by the invariant expression of a phenotype in the face of a genetic and/or environmental perturbation. Although phenotypic variance is a central measure in the mapping of the genotype and environment to the phenotype in quantitative evolutionary genetics, robustness is also a key feature in systems biology, resulting from nonlinearities in quantitative relationships between upstream and downstream components. In this Review, we provide a synthesis of these two lines of investigation, converging on understanding how variation propagates across biological systems. We critically assess the recent proliferation of studies identifying robustness-conferring genes in the context of the nonlinearity in biological systems. PMID:26184598
Stretched exponential relaxation in molecular and electronic glasses
NASA Astrophysics Data System (ADS)
Phillips, J. C.
1996-09-01
Stretched exponential relaxation, 0034-4885/59/9/003/img1, fits many relaxation processes in disordered and quenched electronic and molecular systems, but it is widely believed that this function has no microscopic basis, especially in the case of molecular relaxation. For electronic relaxation the appearance of the stretched exponential is often described in the context of dispersive transport, where 0034-4885/59/9/003/img2 is treated as an adjustable parameter, but in almost all cases it is generally assumed that no microscopic meaning can be assigned to 0034-4885/59/9/003/img3 even at 0034-4885/59/9/003/img4, a glass transition temperature. We show that for molecular relaxation 0034-4885/59/9/003/img5 can be understood, providing that one separates extrinsic and intrinsic effects, and that the intrinsic effects are dominated by two magic numbers, 0034-4885/59/9/003/img6 for short-range forces, and 0034-4885/59/9/003/img7 for long-range Coulomb forces, as originally observed by Kohlrausch for the decay of residual charge on a Leyden jar. Our mathematical model treats relaxation kinetics using the Lifshitz - Kac - Luttinger diffusion to traps depletion model in a configuration space of effective dimensionality, the latter being determined using axiomatic set theory and Phillips - Thorpe constraint theory. The experiments discussed include ns neutron scattering experiments, particularly those based on neutron spin echoes which measure S( Q,t) directly, and the traditional linear response measurements which span the range from 0034-4885/59/9/003/img8 to s, as collected and analysed phenomenologically by Angell, Ngai, Böhmer and others. The electronic materials discussed include a-Si:H, granular 0034-4885/59/9/003/img9, semiconductor nanocrystallites, charge density waves in 0034-4885/59/9/003/img10, spin glasses, and vortex glasses in high-temperature semiconductors. The molecular materials discussed include polymers, network glasses, electrolytes and alcohols, Van
Dynamics and stability of parametrically excited gyroscopic systems
NASA Astrophysics Data System (ADS)
Vedula, Narayana L.
We study the reduction, dynamics and stability of two-degree-of-freedom mechanical systems. We are particularly interested in understanding energy transfer between modes in such systems. The first part of this research is concerned with the stochastic stability of a two-degree-of-freedom linear system: (a) with one asymptotically stable and one critical mode, (b) with both modes critical and one of the modes corresponding to a nilpotent structure. We obtain asymptotic expansions for the moment and maximal Lyapunov exponents which characterize the exponential growth rate of the amplitude. The results from (a) indicate that the presence of noise may have a stabilizing effect and are applied to explain experimental observations on fluid flow over tube bundles. The results from (b) are applied to show that the effects of noise on a pipe conveying fluid close to divergence are always destabilising in nature. The second part of this research involves the reduction of two-degree-of-freedom randomly perturbed nonlinear gyroscopic systems close to a double zero resonance. It is shown that the long term behaviour of the original four-dimensional system can be approximated by a one dimensional Markov process which take values on a line or a graph. These results are applied to study the dynamics and stability of a rotating shaft subjected to fluctuating axial load. In the final part of this research, we study the dynamics and stability of nonlinear delay gyroscopic systems with periodically varying delay. The center manifold and normal form methods are used to obtain an approximate and simpler two dimensional system. Analysis of this simpler system shows that periodic variations in the delay may lead to larger stability boundaries. These results are applied to demonstrate that greater depths of cut may be achieved in a boring process when the speed of the spindle is modulated sinusoidally instead of being kept constant. A detailed knowledge of the machine-tool structure
Robust Optimization of Biological Protocols
Flaherty, Patrick; Davis, Ronald W.
2015-01-01
When conducting high-throughput biological experiments, it is often necessary to develop a protocol that is both inexpensive and robust. Standard approaches are either not cost-effective or arrive at an optimized protocol that is sensitive to experimental variations. We show here a novel approach that directly minimizes the cost of the protocol while ensuring the protocol is robust to experimental variation. Our approach uses a risk-averse conditional value-at-risk criterion in a robust parameter design framework. We demonstrate this approach on a polymerase chain reaction protocol and show that our improved protocol is less expensive than the standard protocol and more robust than a protocol optimized without consideration of experimental variation. PMID:26417115
Dosimetry robustness with stochastic optimization
NASA Astrophysics Data System (ADS)
Nohadani, Omid; Seco, Joao; Martin, Benjamin C.; Bortfeld, Thomas
2009-06-01
All radiation therapy treatment planning relies on accurate dose calculation. Uncertainties in dosimetric prediction can significantly degrade an otherwise optimal plan. In this work, we introduce a robust optimization method which handles dosimetric errors and warrants for high-quality IMRT plans. Unlike other dose error estimations, we do not rely on the detailed knowledge about the sources of the uncertainty and use a generic error model based on random perturbation. This generality is sought in order to cope with a large variety of error sources. We demonstrate the method on a clinical case of lung cancer and show that our method provides plans that are more robust against dosimetric errors and are clinically acceptable. In fact, the robust plan exhibits a two-fold improved equivalent uniform dose compared to the non-robust but optimized plan. The achieved speedup will allow computationally extensive multi-criteria or beam-angle optimization approaches to warrant for dosimetrically relevant plans.
Predictors of the peak width for networks with exponential links
Troutman, B.M.; Karlinger, M.R.
1989-01-01
We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations of S and T given network magnitude N and given mainstream length H. In addition, a simulation study is performed to examine various predictors of S and T, including N, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor of S is N, of T is H, and of the scaled peak (S divided by the area under the width function) is H. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predicting S and T despite probable violations of the original assumptions. ?? 1989 Springer-Verlag.
On the mono-exponential fitting of phosphorescence decays
NASA Astrophysics Data System (ADS)
Fuhrmann, N.; Brübach, J.; Dreizler, A.
2014-08-01
Several methods for mono-exponential fitting of decay curves are presented and compared among each other in terms of precision, accuracy and computational time. Simulated noisy data sets are generated and evaluated in order to determine the main contributors to a loss in performance. The influence of the temporal discretization of the decay curve on the precision of the fitting methods is discussed. Correlations between the background offset and the decay time are analyzed. Variations of the signal-to-noise ratio are shown, allowing for evaluation of systematic errors and precision in the presence of noise. Finally, the algorithms are applied to experimental data, and the computational efforts for the different algorithms are compared. The results of this latter investigation confirm the conclusions drawn from the simulated data and the following conclusions are drawn: The frequently applied method of performing a linear regression to the logarithm of a background-corrected decay showed systematic errors in the presence of noise. Best results in terms of precision and accuracy were obtained by a nonlinear least-squares approximation and a method denoted as the linear regression of the sum. Additionally, this latter method required the lowest computational time and is finally recommended for determining decay times from experimental data.
Non-exponential T2* decay in White Matter
van Gelderen, Peter; de Zwart, Jacco A.; Lee, Jongho; Sati, Pascal; Reich, Daniel S.; Duyn, Jeff H.
2011-01-01
Visualizing myelin in human brain may help the study of diseases such as multiple sclerosis. Previous studies based on T1 and T2 relaxation contrast have suggested the presence of a distinct water pool that may report directly on local myelin content. Recent work indicates that T2* contrast may offer particular advantages over T1 and T2 contrast, especially at high field. However, the complex mechanism underlying T2* relaxation may render interpretation difficult. To address this issue, T2* relaxation behavior in human brain was studied at 3 and 7 tesla. Multiple gradient echoes covering most of the decay curve were analyzed for deviations from mono-exponential behavior. The data confirm the previous finding of a distinct rapidly relaxing signal component (T2* ~ 6 ms), tentatively attributed to myelin water. However, in extension to previous findings, this rapidly relaxing component displayed a substantial resonance frequency shift, reaching 36 Hz in the corpus callosum at 7 T. The component’s fractional amplitude and frequency shift appeared to depend on both field strength and fiber orientation, consistent with a mechanism originating from magnetic susceptibility effects. The findings suggest that T2* contrast at high field may be uniquely sensitive to tissue myelin content, and that proper interpretation will require modeling of susceptibility-induced resonance frequency shifts. PMID:21630352
Exponential flux-controlled memristor model and its floating emulator
NASA Astrophysics Data System (ADS)
Liu, Wei; Wang, Fa-Qiang; Ma, Xi-Kui
2015-11-01
As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the memristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance (memristance) will keep monotonically increasing or decreasing unless the voltage’s polarity reverses (if not approach the boundaries), is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor (especially the demand for a larger current). The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator. Project supported by the National Natural Science Foundation of China (Grant Nos. 51377124 and 51221005), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201337), the Program for New Century Excellent Talents in University of China (Grant No. NCET-13-0457), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2012JQ7026).
Stretched exponential relaxation of piezovoltages in wet bovine bone.
Xu, Lianyun; Hou, Zhende; Fu, Donghui; Qin, Qing-Hua; Wang, Yihan
2015-01-01
It is important to determine the amplitude and variation characteristics of piezovoltage in wet bone, which can, in turn, be taken as a basis for studying whether electrical signals induced by external forces can affect the growth of bone cells. This work measured the characteristics of piezoelectric effects under dynamic and static loading. The results show that the variations of piezovoltage in wet bone in both loading and load holding periods follow a stretched exponential relaxation law, and the relaxation time constants of the piezovoltages are much larger than those of dry bone. This finding means that the active time of piezovoltage in wet bone is much longer than that of dry bone. Regardless of the loading and load holding processes, continuously increasing deformation in wet bone caused piezoelectric charges to be continuously induced and increased the dielectric constant of wet bone along with the deformation process. In general, compared with piezovoltage in dry bone, that in wet bone had lower amplitude and could exist for a longer duration. It can be inferred, therefore, that piezoelectricity might create coupling with the streaming potential in bone by changing the thickness of the double electrode layer. PMID:25460408
Exponential estimates for oscillatory integrals with degenerate phase functions
NASA Astrophysics Data System (ADS)
Cardin, F.; Gramchev, T.; Lovison, A.
2008-03-01
In this paper we give precise asymptotic expansions and estimates of the remainder R(λ) for oscillatory integrals with non Morse phase functions, having degeneracies of any order k >= 2. We provide an algorithm for writing down explicitly the coefficients of the asymptotic expansion analysing precisely the combinatorial behaviour of the coefficients (Gevrey type) and deriving optimal exponential decay estimates for the remainder when λ → ∞. We recapture the fundamental asymptotic expansions by Erdélyi (1956 Asymptotic Expansions (New York: Dover)). As it concerns the remainder estimates, it seems they are novel even for the classical cases. The main application of this machinery is a derivation of uniform estimates with respect to control parameters of celebrated oscillatory integrals in optics appearing in the calculations of the intensity of the light along the caustics (umbilics), see e.g. Arnold (1988 Singularities of Differentiable Maps vol II (Boston: Birkhäuser Boston Inc.)), (1974 USP. Mat. Nauk. 29 11-49) and Berry and Upstill (1980 Prog. Opt. 18 257-346). Finally, we mention that as an outcome of our abstract approach we obtain refinements for Morse phase functions provided suitable symmetry and Gevrey type regularity conditions on the phase functions and amplitudes hold. As far as we know, even this asymptotic expansion for the elliptic umbilic is a novelty.
Exponential 6 parameterization for the JCZ3-EOS
McGee, B.C.; Hobbs, M.L.; Baer, M.R.
1998-07-01
A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials. The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules. All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant. These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS. This database can be used with the CHEETAH 1.40 or CHEETAH 2.0 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species. The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition.
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, W. R.; Moser, D. E.; Suggs, R. M.; Cooke, W. J.
2011-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, eta, is a unique function of velocity with an extremely large variation in the laboratory range of under 6 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from both laboratory impacts and from lunar impact observations. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors. Keywords hypervelocity impact impact flash luminous efficiency lunar impact meteoroid 1
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, Wesley R.; Moser, D.E.; Suggs, Robb M.; Cooke, W.J.
2010-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, Eta is a unique function of velocity with an extremely large variation in the laboratory range of under 8 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from laboratory impacts and from astronomical determinations and scaling factors are estimated. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors
A comparison of the generalized gamma and exponentiated Weibull distributions.
Cox, Christopher; Matheson, Matthew
2014-09-20
This paper provides a comparison of the three-parameter exponentiated Weibull (EW) and generalized gamma (GG) distributions. The connection between these two different families is that the hazard functions of both have the four standard shapes (increasing, decreasing, bathtub, and arc shaped), and in fact, the shape of the hazard is the same for identical values of the three parameters. For a given EW distribution, we define a matching GG using simulation and also by matching the 5 (th) , 50 (th) , and 95 (th) percentiles. We compare EW and matching GG distributions graphically and using the Kullback-Leibler distance. We find that the survival functions for the EW and matching GG are graphically indistinguishable, and only the hazard functions can sometimes be seen to be slightly different. The Kullback-Leibler distances are very small and decrease with increasing sample size. We conclude that the similarity between the two distributions is striking, and therefore, the EW represents a convenient alternative to the GG with the identical richness of hazard behavior. More importantly, these results suggest that having the four basic hazard shapes may to some extent be an important structural characteristic of any family of distributions. PMID:24700647
Mutant number distribution in an exponentially growing population
NASA Astrophysics Data System (ADS)
Keller, Peter; Antal, Tibor
2015-01-01
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.
Effect of coronal structure on loop oscillations: exponential profiles
NASA Astrophysics Data System (ADS)
Díaz, A. J.; Donnelly, G. R.; Roberts, B.
2007-12-01
Aims:The role of longitudinal structuring of the surrounding corona on the modes of oscillation of a coronal magnetic flux tube was studied in Donnelly et al. (2006) for a piecewise uniform profile. Here we investigate whether a more realistic continuous exponential profile changes the conclusions drawn from that paper. Methods: A partial differential equation is derived for the total pressure perturbation of the fast modes, which is then decomposed by separation of variables. The longitudinal part is solved numerically, obtaining a dispersion relation. These results are supported by an analytical investigation in terms of Bessel functions of purely imaginary order. Results: Structure in the interior of the loop shifts the frequencies of the modes (and may trap higher harmonics), an effect which can be understood by taking an averaged profile with a suitable weight. Structure in the environment modifies only slightly the frequencies, but displaces the cutoff frequency. The shift due to the structure in the fundamental period is small, but the ratio between the periods of the fundamental mode and its harmonics can be used to probe the structure. Conclusions: The results support our previous study in a more realistic, continuously varying profile and provide limits to the conclusions drawn in coronal seismology if an unstructured loop is used. Also, the ratio between the period of the fundamental kink (even) mode and its first (odd) harmonic is proven as an extra seismological tool for coronal loops.
COMMUNICATION: Neuron network activity scales exponentially with synapse density
NASA Astrophysics Data System (ADS)
Brewer, G. J.; Boehler, M. D.; Pearson, R. A.; DeMaris, A. A.; Ide, A. N.; Wheeler, B. C.
2009-02-01
Neuronal network output in the cortex as a function of synapse density during development has not been explicitly determined. Synaptic scaling in cortical brain networks seems to alter excitatory and inhibitory synaptic inputs to produce a representative rate of synaptic output. Here, we cultured rat hippocampal neurons over a three-week period to correlate synapse density with the increase in spontaneous spiking activity. We followed the network development as synapse formation and spike rate in two serum-free media optimized for either (a) neuron survival (Neurobasal/B27) or (b) spike rate (NbActiv4). We found that while synaptophysin synapse density increased linearly with development, spike rates increased exponentially in developing neuronal networks. Synaptic receptor components NR1, GluR1 and GABA-A also increase linearly but with more excitatory receptors than inhibitory. These results suggest that the brain's information processing capability gains more from increasing connectivity of the processing units than increasing processing units, much as Internet information flow increases much faster than the linear number of nodes and connections.
Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions
Ostrovsky, V. N.
2003-07-01
The nonstationary Schroedinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic {approx}1/t time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schroedinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as t{yields}{infinity} in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time t{yields}+0). The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.
Robustness Elasticity in Complex Networks
Matisziw, Timothy C.; Grubesic, Tony H.; Guo, Junyu
2012-01-01
Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems. PMID:22808060
/q-exponential, Weibull, and /q-Weibull distributions: an empirical analysis
NASA Astrophysics Data System (ADS)
Picoli, S.; Mendes, R. S.; Malacarne, L. C.
2003-06-01
In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law ( q-exponential with q>1) controversy.
The application of cost averaging techniques to robust control of the benchmark problem
NASA Technical Reports Server (NTRS)
Hagood, Nesbitt W.; Crawley, Edward F.
1991-01-01
A method is presented for the synthesis of robust controllers for linear time invariant systems with parameterized uncertainty structures. The method involves minimizing the average quadratic (H2) cost over the parameterized system. Bonded average cost implies stability over the set of systems. The average cost functional is minimized to derive robust fixed-order dynamic compensators. The robustness properties of these controllers are demonstrated on the sample problem.
NASA Technical Reports Server (NTRS)
Waszak, Martin R.
1997-01-01
The Benchmark Active Controls Technology (BACT) project is part of NASA Langley Research Center s Benchmark Models Program for studying transonic aeroelastic phenomena. In January of 1996 the BACT wind-tunnel model was used to successfully demonstrate the application of robust multivariable control design methods (H and -synthesis) to flutter suppression. This paper addresses the design and experimental evaluation of robust multivariable flutter suppression control laws with particular attention paid to the degree to which stability and performance robustness was achieved.
Robust, Practical Adaptive Control for Launch Vehicles
NASA Technical Reports Server (NTRS)
Orr, Jeb. S.; VanZwieten, Tannen S.
2012-01-01
A modern mechanization of a classical adaptive control concept is presented with an application to launch vehicle attitude control systems. Due to a rigorous flight certification environment, many adaptive control concepts are infeasible when applied to high-risk aerospace systems; methods of stability analysis are either intractable for high complexity models or cannot be reconciled in light of classical requirements. Furthermore, many adaptive techniques appearing in the literature are not suitable for application to conditionally stable systems with complex flexible-body dynamics, as is often the case with launch vehicles. The present technique is a multiplicative forward loop gain adaptive law similar to that used for the NASA X-15 flight research vehicle. In digital implementation with several novel features, it is well-suited to application on aerodynamically unstable launch vehicles with thrust vector control via augmentation of the baseline attitude/attitude-rate feedback control scheme. The approach is compatible with standard design features of autopilots for launch vehicles, including phase stabilization of lateral bending and slosh via linear filters. In addition, the method of assessing flight control stability via classical gain and phase margins is not affected under reasonable assumptions. The algorithm s ability to recover from certain unstable operating regimes can in fact be understood in terms of frequency-domain criteria. Finally, simulation results are presented that confirm the ability of the algorithm to improve performance and robustness in realistic failure scenarios.
NASA Astrophysics Data System (ADS)
Kwakkel, Jan; Haasnoot, Marjolijn
2015-04-01
In response to climate and socio-economic change, in various policy domains there is increasingly a call for robust plans or policies. That is, plans or policies that performs well in a very large range of plausible futures. In the literature, a wide range of alternative robustness metrics can be found. The relative merit of these alternative conceptualizations of robustness has, however, received less attention. Evidently, different robustness metrics can result in different plans or policies being adopted. This paper investigates the consequences of several robustness metrics on decision making, illustrated here by the design of a flood risk management plan. A fictitious case, inspired by a river reach in the Netherlands is used. The performance of this system in terms of casualties, damages, and costs for flood and damage mitigation actions is explored using a time horizon of 100 years, and accounting for uncertainties pertaining to climate change and land use change. A set of candidate policy options is specified up front. This set of options includes dike raising, dike strengthening, creating more space for the river, and flood proof building and evacuation options. The overarching aim is to design an effective flood risk mitigation strategy that is designed from the outset to be adapted over time in response to how the future actually unfolds. To this end, the plan will be based on the dynamic adaptive policy pathway approach (Haasnoot, Kwakkel et al. 2013) being used in the Dutch Delta Program. The policy problem is formulated as a multi-objective robust optimization problem (Kwakkel, Haasnoot et al. 2014). We solve the multi-objective robust optimization problem using several alternative robustness metrics, including both satisficing robustness metrics and regret based robustness metrics. Satisficing robustness metrics focus on the performance of candidate plans across a large ensemble of plausible futures. Regret based robustness metrics compare the
Stability of Stochastic Neutral Cellular Neural Networks
NASA Astrophysics Data System (ADS)
Chen, Ling; Zhao, Hongyong
In this paper, we study a class of stochastic neutral cellular neural networks. By constructing a suitable Lyapunov functional and employing the nonnegative semi-martingale convergence theorem we give some sufficient conditions ensuring the almost sure exponential stability of the networks. The results obtained are helpful to design stability of networks when stochastic noise is taken into consideration. Finally, two examples are provided to show the correctness of our analysis.
NASA Astrophysics Data System (ADS)
Chen, Bingling; Guo, Zhouyi
2008-12-01
Conventional analyses of OCT signal measurements resolve the signal decay profile in terms of single discrete exponential function with distinct exponential model. In symmetrical medium, mono-exponential decay function can appear to provide a well fit to OCT signal decay data, but the assuption of symmetrical components is essentially arbitrary and is often erroneous. Actually, the real biological samples such as tissue contained more complex components and are more heterogeneous. To avoid the shortages of mono-exponential decay function fitting to OCT signal decay data from heterogeneous biological tissues, a novel model of flexible exponential function has been developed. The main idea of the flexible exponential function modle is based on the assuption that heterogeneous biological tissue can be considered as a multi-layered tissue. Each layer is symmetric and the OCT signal decay profile in each layer obeies to a distinct single exponential function. If we can find out all the distinct single exponential function for each layer, the total flexible exponential function is determined by summing up all the single exponential functions. As pilot studies on the practical application of flexibleexponential decay model for monitoring and quantifying the diffusion of different analytes in turbid biological tissues in vivo by using OCT system, we demonstrate an experiment of monitoring of glucose diffusion in agar gel. In addition, the flexible-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the analysis of turbid tissues OCT map using the flexible-exponential decay model can reveal subtle tissue differences that other models fail to show.
Robustness properties of discrete time regulators, LOG regulators and hybrid systems
NASA Technical Reports Server (NTRS)
Stein, G.; Athans, M.
1979-01-01
Robustness properites of sample-data LQ regulators are derived which show that these regulators have fundamentally inferior uncertainty tolerances when compared to their continuous-time counterparts. Results are also presented in stability theory, multivariable frequency domain analysis, LQG robustness, and mathematical representations of hybrid systems.
NASA Astrophysics Data System (ADS)
Athans, M.; Lee, W. H.; Lehtomaki, N. A.; Levy, B. C.; Ng, P. T. P.
1982-05-01
The robustness of the stability of multivariable linear time-invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available and new robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point of a single-input, single-output (SISO) Nyquist diagram. Using the return difference transfer matrix a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness of linear-quadratic-Gaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a cross-feed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linear-quadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1977-01-01
Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.
The double exponential sinc collocation method for singular Sturm-Liouville problems
NASA Astrophysics Data System (ADS)
Gaudreau, P.; Slevinsky, R.; Safouhi, H.
2016-04-01
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville boundary value problems. The proposed method uses the double exponential formula coupled with sinc collocation method. This method produces a symmetric positive-definite generalized eigenvalue system and has exponential convergence rate. Numerical examples are presented and comparisons with single exponential sinc collocation method clearly illustrate the advantage of using the double exponential formula.
Stability of polymer solar cells.
Jørgensen, Mikkel; Norrman, Kion; Gevorgyan, Suren A; Tromholt, Thomas; Andreasen, Birgitta; Krebs, Frederik C
2012-02-01
Organic photovoltaics (OPVs) evolve in an exponential manner in the two key areas of efficiency and stability. The power conversion efficiency (PCE) has in the last decade been increased by almost a factor of ten approaching 10%. A main concern has been the stability that was previously measured in minutes, but can now, in favorable circumstances, exceed many thousands of hours. This astonishing achievement is the subject of this article, which reviews the developments in stability/degradation of OPVs in the last five years. This progress has been gained by several developments, such as inverted device structures of the bulk heterojunction geometry device, which allows for more stable metal electrodes, the choice of more photostable active materials, the introduction of interfacial layers, and roll-to-roll fabrication, which promises fast and cheap production methods while creating its own challenges in terms of stability. PMID:22213056
Partial stabilization-based guidance.
Shafiei, M H; Binazadeh, T
2012-01-01
A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations. PMID:21963401
EXPONENTIAL TIME DIFFERENCING FOR HODGKIN-HUXLEY-LIKE ODES.
Börgers, Christoph; Nectow, Alexander R
2013-01-01
Several authors have proposed the use of exponential time differencing (ETD) for Hodgkin-Huxley-like partial and ordinary differential equations (PDEs and ODEs). For Hodgkin-Huxley-like PDEs, ETD is attractive because it can deal effectively with the stiffness issues that diffusion gives rise to. However, large neuronal networks are often simulated assuming "space-clamped" neurons, i.e., using the Hodgkin-Huxley ODEs, in which there are no diffusion terms. Our goal is to clarify whether ETD is a good idea even in that case. We present a numerical comparison of first- and second-order ETD with standard explicit time-stepping schemes (Euler's method, the midpoint method, and the classical fourth-order Runge-Kutta method). We find that in the standard schemes, the stable computation of the very rapid rising phase of the action potential often forces time steps of a small fraction of a millisecond. This can result in an expensive calculation yielding greater overall accuracy than needed. Although it is tempting at first to try to address this issue with adaptive or fully implicit time-stepping, we argue that neither is effective here. The main advantage of ETD for Hodgkin-Huxley-like systems of ODEs is that it allows underresolution of the rising phase of the action potential without causing instability, using time steps on the order of one millisecond. When high quantitative accuracy is not necessary and perhaps, because of modeling inaccuracies, not even useful, ETD allows much faster simulations than standard explicit time-stepping schemes. The second-order ETD scheme is found to be substantially more accurate than the first-order one even for large values of Δt. PMID:24058276
Generalized Exponential Distribution in Flood Frequency Analysis for Polish Rivers
Markiewicz, Iwona; Strupczewski, Witold G.; Bogdanowicz, Ewa; Kochanek, Krzysztof
2015-01-01
Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles. PMID:26657239
EXPONENTIAL TIME DIFFERENCING FOR HODGKIN–HUXLEY-LIKE ODES
Börgers, Christoph; Nectow, Alexander R.
2013-01-01
Several authors have proposed the use of exponential time differencing (ETD) for Hodgkin–Huxley-like partial and ordinary differential equations (PDEs and ODEs). For Hodgkin–Huxley-like PDEs, ETD is attractive because it can deal effectively with the stiffness issues that diffusion gives rise to. However, large neuronal networks are often simulated assuming “space-clamped” neurons, i.e., using the Hodgkin–Huxley ODEs, in which there are no diffusion terms. Our goal is to clarify whether ETD is a good idea even in that case. We present a numerical comparison of first- and second-order ETD with standard explicit time-stepping schemes (Euler’s method, the midpoint method, and the classical fourth-order Runge–Kutta method). We find that in the standard schemes, the stable computation of the very rapid rising phase of the action potential often forces time steps of a small fraction of a millisecond. This can result in an expensive calculation yielding greater overall accuracy than needed. Although it is tempting at first to try to address this issue with adaptive or fully implicit time-stepping, we argue that neither is effective here. The main advantage of ETD for Hodgkin–Huxley-like systems of ODEs is that it allows underresolution of the rising phase of the action potential without causing instability, using time steps on the order of one millisecond. When high quantitative accuracy is not necessary and perhaps, because of modeling inaccuracies, not even useful, ETD allows much faster simulations than standard explicit time-stepping schemes. The second-order ETD scheme is found to be substantially more accurate than the first-order one even for large values of Δt. PMID:24058276
Robust adaptive dynamic programming with an application to power systems.
Jiang, Yu; Jiang, Zhong-Ping
2013-07-01
This brief presents a novel framework of robust adaptive dynamic programming (robust-ADP) aimed at computing globally stabilizing and suboptimal control policies in the presence of dynamic uncertainties. A key strategy is to integrate ADP theory with techniques in modern nonlinear control with a unique objective of filling up a gap in the past literature of ADP without taking into account dynamic uncertainties. Neither the system dynamics nor the system order are required to be precisely known. As an illustrative example, the computational algorithm is applied to the controller design of a two-machine power system. PMID:24808528
Robust model-based controller synthesis for the SCOLE configuration
NASA Technical Reports Server (NTRS)
Armstrong, E. S.; Joshi, S. M.; Stewart, E. J.
1988-01-01
The design of a robust compensator is considered for the SCOLE configuration using a frequency-response shaping technique based on the LQG/LTR algorithm. Results indicate that a tenth-order compensator can be used to meet stability-performance-robustness conditions for a 26th-order SCOLE model without destabilizing spillover effects. Since the SCOLE configuration is representative of many proposed spaceflight experiments, the results and design techniques employed potentially should be applicable to a wide range of large space structure control problems.
Design of robust level control system of nuclear steam generator
NASA Astrophysics Data System (ADS)
Lee, Y. J.; Na, M. G.
2007-12-01
The nuclear steam generator feedwater control system is designed by the robust control methods. The design is divided into two steps. First, the feedwater controller in the feedwater station is designed by H ∞ and MWS methods. Then the controller located on the feedback loop is designed both by classical PID and by robust technique. It is found that the feedback controller of simple PID whose coefficients vary with the power is proper for the system performance. The simulations show that the hybrid system of H ∞ and PID has a good performance with proper stability margins.
Robust vibration control of flexible linkage mechanisms using piezoelectric films
NASA Astrophysics Data System (ADS)
Liao, Wen-Hwei; Chou, Jyh-Horng; Horng, Ing-Rong
1997-08-01
Based on the state space model of the flexible linkage mechanism equipped with piezoelectric films, a robust control methodology for suppressing elastodynamic responses of the high-speed flexible linkage mechanism with linear time-varying parameter perturbations by employing an observer-based feedback controller is presented. The instability caused by the linear time-varying parameter perturbations and the instability caused by the combined effect of control and observation spillover are investigated and carefully prevented by two robust stability criteria proposed in this paper. Numerical simulation of a slider - crank mechanism example is performed to evaluate the improvement of the elastodynamic responses.
Variable neural adaptive robust control: a switched system approach.
Lian, Jianming; Hu, Jianghai; Żak, Stanislaw H
2015-05-01
Variable neural adaptive robust control strategies are proposed for the output tracking control of a class of multiinput multioutput uncertain systems. The controllers incorporate a novel variable-structure radial basis function (RBF) network as the self-organizing approximator for unknown system dynamics. It can determine the network structure online dynamically by adding or removing RBFs according to the tracking performance. The structure variation is systematically considered in the stability analysis of the closed-loop system using a switched system approach with the piecewise quadratic Lyapunov function. The performance of the proposed variable neural adaptive robust controllers is illustrated with simulations. PMID:25881366
Robust on-off pulse control of flexible space vehicles
NASA Technical Reports Server (NTRS)
Wie, Bong; Sinha, Ravi
1993-01-01
The on-off reaction jet control system is often used for attitude and orbital maneuvering of various spacecraft. Future space vehicles such as the orbital transfer vehicles, orbital maneuvering vehicles, and space station will extensively use reaction jets for orbital maneuvering and attitude stabilization. The proposed robust fuel- and time-optimal control algorithm is used for a three-mass spacing model of flexible spacecraft. A fuel-efficient on-off control logic is developed for robust rest-to-rest maneuver of a flexible vehicle with minimum excitation of structural modes. The first part of this report is concerned with the problem of selecting a proper pair of jets for practical trade-offs among the maneuvering time, fuel consumption, structural mode excitation, and performance robustness. A time-optimal control problem subject to parameter robustness constraints is formulated and solved. The second part of this report deals with obtaining parameter insensitive fuel- and time- optimal control inputs by solving a constrained optimization problem subject to robustness constraints. It is shown that sensitivity to modeling errors can be significantly reduced by the proposed, robustified open-loop control approach. The final part of this report deals with sliding mode control design for uncertain flexible structures. The benchmark problem of a flexible structure is used as an example for the feedback sliding mode controller design with bounded control inputs and robustness to parameter variations is investigated.
Optimal and robust control of transition
NASA Technical Reports Server (NTRS)
Bewley, T. R.; Agarwal, R.
1996-01-01
Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.
Robust Transient Dynamics and Brain Functions
Rabinovich, Mikhail I.; Varona, Pablo
2011-01-01
In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework – heteroclinic sequential dynamics – to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory – a vital cognitive function –, and to find specific dynamical signatures – different kinds of instabilities – of several brain functions and mental diseases. PMID:21716642
Robust transient dynamics and brain functions.
Rabinovich, Mikhail I; Varona, Pablo
2011-01-01
In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework - heteroclinic sequential dynamics - to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases. PMID:21716642
Robust ferromagnetism in monolayer chromium nitride
Zhang, Shunhong; Li, Yawei; Zhao, Tianshan; Wang, Qian
2014-01-01
Design and synthesis of two-dimensional (2D) materials with robust ferromagnetism and biocompatibility is highly desirable due to their potential applications in spintronics and biodevices. However, the hotly pursued 2D sheets including pristine graphene, monolayer BN, and layered transition metal dichalcogenides are nonmagnetic or weakly magnetic. Using biomimetic particle swarm optimization (PSO) technique combined with ab initio calculations we predict the existence of a 2D structure, a monolayer of rocksalt-structured CrN (100) surface, which is both ferromagnetic and biocompatible. Its dynamic, thermal and magnetic stabilities are confirmed by carrying out a variety of state-of-the-art theoretical calculations. Analyses of its band structure and density of states reveal that this material is half-metallic, and the origin of the ferromagnetism is due to p-d exchange interaction between the Cr and N atoms. We demonstrate that the displayed ferromagnetism is robust against thermal and mechanical perturbations. The corresponding Curie temperature is about 675 K which is higher than that of most previously studied 2D monolayers. PMID:24912562
Robust controllers for the Middeck Active Control Experiment using Popov controller synthesis
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Hall, Steven R.
1993-01-01
Recent work in robust control with real parameter uncertainties has focused on absolute stability and its connections to real mu theory. In particular, the research has investigated the Popov stability criterion and its associated Lur'e-Postnikov Liapunov functions. State space representations of this Popov stability analysis tests are included in an H2 design formulation to provide a powerful technique for robust controller synthesis. This synthesis approach uses a state space optimization procedure to design controllers that minimize an overbound of an H2 cost functional and satisfy stability analysis tests based on the Popov multiplier. The controller and stability multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K algorithm of mu synthesis. While previous work has demonstrated this synthesis approach on benchmark control problems, the purpose of this paper is to use Popov controller synthesis to design robust compensators for the Middeck Active Control Experiment (MACE).
Robust adiabatic sum frequency conversion.
Suchowski, Haim; Prabhudesai, Vaibhav; Oron, Dan; Arie, Ady; Silberberg, Yaron
2009-07-20
We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems. PMID:19654679
Robust Coordinated AVR-PSS Design Using H∞ Static Output Feedback Control
NASA Astrophysics Data System (ADS)
Bevrani, Hassan; Hiyama, Takashi
This paper addresses a new robust control methodology to enhance the power system stability and voltage regulation as an integrated design approach. The automatic voltage regulation (AVR) and power system stabilizer (PSS) design problems are reduced to solve a single H∞ based static output feedback control problem. To determine the optimal gains, an iterative linear matrix inequalities (LMI) algorithm is used. A four-machine infinite-bus system example is given to demonstrate the efficiency of developed approach. The proposed robust technique is shown to maintain the robust performance and minimize the effects of disturbances, properly.
Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth
ERIC Educational Resources Information Center
Castillo-Garsow, Carlos
2010-01-01
Both Thompson and the duo of Confrey and Smith describe how students might be taught to build "ways of thinking" about exponential behavior by coordinating the covariation of two changing quantities, however, these authors build exponential behavior from different meanings of covariation. Confrey and Smith advocate beginning with discrete additive…
Gradient flow of the stochastic relaxation on a generic exponential family
Malagò, Luigi; Pistone, Giovanni
2015-01-13
We study the natural gradient flow of the expected value E{sub p} [f] of an objective function f for p in an exponential family. We parameterize the exponential family with the expectation parameters and we show that the dynamical system associated to the natural gradient flow can be extended outside the marginal polytope.
Method for numerical simulation of two-term exponentially correlated colored noise
Yilmaz, B.; Ayik, S.; Abe, Y.; Gokalp, A.; Yilmaz, O.
2006-04-15
A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.
Robust and efficient estimation with weighted composite quantile regression
NASA Astrophysics Data System (ADS)
Jiang, Xuejun; Li, Jingzhi; Xia, Tian; Yan, Wanfeng
2016-09-01
In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student's t, Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results.
Survival analysis approach to account for non-exponential decay rate effects in lifetime experiments
NASA Astrophysics Data System (ADS)
Coakley, K. J.; Dewey, M. S.; Huber, M. G.; Huffer, C. R.; Huffman, P. R.; Marley, D. E.; Mumm, H. P.; O`Shaughnessy, C. M.; Schelhammer, K. W.; Thompson, A. K.; Yue, A. T.
2016-03-01
In experiments that measure the lifetime of trapped particles, in addition to loss mechanisms with exponential survival probability functions, particles can be lost by mechanisms with non-exponential survival probability functions. Failure to account for such loss mechanisms produces systematic measurement error and associated systematic uncertainties in these measurements. In this work, we develop a general competing risks survival analysis method to account for the joint effect of loss mechanisms with either exponential or non-exponential survival probability functions, and a method to quantify the size of systematic effects and associated uncertainties for lifetime estimates. As a case study, we apply our survival analysis formalism and method to the Ultra Cold Neutron lifetime experiment at NIST. In this experiment, neutrons can escape a magnetic trap before they decay due to a wall loss mechanism with an associated non-exponential survival probability function.
The Existence of Weak D-Pullback Exponential Attractor for Nonautonomous Dynamical System.
Li, Yongjun; Wei, Xiaona; Zhang, Yanhong
2016-01-01
First, for a process {U(t, τ)∣t ≥ τ}, we introduce a new concept, called the weak D-pullback exponential attractor, which is a family of sets {ℳ(t)∣t ≤ T}, for any T ∈ ℝ, satisfying the following: (i) ℳ(t) is compact, (ii) ℳ(t) is positively invariant, that is, U(t, τ)ℳ(τ) ⊂ ℳ(t), and (iii) there exist k, l > 0 such that dist(U(t, τ)B(τ), ℳ(t)) ≤ ke (-(t-τ)); that is, ℳ(t) pullback exponential attracts B(τ). Then we give a method to obtain the existence of weak D-pullback exponential attractors for a process. As an application, we obtain the existence of weak D-pullback exponential attractor for reaction diffusion equation in H 0 (1) with exponential growth of the external force. PMID:27119090
An exact formulation of the time-ordered exponential using path-sums
Giscard, P.-L.; Lui, K.; Thwaite, S. J.; Jaksch, D.
2015-05-15
We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
An exact formulation of the time-ordered exponential using path-sums
NASA Astrophysics Data System (ADS)
Giscard, P.-L.; Lui, K.; Thwaite, S. J.; Jaksch, D.
2015-05-01
We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
Robust surface roughness indices and morphological interpretation
NASA Astrophysics Data System (ADS)
Trevisani, Sebastiano; Rocca, Michele
2016-04-01
Geostatistical-based image/surface texture indices based on variogram (Atkison and Lewis, 2000; Herzfeld and Higginson, 1996; Trevisani et al., 2012) and on its robust variant MAD (median absolute differences, Trevisani and Rocca, 2015) offer powerful tools for the analysis and interpretation of surface morphology (potentially not limited to solid earth). In particular, the proposed robust index (Trevisani and Rocca, 2015) with its implementation based on local kernels permits the derivation of a wide set of robust and customizable geomorphometric indices capable to outline specific aspects of surface texture. The stability of MAD in presence of signal noise and abrupt changes in spatial variability is well suited for the analysis of high-resolution digital terrain models. Moreover, the implementation of MAD by means of a pixel-centered perspective based on local kernels, with some analogies to the local binary pattern approach (Lucieer and Stein, 2005; Ojala et al., 2002), permits to create custom roughness indices capable to outline different aspects of surface roughness (Grohmann et al., 2011; Smith, 2015). In the proposed poster, some potentialities of the new indices in the context of geomorphometry and landscape analysis will be presented. At same time, challenges and future developments related to the proposed indices will be outlined. Atkinson, P.M., Lewis, P., 2000. Geostatistical classification for remote sensing: an introduction. Computers & Geosciences 26, 361-371. Grohmann, C.H., Smith, M.J., Riccomini, C., 2011. Multiscale Analysis of Topographic Surface Roughness in the Midland Valley, Scotland. IEEE Transactions on Geoscience and Remote Sensing 49, 1220-1213. Herzfeld, U.C., Higginson, C.A., 1996. Automated geostatistical seafloor classification - Principles, parameters, feature vectors, and discrimination criteria. Computers and Geosciences, 22 (1), pp. 35-52. Lucieer, A., Stein, A., 2005. Texture-based landform segmentation of LiDAR imagery
Neurodynamics-Based Robust Pole Assignment for High-Order Descriptor Systems.
Le, Xinyi; Wang, Jun
2015-11-01
In this paper, a neurodynamic optimization approach is proposed for synthesizing high-order descriptor linear systems with state feedback control via robust pole assignment. With a new robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. A neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high-order singular systems with guaranteed optimality and exact pole assignment. Two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach. PMID:26357408