Control and estimation of piecewise affine systems
Xu, Jun
2014-01-01
As a powerful tool to study nonlinear systems and hybrid systems, piecewise affine (PWA) systems have been widely applied to mechanical systems. Control and Estimation of Piecewise Affine Systems presents several research findings relating to the control and estimation of PWA systems in one unified view. Chapters in this title discuss stability results of PWA systems, using piecewise quadratic Lyapunov functions and piecewise homogeneous polynomial Lyapunov functions. Explicit necessary and sufficient conditions for the controllability and reachability of a class of PWA systems are
Non-Zenoness of piecewise affine dynamical systems and affine complementarity systems with inputs
Institute of Scientific and Technical Information of China (English)
Le Quang THUAN
2014-01-01
In the context of continuous piecewise affine dynamical systems and affine complementarity systems with inputs, we study the existence of Zeno behavior, i.e., infinite number of mode transitions in a finite-length time interval, in this paper. The main result reveals that continuous piecewise affine dynamical systems with piecewise real-analytic inputs do not exhibit Zeno behavior. Applied the achieved result to affine complementarity systems with inputs, we also obtained a similar conclusion. A direct benefit of the main result is that one can apply smooth ordinary differential equations theory in a local manner for the analysis of continuous piecewise affine dynamical systems with inputs.
Combinatorial Vector Fields for Piecewise Affine Control Systems
DEFF Research Database (Denmark)
Wisniewski, Rafal; Larsen, Jesper Abildgaard
2008-01-01
This paper is intended to be a continuation of Habets and van Schuppen (2004) and Habets, Collins and van Schuppen (2006), which address the control problem for piecewise-affine systems on an arbitrary polytope or a family of these. Our work deals with the underlying combinatorics of the underlyi...
Feedback control design for discrete-time piecewise affine systems
Institute of Scientific and Technical Information of China (English)
XU Jun; XIE Li-hua
2007-01-01
This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine (PWA) systems. The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods. We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality (BMI) problem. Then, two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI. Several simulation examples are given to demonstrate the advantages of the proposed design.
Construction of a Class of Four-Dimensional Piecewise Affine Systems with Homoclinic Orbits
Wu, Tiantian; Yang, Xiao-Song
2016-06-01
Based on mathematical analysis, this paper provides a methodology to ensure the existence of homoclinic orbits in a class of four-dimensional piecewise affine systems. In addition, an example is provided to illustrate the effectiveness of the method.
Model predictive control for Max-Plus-Linear and piecewise affine systems
Necoara, I.
2006-01-01
This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event
Model predictive control for Max-Plus-Linear and piecewise affine systems
Necoara, I.
2006-01-01
This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event s
A Piecewise Affine Hybrid Systems Approach to Fault Tolerant Satellite Formation Control
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran; Larsen, Jesper Abildgaard; Bak, Thomas
2008-01-01
In this paper a procedure for modelling satellite formations including failure dynamics as a piecewise-affine hybrid system is shown. The formulation enables recently developed methods and tools for control and analysis of piecewise-affine systems to be applied leading to synthesis of fault...... tolerant controllers and analysis of the system behaviour given possible faults. The method is illustrated using a simple example involving two satellites trying to reach a specific formation despite of actuator faults occurring....
A Piecewise Affine Hybrid Systems Approach to Fault Tolerant Satellite Formation Control
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran; Larsen, Jesper Abildgaard; Bak, Thomas
2008-01-01
In this paper a procedure for modelling satellite formations including failure dynamics as a piecewise-affine hybrid system is shown. The formulation enables recently developed methods and tools for control and analysis of piecewise-affine systems to be applied leading to synthesis of fault...... tolerant controllers and analysis of the system behaviour given possible faults. The method is illustrated using a simple example involving two satellites trying to reach a specific formation despite of actuator faults occurring....
Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas
2012-01-01
In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition...... for the exis- tence of a passive fault-tolerant controller is derived and formulated as the feasibility of a set of linear matrix inequalities (LMIs). The upper bound on the performance cost can be minimized using a convex optimization problem with LMI constraints which can be solved efficiently. The approach...
Automated Controller Synthesis for non-Deterministic Piecewise-Affine Hybrid Systems
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran
a computational tree logic formula and refining the resulting solution to a catalogue of piecewise-affine controllers. The method has been implemented as aMatlab toolbox, PAHSCTRL , using linear matrix inequality feasibility computations for finding the discrete abstraction, UppAal Tiga for solving the discrete...... formations. This thesis uses a hybrid systems model of a satellite formation with possible actuator faults as a motivating example for developing an automated control synthesis method for non-deterministic piecewise-affine hybrid systems (PAHS). The method does not only open an avenue for further research...... in fault tolerant satellite formation control, but can be used to synthesise controllers for a wide range of systems where external events can alter the system dynamics. The synthesis method relies on abstracting the hybrid system into a discrete game, finding a winning strategy for the game meeting...
Passive Fault Tolerant Control of Piecewise Affine Systems Based on H Infinity Synthesis
DEFF Research Database (Denmark)
Gholami, Mehdi; Cocquempot, vincent; Schiøler, Henrik
2011-01-01
In this paper we design a passive fault tolerant controller against actuator faults for discretetime piecewise affine (PWA) systems. By using dissipativity theory and H analysis, fault tolerant state feedback controller design is expressed as a set of Linear Matrix Inequalities (LMIs). In the cur......). In the current paper, the PWA system switches not only due to the state but also due to the control input. The method is applied on a large scale livestock ventilation model....
Set-membership state estimation for discrete time piecewise affine systems using zonotopes
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Stoustrup, Jakob
2013-01-01
This paper presents a method for guaranteed state estimation of discrete time piecewise affine systems with unknown but bounded noise and disturbance. Using zonotopic set representations, the proposed method computes the set of states that are consistent with the model, observation, and bounds...... on the noise and disturbance such that the real state of the system is guaranteed to lie in this set. Because in piecewise affine systems, the state space is partitioned into a number of polyhedral sets, at each iteration the intersection of the zonotopes containing a set-valued estimation of the states...... with each of the polyhedral partitions must be computed. We use an analytic method to compute the intersection as a zonotope and minimize the size of the intersection. A numerical example is provided to illuminate the algorithm....
A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains
Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto
2016-05-01
This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.
Reconfigurability of Piecewise Affine Systems Against Actuator Faults
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Gholami, Mehdi; Bak, Thomas
2011-01-01
In this paper, we consider the problem of recongurability of peicewise ane (PWA) systems. Actuator faults are considered. A system subject to a fault is considered as recongurable if it can be stabilized by a state feedback controller and the optimal cost of the performance of the systems...
Wu, Tiantian; Yang, Xiao-Song
2016-05-01
Based on mathematical analysis, this paper provides a methodology to ensure the existence of heteroclinic cycles in a class of four-dimensional piecewise affine systems. In addition, examples are provided to illustrate the effectiveness of the method.
Data-based identification and control of nonlinear systems via piecewise affine approximation.
Lai, Chow Yin; Xiang, Cheng; Lee, Tong Heng
2011-12-01
The piecewise affine (PWA) model represents an attractive model structure for approximating nonlinear systems. In this paper, a procedure for obtaining the PWA autoregressive exogenous (ARX) (autoregressive systems with exogenous inputs) models of nonlinear systems is proposed. Two key parameters defining a PWARX model, namely, the parameters of locally affine subsystems and the partition of the regressor space, are estimated, the former through a least-squares-based identification method using multiple models, and the latter using standard procedures such as neural network classifier or support vector machine classifier. Having obtained the PWARX model of the nonlinear system, a controller is then derived to control the system for reference tracking. Both simulation and experimental studies show that the proposed algorithm can indeed provide accurate PWA approximation of nonlinear systems, and the designed controller provides good tracking performance.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In t...
DEFF Research Database (Denmark)
Gholami, M.; Cocquempot, V.; Schiøler, H.
2014-01-01
An active fault tolerant control (AFTC) method is proposed for discrete-time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable...... the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large-scale live-stock ventilation model.......An active fault tolerant control (AFTC) method is proposed for discrete-time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable...... performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault-free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive...
Automated Controller Synthesis for non-Deterministic Piecewise-Affine Hybrid Systems
DEFF Research Database (Denmark)
Grunnet, Jacob Deleuran
formations. This thesis uses a hybrid systems model of a satellite formation with possible actuator faults as a motivating example for developing an automated control synthesis method for non-deterministic piecewise-affine hybrid systems (PAHS). The method does not only open an avenue for further research......To further advance space based science the need for ever more precise measurement techniques increases. One of the most promising new ideas are satellite formations where accurate spatial control of multiple spacecraft can be used to create very large virtual apertures or very sensitive...... interferometric measurements. Control of satellite formations presents a whole new set of challenges for spacecraft control systems requiring advances in actuation, sensing, communication, and control algorithms. Specifically having the control system duplicated onto multiple satellites increases the possibility...
Le Quang, Thuan; Camlibel, M. K.
2014-01-01
In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in t
An improved LMI-based approach for stability of piecewise affine time-delay systems with uncertainty
Duan, Shiming; Ni, Jun; Galip Ulsoy, A.
2012-09-01
The stability problem for uncertain piecewise affine (PWA) time-delay systems is investigated in this article. It is assumed that there exists a known constant time delay in the system and the uncertainly is norm-bounded. Sufficient conditions for the stability of nominal systems and the stability of systems subject to uncertainty are derived using the Lyapunov-Krasovskii functional with a triple integration term. This approach handles switching based on the delayed states (in addition to the states) for a PWA time-delay system, considers structured as well as unstructured uncertainty and reduces the conservativeness of previous approaches. The effectiveness of the proposed approach is demonstrated by comparing with the existing methods through numerical examples.
Directory of Open Access Journals (Sweden)
Zhenhua Zhou
2015-01-01
Full Text Available This paper is concerned with the problem of designing robust H-infinity output feedback controller and resilient filtering for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the H-infinity stabilization condition is established and the resilient H-infinity filtering error dynamic system is investigated, and, meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the input saturation disturbance tolerance condition is proposed; then, the resilient H-infinity filter is designed in some restricted region. It is shown that the controller gains and filter design parameters can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile, by using the corresponding optimization methods, the domain of attraction and the disturbance tolerance level is maximized, and the H-infinity performance γ is minimized. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Piecewise affine models of chaotic attractors: The Rössler and Lorenz systems
Amaral, Gleison F. V.; Letellier, Christophe; Aguirre, Luis Antonio
2006-03-01
This paper proposes a procedure by which it is possible to synthesize Rössler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.
Letellier, Christophe; Amaral, Gleison F. V.; Aguirre, Luis A.
2007-06-01
The characterization of chaotic attractors has been a widely addressed problem and there are now many different techniques to define their nature in a rather accurate way, at least in the case of a three-dimensional system. Nevertheless, the link between the structure of the ordinary differential equations and the topology of their solutions is still missing and only a few necessary conditions on the algebraic structure are known today. By using a feedback circuit analysis, it is shown that it is possible to identify the relevant terms of the equations, that is, the terms that really contribute to the structure of the phase portrait. Such analysis also provides some guidelines for constructing piecewise affine models. Moreover, equivalence classes can be defined on the basis of the active feedback circuits involved.
Hirata, Yoshito; Aihara, Kazuyuki
2012-06-01
We introduce a low-dimensional description for a high-dimensional system, which is a piecewise affine model whose state space is divided by permutations. We show that the proposed model tends to predict wind speeds and photovoltaic outputs for the time scales from seconds to 100 s better than by global affine models. In addition, computations using the piecewise affine model are much faster than those of usual nonlinear models such as radial basis function models.
Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model
Institute of Scientific and Technical Information of China (English)
ZHANG Tong; ZHUANG Zhuo
2007-01-01
Iterated function system (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a "mapping partial derivative", and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rn. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.
Quantization of a class of piecewise affine transformations on the torus
De Bièvre, S; De Bievre, S; Giachetti, R
1995-01-01
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of ``chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.
基于仿射混杂系统控制设计的机器人导航控制%Robot Navigation Based on Control Synthesis of Piecewise Affine Hybrid Systems
Institute of Scientific and Technical Information of China (English)
王慧芳; 陈阳舟
2008-01-01
Control synthesis and reachability analysis of the piecewise affine hybrid systems on simplices were applied for safely steering a robot from a given position to a final position with consideration of optimality. Based on the triangulation of the state space of a robot, a dual graph was constructed following the target attractive principle, and then a path planning algorithm was presented to find a sequence of adjacent triangles that were traversed by the shortest path. According to the characteristics of affine systems on simplices, a motion planning algorithm was proposed to determine the translational and rotational velocities for a robot. The simulation results demonstrate the effectiveness of the algorithms.%根据单纯形仿射混杂系统的可达性分析设计控制律,使机器人在平面任意两点间运行,保证其安全性并考虑其最优性.对机器人的状态空间进行三角划分,根据目标吸引原理来建立其对偶图,针对对偶图提出路径规划算法得到最短路径穿越的三角形序列.然后根据仿射系统在单纯形中的性质,提出运动规划算法,得到机器人的角速度和线速度,控制机器人穿越给定的三角形序列到达目标点.仿真结果表明了方法的有效性.
H∞ controller synthesis of piecewise discrete time linear systems
Institute of Scientific and Technical Information of China (English)
Gang FENG
2003-01-01
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomance and the controller can be obtained by solvng a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapnnov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
Abou-Jaoudé, Wassim; Chaves, Madalena; Gouzé, Jean-Luc
2014-12-01
A class of piecewise affine differential (PWA) models, initially proposed by Glass and Kauffman (in J Theor Biol 39:103-129, 1973), has been widely used for the modelling and the analysis of biological switch-like systems, such as genetic or neural networks. Its mathematical tractability facilitates the qualitative analysis of dynamical behaviors, in particular periodic phenomena which are of prime importance in biology. Notably, a discrete qualitative description of the dynamics, called the transition graph, can be directly associated to this class of PWA systems. Here we present a study of periodic behaviours (i.e. limit cycles) in a class of two-dimensional piecewise affine biological models. Using concavity and continuity properties of Poincaré maps, we derive structural principles linking the topology of the transition graph to the existence, number and stability of limit cycles. These results notably extend previous works on the investigation of structural principles to the case of unequal and regulated decay rates for the 2-dimensional case. Some numerical examples corresponding to minimal models of biological oscillators are treated to illustrate the use of these structural principles.
Dynamics of delayed piecewise linear systems
Directory of Open Access Journals (Sweden)
Laszlo E. Kollar
2003-02-01
Full Text Available In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid and the belt (elastic introduces a nonlinearity known as ``backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results.
Output feedback controller design for uncertain piecewise linear systems
Institute of Scientific and Technical Information of China (English)
Jianxiong ZHANG; Wansheng TANG
2007-01-01
This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.
Harnessing piecewise-linear systems to construct dynamic logic architecture.
Peng, Haipeng; Yang, Yixian; Li, Lixiang; Luo, Hong
2008-09-01
This paper explores piecewise-linear systems to construct dynamic logic architecture. We present three schemes to obtain various basic logic gates, adders, and memory by using piecewise-linear systems. These schemes can switch easily among different operational roles by changing parameters. The proposed schemes are computationally efficient and easy to use. It is convenient for us to study and analyze them with the theory of linear systems.
Existence of homoclinic connections in continuous piecewise linear systems.
Carmona, Victoriano; Fernández-Sánchez, Fernando; García-Medina, Elisabeth; Teruel, Antonio E
2010-03-01
Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system, which can be considered to be a version of the widely studied Michelson system. Although the computations developed in this proof are specific to the system, the techniques can be extended to other piecewise linear systems.
Virtual estimator for piecewise linear systems based on observability analysis.
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés, Luis G; Beltrán, Carlos Daniel García
2013-02-27
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel
2013-01-01
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007
Continuous Approximations of a Class of Piecewise Continuous Systems
Danca, Marius-F.
In this paper, we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piecewise continuous functions. By using techniques from the theory of differential inclusions, the underlying piecewise functions can be locally or globally approximated. The approximation results can be used to model piecewise continuous-time dynamical systems of integer or fractional-order. In this way, by overcoming the lack of numerical methods for differential equations of fractional-order with discontinuous right-hand side, unattainable procedures for systems modeled by this kind of equations, such as chaos control, synchronization, anticontrol and many others, can be easily implemented. Several examples are presented and three comparative applications are studied.
Characterization of well-posedness of piecewise linear systems
Imura, J.-I.; Schaft, van der A.J.
1998-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\\'eodory
Characterization of well-posedness of piecewise linear systems
Imura, Jun-ichi; Schaft, van der Arjan
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Caratheodory. T
Characterization of Well-Posedness of Piecewise-Linear Systems
Imura, Jun-ichi; Schaft, Arjan van der
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carathéodory. T
Limit Cycles and Bifurcation in Piecewise-Analytic Systems: 1. General Theory
Banks, S.P.; Khathur, Saadi. A.
1989-01-01
The existence of limit cycles and periodic doubling bifurcations in piecewise-linear and piecewise-analytic systems is studied. Some theoretical sufficient conditions are obtained directly in terms of the right hand sided of the system.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Directory of Open Access Journals (Sweden)
Ilse Cervantes
2013-02-01
Full Text Available This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system’s outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Feedback linearization of piecewise linear systems
Camlibel, Kanat; Ustoglu, Ilker
2005-01-01
One of the classical problems of nonlinear systems and control theory is feedback linearization. Its obvious motivation is that one can utilize linear control theory if the nonlinear system at hand is linearizable by feedback. This problem is well-understood for the smooth nonlinear systems. In the
On Dynamic Systems with Piecewise Linear Feature
Directory of Open Access Journals (Sweden)
Amalia Ţîrdea
2010-10-01
Full Text Available Impact dynamics is considered to be one of the most important problems which arise in vibrating systems. Such impact oscillator occurs in the motion with amplitude constraining stop. In the past years, this simple model has been found rich phenomena and given benefit for understanding of impact systems. Different types of impacting response, such as periodic and non-periodic oscillations, can be predicted by using bifurcation diagrams. Many mechanical systems in engineering applications represent systems which are driven in some way and which undergo intermittent or a continuous sequence of contacts with limiting motion by constraints. For example, the principles of the operation of vibration hammers, impact dampers, inertial shakers, milling and forming machines etc, are based on the impact action for moving bodies. With other equipment, machines with clearances, heat exchangers, steam generator tubes, fuel rods in nuclear power plants, rolling railway wheel sets, piping systems, gear transmissions and so on, impacts also occur, but they are undesirable as they bring about failures, strains, and increased noise levels.
Hidden Degeneracies in Piecewise Smooth Dynamical Systems
Jeffrey, Mike R.
When a flow suffers a discontinuity in its vector field at some switching surface, the flow can cross through or slide along the surface. Sliding along the switching surface can be understood as the flow along an invariant manifold inside a switching layer. It turns out that the usual method for finding sliding modes — the Filippov convex combination or Utkin equivalent control — results in a degeneracy in the switching layer whenever the flow is tangent to the switching surface from both sides. We derive the general result and analyze the simplest case here, where the flow curves parabolically on either side of the switching surface (the so-called fold-fold or two-fold singularities). The result is a set of zeros of the fast switching flow inside the layer, which is structurally unstable to perturbation by terms nonlinear in the switching parameter, terms such as (signx)2 [where the superscript does mean “squared”]. We provide structurally stable forms, and show that in this form the layer system is equivalent to a generic singularity of a two timescale system. Finally we show that the same degeneracy arises when a discontinuity is smoothed using standard regularization methods.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border...
Oliveri, Alberto; Masi, Alessandro; Storace, Marco
2015-01-01
In this paper a piecewise affine virtual sensor is used for the estimation of the motor-side current of hybrid stepper motors, which actuate the LHC (Large Hadron Collider) collimators at CERN. The estimation is performed starting from measurements of the current in the driver, which is connected to the motor by a long cable (up to 720 m). The measured current is therefore affected by noise and ringing phenomena. The proposed method does not require a model of the cable, since it is only based on measured data and can be used with cables of different length. A circuit architecture suitable for FPGA implementation has been designed and the effects of fixed point representation of data are analyzed.
Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays
Institute of Scientific and Technical Information of China (English)
Ou Ou; Hong-Bin Zhang; Jue-Bang Yu
2009-01-01
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
Piecewise Sliding Mode Decoupling Fault Tolerant Control System
Directory of Open Access Journals (Sweden)
Rafi Youssef
2010-01-01
Full Text Available Problem statement: Proposed method in the present study could deal with fault tolerant control system by using the so called decentralized control theory with decoupling fashion sliding mode control, dealing with subsystems instead of whole system and to the knowledge of the author there is no known computational algorithm for decentralized case, Approach: In this study we present a decoupling strategy based on the selection of sliding surface, which should be in piecewise sliding surface partition to apply the PwLTool which have as purpose in our case to delimit regions where sliding mode occur, after that as Results: We get a simple linearized model selected in those regions which could depict the complex system, Conclusion: With the 3 water tank level system as example we implement this new design scenario and since we are interested in networked control system we believe that this kind of controller implementation will not be affected by network delays.
Model Based Adaptive Piecewise Linear Controller for Complicated Control Systems
Directory of Open Access Journals (Sweden)
Tain-Sou Tsay
2014-01-01
Full Text Available A model based adaptive piecewise linear control scheme for industry processes with specifications on peak overshoots and rise times is proposed. It is a gain stabilized control technique. Large gain is used for large tracking error to get fast response. Small gain is used between large and small tracking error for good performance. Large gain is used again for small tracking error to cope with large disturbance. Parameters of the three-segment piecewise linear controller are found by an automatic regulating time series which is function of output characteristics of the plant and reference model. The time series will be converged to steady values after the time response of the considered system matching that of the reference model. The proposed control scheme is applied to four numerical examples which have been compensated by PID controllers. Parameters of PID controllers are found by optimization method. It gives an almost command independent response and gives significant improvements for response time and performance.
Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
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Hong Shi
2012-01-01
Full Text Available Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.
Bifurcation in a Class of Planar Piecewise Smo oth Systems with 3-parameters
Institute of Scientific and Technical Information of China (English)
Liu Yuan-yuan; Chai Zhen-hua; Ma Fu-ming(Communicated)
2014-01-01
This paper is concerned with the bifurcation properties on the line of discontinuity of planar piecewise smooth systems. The existence of equilibria and periodic solutions with sliding motion in a class of planar piecewise smooth systems with 3-parameters is investigated in this paper using the theory of differential inclu-sion and tools of Poincar´e maps.
Analysis and control for a new chaotic system via piecewise linear feedback
Energy Technology Data Exchange (ETDEWEB)
Zhang Jianxiong [Institute of Systems Engineering, Tianjin University, Tianjin 300072 (China)], E-mail: jxzhang@tju.edu.cn; Tang Wansheng [Institute of Systems Engineering, Tianjin University, Tianjin 300072 (China)
2009-11-30
This paper presents a new three-dimensional chaotic system containing two system parameters and a nonlinear term in the form of arc-hyperbolic sine function. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and Lyapunov exponents spectrum. The system proposed is converted to an uncertain piecewise linear system. Then, based on piecewise quadratic Lyapunov function technique, the global control of the new chaotic system with {alpha}-stability constraint via piecewise linear state feedback is studied, where the optimal controller maximizing the decay rate {alpha} can be obtained by solving an optimization problem under bilinear matrix inequalities (BMIs) constraints.
Vision servoing of robot systems using piecewise continuous controllers and observers
Wang, H. P.; Vasseur, C.; Christov, N.; Koncar, V.
2012-11-01
This paper deals with the visual servoing of X-Y robot systems using low cost CCD camera. The proposed approach is based on the theory of piecewise continuous systems which are a particular class of hybrid systems with autonomous switching and controlled impulses. Visual trajectory tracking systems comprising piecewise continuous controllers and observers, are developed. Real-time results are given to illustrate the effectiveness of the proposed visual control system.
REAL PIECEWISE ALGEBRAIC VARIETY
Institute of Scientific and Technical Information of China (English)
Ren-hong Wang; Yi-sheng Lai
2003-01-01
We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in Cμ spline ring.
A Piecewise Hysteresis Model for a Damper of HIS System
Directory of Open Access Journals (Sweden)
Kaidong Tian
2016-01-01
Full Text Available A damper of the hydraulically interconnected suspension (HIS system, as a quarter HIS, is prototyped and its damping characteristic is tested to characterize the damping property. The force-velocity characteristic of the prototype is analyzed based on a set of testing results and accordingly a piecewise hysteresis model for the damper is proposed. The proposed equivalent parametric model consists of two parts: hysteresis model in low speed region and saturation model in high speed region which are used to describe the hysteresis phenomenon in low speed and nonhysteresis phenomenon in high speed, respectively. The parameters of the model are identified based on genetic algorithm by setting the constraints of parameters according to their physical significances and the corresponding testing results. The advantages of the model are highlighted by comparing to the nonhysteresis model and the permanent hysteresis model. The numerical simulation results are compared with the testing results to validate the accuracy and effectiveness of the proposed model. Finally, to further verify the proposed model’s wide applicability under different excitation conditions, its results are compared to the testing results in three-dimensional space. The research in this paper is significant for the dynamic analysis of the HIS vehicle.
Border-Collision Bifurcations and Chaotic Oscillations in a Piecewise-Smooth Dynamical System
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Soukhoterin, E.A.; Mosekilde, Erik
2002-01-01
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject...... of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border......-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling...
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
Senthilkumar, D. V.; Lakshmanan, M.
2004-01-01
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attain...
On the Kamke-Muller conditions, monotonicity and continuity for bi-modal piecewise-smooth systems
O'Donoghue, Yoann; Mason, Oliver; Middleton, Rick
2012-01-01
We show that the Kamke-Muller conditions for bimodal piecewise-smooth systems are equivalent to simple conditions on the vector elds dening the system. As a consequence, we show that for a specic class of such systems, monotonicity is equivalent to continuity. Furthermore, we apply our results to derive a stability condition for piecewise positive linear systems.
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite...... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...
Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Bak, Thomas
2013-01-01
In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the es...
Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilizationof uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robuststability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, show-ing the advanteges of the proposed method.
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then...
Directory of Open Access Journals (Sweden)
S. S. Motsa
2012-01-01
Full Text Available This paper centres on the application of the new piecewise successive linearization method (PSLM in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.
DEFF Research Database (Denmark)
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then......, the estimate of fault is used to compensate for the effect of the fault. Hence, using the estimate of fault, a fault tolerant controller using a piecewise linear static output feedback is designed such that it stabilizes the system and provides an upper bound on the H∞ performance of the faulty system....... Sufficient conditions for the existence of robust fault estimator and fault tolerant controller are derived in terms of linear matrix inequalities. Upper bounds on the H∞ performance can be minimized by solving convex optimization problems with linear matrix inequality constraints. The efficiency...
Identification of Wiener systems with nonlinearity being piecewise-linear function
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Identification of the Wiener system with the nonlinear block being a piecewise-linear function is considered in the paper, generalizing the results given by H. E. Chen to the case of noisy observation. Recursive algorithms are given for estimating all unknown parameters contained in the system, and their strong consistency is proved. The estimation method is similar to that used by H. E. Chen for Hammerstein systems with the same nonlinearity. However, the assumption imposed by H. E. Chen on the availability of an upper bound for the nonsmooth points of the piecewise-linear function has been removed in this paper with the help of designing an additional algorithm for estimating the upper bound.
A New 3-D Piecewise-Linear System for Chaos Generation
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Z. Elhadj
2007-06-01
Full Text Available We propose in this paper a new simple continuous-time piecewise-linear three dimensional system for chaos generation. Nonlinearity in this model is introduced by the characteristic function of the Chua's circuit given in [1]. Simulated results of some chaotic attractors are shown and justified numerically via computing the largest Lyapunov exponent. The possibility and the robustness of the circuitry realization is also given and discussed.
Jump bifurcations in some degenerate planar piecewise linear differential systems with three zones
Euzébio, Rodrigo; Pazim, Rubens; Ponce, Enrique
2016-06-01
We consider continuous piecewise-linear differential systems with three zones where the central one is degenerate, that is, the determinant of its linear part vanishes. By moving one parameter which is associated to the equilibrium position, we detect some new bifurcations exhibiting jump transitions both in the equilibrium location and in the appearance of limit cycles. In particular, we introduce the scabbard bifurcation, characterized by the birth of a limit cycle from a continuum of equilibrium points. Some of the studied bifurcations are detected, after an appropriate choice of parameters, in a piecewise linear Morris-Lecar model for the activity of a single neuron activity, which is usually considered as a reduction of the celebrated Hodgkin-Huxley equations.
Some Applications of Piece-Wise Smooth Dynamical Systems
Janovská, Drahoslava; Hanus, Tomáš; Biák, Martin
2010-09-01
The Filippov systems theory is applied to selected problems from biology and chemical engineering, namely we explore and simulate Bazykin's ecological model, an ideal closed gas-liquid system including its dimensionless formulation. The last investigated system is a CSTR with an outfall and the CSTR with a reactor volume control.
Energy Balance for Random Vibrations of Piecewise-Conservative Systems
IOURTCHENKO, D. V.; DIMENTBERG, M. F.
2001-12-01
Vibrations of systems with instantaneous or stepwise energy losses, e.g., due to impacts with imperfect rebounds, dry friction forces(s) (in which case the losses may be treated as instantaneous ones by appropriate introduction of the response energy) and/or active feedback “bang-bang” control of the systems' response are considered. Response of such (non-linear) systems to a white-noise random excitation is considered for the case where there are no other response energy losses. Thus, a simple linear energy growth with time between “jumps” is observed. Explicit expressions for the expected response energy are derived by direct application of the stochastic differential equations calculus, which contains the expected time interval between two consecutive jumps. The latter may be predicted as a solution to the relevant first-passage problem. Perturbational analysis of the relevant PDE for this problem for a certain vibroimpact system demonstrated the possibility for using the solution to the corresponding free vibration problem as a zero order approximation. The method is applied to an s.d.o.f. system with a feedback inertia control, designed according to a certain previously introduced “generalized reversed swings law”. Extensive Monte-Carlo simulation results are presented for this system as well as for several previously analyzed ones: system with impacts; system with dry friction; system with stiffness control; pendulum with controlled length. The results are compared with those due to the asymptotic stochastic averaging approach. Both methods are shown to provide adequate accuracy far beyond the expected applicability range of the asymptotic approach (which requires both excitation intensity and losses to be small), with direct energy balance being generally superior.
Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension
Institute of Scientific and Technical Information of China (English)
Shun ZHONG; Yu-shu CHEN
2009-01-01
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established.Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory.Transition sets of the system and 40 groups of bifurcation diagrams are obtained.The local bifurcation is found,and shows the overall characteristics of bifurcation.Based on the relationship between parameters and the topological bifurcation solutions,motion characteristics with different parameters are obtained.The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
Topological invariants in forced piecewise-linear FitzHugh-Nagumo-like systems
Energy Technology Data Exchange (ETDEWEB)
Duarte, Jorge E-mail: jduarte@deq.isel.pt; Ramos, J. Sousa. E-mail: sramos@math.ist.utl.pt
2005-03-01
Mathematical models for periodically-forced excitable systems arise in many biological and physiological contexts. Chaotic dynamics of a forced piecewise-linear Fitzhugh-Nagumo-like system under large-amplitude forcing was identified by Othmer and Xie in their work [J. Math. Biol. 39 (1999) 139]. Using kneading theory we study the topological entropy of some chaotic return maps associated with a singular system. Finally we introduce a new topological invariant to distinguish isentropic dynamics and we exhibit numerical results about maps with the same topological entropy, that suggest the existence of a relation between the parameters A and {theta}, when T is fixed.
Reflectable bases for affine reflection systems
Azam, Saeid; Yousofzadeh, Malihe
2011-01-01
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root systems such as extended affine root systems and affine reflection systems. As an alternative, we introduce the notion of a "reflectable base", a minimal subset $\\Pi$ of roots such that the non-isotropic part of the root system can be recovered by reflecting roots of $\\Pi$ relative to the hyperplanes determined by $\\Pi$. We give a full characterization of reflectable bases for tame irreducible affine reflection systems of reduced types, excluding types $E_{6,7,8}$. As a byproduct of our results, we show that if the root system under consideration is locally finite then any reflectable base is an integral base.
Introduction to Piecewise Differentiable Equations
Scholtes, Stefan
2012-01-01
This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the non smooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop
The Melnikov method and subharmonic orbits in a piecewise smooth system
Granados, A; Seara, T M
2012-01-01
In this work we consider a two-dimensional piecewise smooth system, defined in two domains separated by the switching manifold $x=0$. We assume that there exists a piecewise-defined continuous Hamiltonian that is a first integral of the system. We also suppose that the system possesses an invisible fold-fold at the origin and two heteroclinic orbits connecting two hyperbolic critical points on either side of $x=0$. Finally, we assume that the region closed by these heteroclinic connections is fully covered by periodic orbits surrounding the origin, whose periods monotonically increase as they approach the heteroclinic connection. When considering a non-autonomous ($T$-periodic) Hamiltonian perturbation of amplitude $\\varepsilon$, using an impact map, we rigorously prove that, for every $n$ and $m$ relatively prime and $\\varepsilon>0$ small enough, there exists a $nT$-periodic orbit impacting $2m$ times with the switching manifold at every period if a modified subharmonic Melnikov function possesses a simple z...
Farcot, Etienne; Gouzé, Jean-Luc
2009-12-01
This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems. Under an alternative assumption, it is shown that a classical fixed point theorem for monotone, concave operators can be applied to these systems. The required assumption is expressed in geometrical terms as an alignment condition on so-called focal points. As an application, we show the existence and uniqueness of a stable periodic orbit for negative feedback loop systems in dimension 3 or more, and of a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only.
Implementation of nonlinear registration of brain atlas based on piecewise grid system
Liu, Rong; Gu, Lixu; Xu, Jianrong
2007-12-01
In this paper, a multi-step registration method of brain atlas and clinical Magnetic Resonance Imaging (MRI) data based on Thin-Plate Splines (TPS) and Piecewise Grid System (PGS) is presented. The method can help doctors to determine the corresponding anatomical structure between patient image and the brain atlas by piecewise nonlinear registration. Since doctors mostly pay attention to particular Region of Interest (ROI), and a global nonlinear registration is quite time-consuming which is not suitable for real-time clinical application, we propose a novel method to conduct linear registration in global area before nonlinear registration is performed in selected ROI. The homogenous feature points are defined to calculate the transform matrix between patient data and the brain atlas to conclude the mapping function. Finally, we integrate the proposed approach into an application of neurosurgical planning and guidance system which lends great efficiency in both neuro-anatomical education and guiding of neurosurgical operations. The experimental results reveal that the proposed approach can keep an average registration error of 0.25mm in near real-time manner.
Generic fractal structure of finite parts of trajectories of piecewise smooth Hamiltonian systems
Hildebrand, R.; Lokutsievskiy, L. V.; Zelikin, M. I.
2013-03-01
Piecewise smooth Hamiltonian systems with tangent discontinuity are studied. A new phenomenon is discovered, namely, the generic chaotic behavior of finite parts of trajectories. The approach is to consider the evolution of Poisson brackets for smooth parts of the initial Hamiltonian system. It turns out that, near second-order singular points lying on a discontinuity stratum of codimension two, the system of Poisson brackets is reduced to the Hamiltonian system of the Pontryagin Maximum Principle. The corresponding optimization problem is studied and the topological structure of its optimal trajectories is constructed (optimal synthesis). The synthesis contains countably many periodic solutions on the quotient space by the scale group and a Cantor-like set of nonwandering points (NW) having fractal Hausdorff dimension. The dynamics of the system is described by a topological Markov chain. The entropy is evaluated, together with bounds for the Hausdorff and box dimension of (NW).
Mixed-Mode Oscillations in a piecewise linear system with multiple time scale coupling
Fernández-García, S.; Krupa, M.; Clément, F.
2016-10-01
In this work, we analyze a four dimensional slow-fast piecewise linear system with three time scales presenting Mixed-Mode Oscillations. The system possesses an attractive limit cycle along which oscillations of three different amplitudes and frequencies can appear, namely, small oscillations, pulses (medium amplitude) and one surge (largest amplitude). In addition to proving the existence and attractiveness of the limit cycle, we focus our attention on the canard phenomena underlying the changes in the number of small oscillations and pulses. We analyze locally the existence of secondary canards leading to the addition or subtraction of one small oscillation and describe how this change is globally compensated for or not with the addition or subtraction of one pulse.
Yuan, Xiao-Tong; Yan, Shuicheng
2012-04-01
We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008), and support vector machines (Cortes & Vapnik, 1995). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Piecewise Smooth Dynamical Systems Theory: The Case of the Missing Boundary Equilibrium Bifurcations
Hogan, S. J.; Homer, M. E.; Jeffrey, M. R.; Szalai, R.
2016-10-01
We present two codimension-one bifurcations that occur when an equilibrium collides with a discontinuity in a piecewise smooth dynamical system. These simple cases appear to have escaped recent classifications. We present them here to highlight some of the powerful results from Filippov's book Differential Equations with Discontinuous Righthand Sides (Kluwer, 1988). Filippov classified the so-called boundary equilibrium collisions without providing their unfolding. We show the complete unfolding here, for the first time, in the particularly interesting case of a node changing its stability as it collides with a discontinuity. We provide a prototypical model that can be used to generate all codimension-one boundary equilibrium collisions, and summarize the elements of Filippov's work that are important in achieving a full classification.
Zhang, Hongbin; Feng, Gang
2008-10-01
This paper is concerned with stability analysis and H(infinity) decentralized control of discrete-time fuzzy large-scale systems based on piecewise Lyapunov functions. The fuzzy large-scale systems consist of J interconnected discrete-time Takagi-Sugeno (T-S) fuzzy subsystems, and the stability analysis is based on Lyapunov functions that are piecewise quadratic. It is shown that the stability of the discrete-time fuzzy large-scale systems can be established if a piecewise quadratic Lyapunov function can be constructed, and moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. The H(infinity) controllers are also designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions. It is demonstrated via numerical examples that the stability and controller synthesis results based on the piecewise quadratic Lyapunov functions are less conservative than those based on the common quadratic Lyapunov functions.
Directory of Open Access Journals (Sweden)
Dongmei Huang
2017-01-01
Full Text Available The principal resonance of a delayed piecewise-smooth (DPWS system with negative stiffness under narrow-band random excitation is investigated in aspects of multiscale analysis, design methodology of the controller, and response properties. The amplitude-frequency response and steady-state moments together with the corresponding stability conditions of the controlled stochastic system are derived, in which the degradation case is also under consideration. Then, from the perspective of the equivalent damping, the comparisons of the response characteristics of the controlled system to the uncontrolled system, such as the phenomenon of frequency island, are fulfilled. Furthermore, sensitivity of the system response to feedback gain and time delay is studied and interesting dynamic properties are found. Meanwhile, the classification of the steady-state solution is also discussed. To control the maximum amplitude, the feedback parameters are determined by the frequency response together with stability boundaries which must be utilized to exclude the combinations of the unstable parameters. For the case with small noise intensity, mean-square responses present the similar characteristics to what is discussed in the deterministic case.
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
In this paper we use the blowup method of Dumortier and Roussarie, in the formulation due to Krupa and Szmolyan, to study the regularization of singularities of piecewise smooth dynamical systems in R3. Using the regularization method of Sotomayor and Teixeira, we first demonstrate the power of our...... approach by considering the case of a fold line. We quickly extend a main result of Reves and Seara in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when...... the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided...
Directory of Open Access Journals (Sweden)
Veronica Chan
2017-03-01
Full Text Available This paper presents the application of a neural network rule extraction algorithm, called the piece-wise linear artificial neural network or PWL-ANN algorithm, on a carbon capture process system dataset. The objective of the application is to enhance understanding of the intricate relationships among the key process parameters. The algorithm extracts rules in the form of multiple linear regression equations by approximating the sigmoid activation functions of the hidden neurons in an artificial neural network (ANN. The PWL-ANN algorithm overcomes the weaknesses of the statistical regression approach, in which accuracies of the generated predictive models are often not satisfactory, and the opaqueness of the ANN models. The results show that the generated PWL-ANN models have accuracies that are as high as the originally trained ANN models of the four datasets of the carbon capture process system. An analysis of the extracted rules and the magnitude of the coefficients in the equations revealed that the three most significant parameters of the CO2 production rate are the steam flow rate through reboiler, reboiler pressure, and the CO2 concentration in the flue gas.
Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system
Sarrouy, E.; Dessombz, O.; Sinou, J.-J.
2013-02-01
This paper proposes numerical developments based on polynomial chaos (PC) expansions to process stochastic eigenvalue problems efficiently. These developments are applied to the problem of linear stability calculations for a simplified brake system: the stability of a finite element model of a brake is investigated when its friction coefficient or the contact stiffness are modeled as random parameters. Getting rid of the statistical point of view of the PC method but keeping the principle of a polynomial decomposition of eigenvalues and eigenvectors, the stochastic space is decomposed into several elements to realize a low degree piecewise polynomial approximation of these quantities. An approach relying on continuation principles is compared to the classical dichotomy method to build the partition. Moreover, a criterion for testing accuracy of the decomposition over each cell of the partition without requiring evaluation of exact eigenmodes is proposed and implemented. Several random distributions are tested, including a uniform-like law for description of friction coefficient variation. Results are compared to Monte Carlo simulations so as to determine the method accuracy and efficiency. Some general rules relative to the influence of the friction coefficient or the contact stiffness are also inferred from these calculations.
AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS
Institute of Scientific and Technical Information of China (English)
熊勇; 史定华
2001-01-01
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
Normal form and limit cycle bifurcation of piecewise smooth differential systems with a center
Wei, Lijun; Zhang, Xiang
2016-07-01
In this paper we prove that any Σ-center (either nondegenerate or degenerate) of a planar piecewise Cr smooth vector field Z is topologically equivalent to that of Z0: (x ˙ , y ˙) = (- 1 , 2 x) for y ≥ 0, (x ˙ , y ˙) = (1 , 2 x) for y ≤ 0, and that the homeomorphism between Z and Z0 is Cr smoothness when restricted to each side of the switching line except at the center p. We illustrate by examples that there are degenerate Σ-centers whose flows are conjugate to that of Z0, and also there exist nondegenerate Σ-centers whose flows cannot be conjugate to that of Z0. Finally applying the normal form Z0 together with the piecewise smooth equivalence, we study the number of limit cycles which can be bifurcated from the Σ-center of Z.
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic variety is a generalization of the classical algebraic variety. This paper discusses some properties of piecewise algebraic varieties and their coordinate rings based on the knowledge of algebraic geometry.
Directory of Open Access Journals (Sweden)
John Alexander Taborda
2014-04-01
Full Text Available In this paper, we propose a novel strategy for the synthesis and the classification of nonsmooth limit cycles and its bifurcations (named Non-Standard Bifurcations or Discontinuity Induced Bifurcations or DIBs in n-dimensional piecewise-smooth dynamical systems, particularly Continuous PWS and Discontinuous PWS (or Filippov-type PWS systems. The proposed qualitative approach explicitly includes two main aspects: multiple discontinuity boundaries (DBs in the phase space and multiple intersections between DBs (or corner manifolds—CMs. Previous classifications of DIBs of limit cycles have been restricted to generic cases with a single DB or a single CM. We use the definition of piecewise topological equivalence in order to synthesize all possibilities of nonsmooth limit cycles. Families, groups and subgroups of cycles are defined depending on smoothness zones and discontinuity boundaries (DB involved. The synthesized cycles are used to define bifurcation patterns when the system is perturbed with parametric changes. Four families of DIBs of limit cycles are defined depending on the properties of the cycles involved. Well-known and novel bifurcations can be classified using this approach.
Institute of Scientific and Technical Information of China (English)
仪晓斌; 陈莹
2016-01-01
针对目前正面人脸合成算法运算量大或合成图像失真较大的问题，提出一种基于分段仿射变换和泊松融合的正面人脸图像合成算法，将多幅输入图像用分段仿射变换（Piecewise Affine Warp，PAW）映射到正面人脸模板，并根据映射时产生的非刚性形变求得其对应的权重矩阵，进而获取每幅映射图像对应的变形掩膜，依次以这些映射图像为前景图像，以其对应的变形掩膜为泊松掩膜，并以上一次的融合图像为背景图像进行泊松融合，生成一幅平滑自然的正面人脸图像。实验结果表明，相比现有算法，该算法生成的正面人脸图像更加逼近真实正面人脸图像，而且很好地保留了输入人脸的个体信息。%In this paper, a frontal face synthesizing strategy based on Poisson image fusion and Piecewise Affine Warp (PAW)is proposed to solve the problem of large-scale computation cost or transformation distortion in general synthesizing methods. The multiple non-frontal input images are mapped to the frontal face template with PAW. The corresponding weight matrices are calculated according to the magnitude of deformation which can be used to obtain the foreground mask for Poisson fusion. Iterative fusion strategy is designed to synthesize one frontal image from multiple non-frontal images. In each step, the PAW image is used as foreground image. The deformation mask is used as foreground mask, and the fusion image of the previous step is used as background. Experiments show that the synthesized frontal image can per-fectly preserve personal facial details and outperforms others in both subjective and objective evaluations.
Energy Technology Data Exchange (ETDEWEB)
Nanda, J.; Bijwe, P.R.; Kothari, D.P.
1982-10-01
A highly effective piecewise fast developed load flow algorithm has been developed which has a promising potential for practical application. The algorithm requires minimal storage which is almost independent of the systems size thus enabling power flow solutions of large systems being accomplished on available small size computers and microprocessors. The potential of the suggested algorithm for practical applications has been demonstrated by obtaining the load flow results for a few sample systems. It is envisaged that the algorithm would immensely appeal to utility engineers who not only need the minimum memory for solving the problem but also can develop the program with utmost care and confidence since the algorithm i devoid of such programming complexities like sparsity exploitation and optimal ordering inherent with modern load programs.
Energy Technology Data Exchange (ETDEWEB)
Nanda, T.; Bijwe, P.R.; Kothari, D.P.
1982-10-01
This paper presents the development of a highly effective piecewise fast developed load flow algorithm which has a promising potential for practical application. The algorithm requires minimal storage which is almost independent of the sytem size thus enabling power flow solutions of large systems being accomplished on available small size computers and microprocessors. The potential of the suggested algorithm for practical application has been demonstrated by obtaining the load flow results for a few sample systems. It is envisaged that the algorithm would immensely appeal to the utility engineers, since the engineer not only needs the minimum memory for solving the problem but also can develop the program with utmost care and confidence since the algorithm is devoid of such programming complexities like sparsity exploitation and optimal ordering inherent with modern load flow programs. It is believed that the algorithm would find great popularity with the utilities.
Energy Technology Data Exchange (ETDEWEB)
Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr [Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS (France)
2016-10-15
We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product, the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.
Directory of Open Access Journals (Sweden)
X. Gao
2014-01-01
Full Text Available A methodology is presented to study the resonance and stability for a single-degree-of-freedom (SDOF system with a piecewise linear-nonlinear stiffness term (i.e., one piece is linear and the other is weakly nonlinear. Firstly, the exact response of the linear governing equation is obtained, and a modified perturbation method is applied to finding the approximate solution of the weakly nonlinear equation. Then, the primary and 1/2 subharmonic resonances are obtained by imposing continuity conditions and periodicity conditions. Furthermore, Jacobian matrix is derived to investigate the stability of resonance responses. Finally, the results of theoretical study are compared with numerical results, and a good agreement is observed.
Institute of Scientific and Technical Information of China (English)
Lu Kun; Liu Xingzhao
2005-01-01
Recognition and correction of ionospheric phase path contamination is a vital part of the global radar signal processing sequence. A number of model-based correction algorithms have been developed to deal with the radar performance degradation due to the ionospheric distortion and contamination. This paper addresses a novel parametric estimation and compensation method based on High-order Ambiguity Function (HAF) to solve the problem of phase path contamination of HF skywave radar signals. When signal-to-noise ratio and data sequence available satisfy the predefined conditions, the ionospheric phase path contamination may be modeled by a polynomial phase signal (PPS). As a new parametric tool for analyzing the PPS, HAF is introduced to estimate parameters of the polynomial-phase model and reconstruct the correction signal. Using the reconstructed correction signal, compensation can be performed before coherent integration so that the original echo spectrum can be restored. A piecewise scheme is proposed to track rapid variation of the phase contamination based on HAF method, and it can remove the Doppler spread effect caused by the ionos phere nonstationarity. Simulation and experimental results are given to demonstrate the efficiency of the proposed algorithm.
Directory of Open Access Journals (Sweden)
Jong-Yun Yoon
2015-08-01
Full Text Available Torsional systems with gear pairs such as the gearbox of wind turbines or vehicle driveline systems inherently show impact phenomena due to clearance-type nonlinearities when the system experiences sinusoidal excitation. This research investigates the vibro-impact energy of unloaded gears in geared systems using the harmonic balance method (HBM in both the frequency and time domains. To achieve accurate simulations, nonlinear models with piecewise and clearance-type nonlinearities and drag torques are defined and implemented in the HBM. Next, the nonlinear frequency responses are examined by focusing on the resonance areas where the impact phenomena occur, along with variations in key parameters such as clutch stiffness, drag torque, and inertias of the flywheel and the unloaded gear. Finally, the effects of the parameters on the vibro-impacts at a specific excitation frequency are explained using bifurcation diagrams. The results are correlated with prior research by defining the gear rattle criteria with key parameters. This article suggests a method to simulate the impact phenomena in torsional systems using the HBM and successfully assesses vibro-impact energy using bifurcation diagrams.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are,in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A), and show an A∞-structure on E(A). Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos.
ℒ1 adaptive controller for a class of non-affine multi-input multi-output nonlinear systems
Luo, Jie; Cao, Chengyu; Yang, Qinmin
2013-02-01
In this article, an extension of the ℒ1 adaptive control design is introduced for a class of non-affine Multi-Input Multi-Output nonlinear systems with unknown dynamics and unmeasured states. The system dynamics is represented in the normal form with the bounded-input-bounded-output internal dynamics. At first, a stable virtual reference counterpart is constructed. Thereafter, a piece-wise continuous adaptive law is introduced to the actual system along with a low-pass filtered control signal that allows for achieving arbitrarily close tracking of the input and the output signals of the reference system. Rigorous mathematical proof is provided, and the theoretical results are verified with the simulation.
Dynamics of a forced 2 dof piece-wise linear system by consideration of the weight
Directory of Open Access Journals (Sweden)
Dimitrijevic Z.
2012-07-01
Full Text Available Energy pumping phenomenon between a linear system and a non-smooth system by taking into account the weight of the system is studied. The system faces bifurcation when it reaches to its unstable border and then according to external forcing term it can follow lower stable branch or to face strongly modulated response by hysteresis jumps between its stable branches.
Wang, Chunhua; Liu, Xiaoming; Xia, Hu
2017-03-01
In this paper, two kinds of novel ideal active flux-controlled smooth multi-piecewise quadratic nonlinearity memristors with multi-piecewise continuous memductance function are presented. The pinched hysteresis loop characteristics of the two memristor models are verified by building a memristor emulator circuit. Using the two memristor models establish a new memristive multi-scroll Chua's circuit, which can generate 2N-scroll and 2N+1-scroll chaotic attractors without any other ordinary nonlinear function. Furthermore, coexisting multi-scroll chaotic attractors are found in the proposed memristive multi-scroll Chua's circuit. Phase portraits, Lyapunov exponents, bifurcation diagrams, and equilibrium point analysis have been used to research the basic dynamics of the memristive multi-scroll Chua's circuit. The consistency of circuit implementation and numerical simulation verifies the effectiveness of the system design.
Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Hogan, S. J.
2015-01-01
rigorously how singular canards can persist and how the bifurcation of pseudo-equilibria is related to bifurcations of equilibria in the regularized system. We also show that PWS limit cycles are connected to Hopf bifurcations of the regularization. In addition, we show how regularization can create another...... type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...
Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems
Energy Technology Data Exchange (ETDEWEB)
Jeffrey, Mike R., E-mail: mike.jeffrey@bristol.ac.uk [Engineering Mathematics, University of Bristol, Merchant Venturer' s Building, Bristol BS8 1UB (United Kingdom)
2015-10-15
Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event, requires a consideration of so-called hidden terms. These are asymptotically vanishing outside the switch, but can be encoded in the form of nonlinear switching terms. A general expression for the switch can be developed in the form of a series of sigmoid functions. We review the key steps in extending Filippov's method of sliding modes to such systems. We show how even slight nonlinear effects can hugely alter the behaviour of an electronic control circuit, and lead to “hidden” attractors inside the switching surface.
Bifurcations of Periodic Orbits and Invariant Sets in Piecewise Linear Dynamical Systems
Fernández García, Soledad
2012-01-01
This year is the 100th anniversary of the death of Jules Henri Poincaré (Nancy, France, 29 April 1854-Paris, France, 17 July 1912), the founding father of Dynamical Systems theory. In mathematics, he is known as The Last Universalist, since he excelled in all fields of the discipline during his life. As it is well-known, the motivation of part of his work was the Celestial Mechanics [82, 83] and more specifically, the three-body problem. Within these more than 100 years, the Dynamic...
Institute of Scientific and Technical Information of China (English)
PIAO; Daxiong
2001-01-01
., Wampler, E. J., Gaskell, C. M., Emission-line properties of optically and radio-selected complete quasars samples, Astrophys. J., 1989, 338: 630.［13］Yong, P., Sargent, W. L. W. A., High-resolution study of the absorption spectra of three QSOs: evidence for cosmological evolution in the lyman-alpha lines, Astrophys. J., 1982, 252: 10.［14］Lawrence, J., Zucker, J. R., Readhead, A. C. S. et al., Optical spectra of a complete sample of radio sources I. The spectra, Astrophys. J. Suppl., 1996, 107: 541.［15］Junkkarinen, V. T. , Burbidge E. M. , Smith, H. E. , Spectrophyotometry of six broad absoption line QSOs, Astrophys. J. ,1987, 317, 460.［16］Laor, A., Babcall, J. N., Jannuzi, B. T. et al., The ultraviolet emission properties of 13 quasars, Astrophys. J. Suppl.,1995, 99: 1.［17］Baldwin, J. A., Rees, M. J., Longair, M. S. et al., QSOs with narrow emission lines, Astrophys. J., 1988, 327: 103.［18］Shaver, P. A. , Boksenberg A. , Robertson, J. G. , Spectroscopy of the QSO pair Q0028 + 003/Q0029 + 003, Astrophys.J., 1982, 261: L7.［19］Baldwin, J. A., Netzer, H., The emission-line regions of high-redshift QSOs, Astrophys. J., 1978, 226: 1.［20］Wills, B. J., Thompson, K. L., Han, M. et al. , The Hubble space telescope sample of radio-loud quasars: Ultraviolet spectra of the first 31 quasars, Astrophys. J., 1995, 447: 139.［21］Osmer, P. S., Smith, M. G. , Discovery and spectroscopic observations of 27 optical selected quasars with 1.4 ＜ z ＜ 2.5,Astrophys. J., 1977, 213: 607.［22］Storrie-Lombardi, L. J., McMabon, R. G., Irwin, M. J. et al., APM Z ＞ = 4 QSO Survey: Spectra and Intervening Ab-sorption Systems, Astrophys. J., 1996, 468: 121.［23］Young, P. , Sargent, W. L. W. , Boksenberg, A. , Clv absorption in an unbiased sample of 33 QSOs: evidence for the inter-vening galaxy hypothesis, Astrophys. J. Suppl., 1982, 48: 455.［24］Zitelli, V., Mignoli, M., Zarano, B. et al., A spectroscopically complete sample of quasars with Bj ≤ 22
On global asymptotic controllability of planar affine nonlinear systems
Institute of Scientific and Technical Information of China (English)
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
This paper proposes a fault tolerant control method for input-affine nonlinear systems using a nonlinear reconfiguration block (RB). The basic idea of the method is to insert the RB between the plant and the nominal controller such that fault tolerance is achieved without re-designing the nominal...
Pretargeting with the affinity enhancement system for radioimmunotherapy.
Barbet, J; Kraeber-Bodéré, F; Vuillez, J P; Gautherot, E; Rouvier, E; Chatal, J F
1999-06-01
The pretargeting technique referred to as the Affinity Enhancement System (AES) uses bispecific antibodies and radiolabeled bivalent haptens that bind cooperatively to target cells in vivo. Experimental and clinical data demonstrate that AES can deliver large radiation doses to tumor cells with high tumor to normal tissue contrast ratios and long activity residence time in tumors. Preliminary clinical results of radioimmunotherapy of medullary thyroid carcinomas and lung cancers look promising.
Directory of Open Access Journals (Sweden)
El Aroudi A.
2014-01-01
Full Text Available In this paper closed-form conditions for predicting the boundary of period-doubling (PD bifurcation or saddle-node (SN bifurcation in a class of PWM piecewise linear systems are obtained from a time-domain asymptotic approach. Examples of switched system considered in this study are switching dc-dc power electronics converters, temperature control systems and hydraulic valve control systems among others. These conditions are obtained from the steady-state discrete-time model using an asymptotic approach without resorting to frequency-domain Fourier analysis and without using the monodromy or the Jacobian matrix of the discrete-time model as it was recently reported in the existing literature on this topic. The availability of such design-oriented boundary expressions allows to understand the effect of the different parameters of the system upon its stability and its dynamical behavior.
Piecewise flat gravitational waves
Energy Technology Data Exchange (ETDEWEB)
Van de Meent, Maarten, E-mail: M.vandeMeent@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, PO Box 80.195, 3508 TD Utrecht (Netherlands)
2011-04-07
We examine the continuum limit of the piecewise flat locally finite gravity model introduced by 't Hooft. In the linear weak field limit, we find the energy-momentum tensor and metric perturbation of an arbitrary configuration of defects. The energy-momentum turns out to be restricted to satisfy certain conditions. The metric perturbation is mostly fixed by the energy-momentum except for its lightlike modes which reproduce linear gravitational waves, despite no such waves being present at the microscopic level.
Piecewise deterministic Markov processes : an analytic approach
Alkurdi, Taleb Salameh Odeh
2013-01-01
The subject of this thesis, piecewise deterministic Markov processes, an analytic approach, is on the border between analysis and probability theory. Such processes can either be viewed as random perturbations of deterministic dynamical systems in an impulsive fashion, or as a particular kind of
Van der Veken, Frederik F
2014-01-01
Wilson lines, being comparators that render non-local operator products gauge invariant, are extensively used in QCD calculations, especially in small-$x$ calculations, calculations concerning validation of factorisation schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express piecewise path ordered exponentials as path ordered integrals over the separate segments, and apply it on linear segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their colour structure. This framework allows one to easily switch results between different Wilson line structures, which is especially useful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.
Piecewise nonlinear image registration using DCT basis functions
Gan, Lin; Agam, Gady
2015-03-01
The deformation field in nonlinear image registration is usually modeled by a global model. Such models are often faced with the problem that a locally complex deformation cannot be accurately modeled by simply increasing degrees of freedom (DOF). In addition, highly complex models require additional regularization which is usually ineffective when applied globally. Registering locally corresponding regions addresses this problem in a divide and conquer strategy. In this paper we propose a piecewise image registration approach using Discrete Cosine Transform (DCT) basis functions for a nonlinear model. The contributions of this paper are three-folds. First, we develop a multi-level piecewise registration framework that extends the concept of piecewise linear registration and works with any nonlinear deformation model. This framework is then applied to nonlinear DCT registration. Second, we show how adaptive model complexity and regularization could be applied for local piece registration, thus accounting for higher variability. Third, we show how the proposed piecewise DCT can overcome the fundamental problem of a large curvature matrix inversion in global DCT when using high degrees of freedoms. The proposed approach can be viewed as an extension of global DCT registration where the overall model complexity is increased while achieving effective local regularization. Experimental evaluation results provide comparison of the proposed approach to piecewise linear registration using an affine transformation model and a global nonlinear registration using DCT model. Preliminary results show that the proposed approach achieves improved performance.
Vibration performance analysis of piecewise linear system%分段线性系统的振动性能分析
Institute of Scientific and Technical Information of China (English)
吴志强; 雷娜
2015-01-01
The vibration performance of a single degree of freedom system with piecewise linear terms and discontinuous damper was investigated,aiming to clarify the influence of some system parameters on the system's behaviors.A mathematic model of the piecewise linear system was built.By employing an averaging method,the magnitude-frequency characteristic and phase-frequency characteristic functions of the system under primary resonance excitation were obtained.The transition boundary was calculated in accordance with the functions on the basis of the constraint bifurcation theory as well as all the types of the amplitude-frequency responses.The functions were also used for stability analysis.The critical parameter boundary to avoid jumping phenmenon was calculated by qualitatively analyzing the amplitude-frequency responses in the sub-regions of the transition sets.The feasibility of the theoretical study was verified by numerical calculations.In addition,the influences of damping and stiffness coefficients on the global force transmissibility were discussed,and it is found that on the transmissibility curve,the multi-solution problem also appears.%分析了一类含非连续阻尼的单自由度分段线性系统的振动性能，以研究某些参数对系统振动性能的影响。首先建立分段线性系统的数学模型，利用平均法求解，获得系统的幅频特性和相频特性；然后利用约束分岔理论，计算转迁集，得到系统可能的幅频响应类型，并利用幅频响应方程进行稳定性分析；最后计算系统的传递率，讨论了阻尼和刚度系数对传递率的影响，同时发现传递率曲线也产生了多解现象。
An affinity-directed protein missile system for targeted proteolysis
Fulcher, Luke J.; Macartney, Thomas; Bozatzi, Polyxeni; Hornberger, Annika; Rojas-Fernandez, Alejandro
2016-01-01
The von Hippel–Lindau (VHL) protein serves to recruit the hypoxia-inducible factor alpha (HIF1α) protein under normoxia to the CUL2 E3 ubiquitin ligase for its ubiquitylation and degradation through the proteasome. In this report, we modify VHL to engineer an affinity-directed protein missile (AdPROM) system to direct specific endogenous target proteins for proteolysis in mammalian cells. The proteolytic AdPROM construct harbours a cameloid anti-green fluorescence protein (aGFP) nanobody that is fused to VHL for either constitutive or tetracycline-inducible expression. For target proteins, we exploit CRISPR/Cas9 to rapidly generate human kidney HEK293 and U2OS osteosarcoma homozygous knock-in cells harbouring GFP tags at the VPS34 (vacuolar protein sorting 34) and protein associated with SMAD1 (PAWS1, aka FAM83G) loci, respectively. Using these cells, we demonstrate that the expression of the VHL-aGFP AdPROM system results in near-complete degradation of the endogenous GFP-VPS34 and PAWS1-GFP proteins through the proteasome. Additionally, we show that Tet-inducible destruction of GFP-VPS34 results in the degradation of its associated partner, UVRAG, and reduction in levels of cellular phosphatidylinositol 3-phosphate. PMID:27784791
Quantized, piecewise linear filter network
DEFF Research Database (Denmark)
Sørensen, John Aasted
1993-01-01
A quantization based piecewise linear filter network is defined. A method for the training of this network based on local approximation in the input space is devised. The training is carried out by repeatedly alternating between vector quantization of the training set into quantization classes an...
The Bezout Number of Piecewise Algebraic Curves
Institute of Scientific and Technical Information of China (English)
Dian Xuan GONG; Ren Hong WANG
2012-01-01
Based on the discussion of the number of roots of univariate spline and the common zero points of two piecewise algebraic curves,a lower upbound of Bezout number of two piecewise algebraic curves on any given non-obtuse-angled triangulation is found.Bezout number of two piecewise algebraic curves on two different partitions is also discussed in this paper.
Piecewise Linear Model-Based Image Enhancement
Directory of Open Access Journals (Sweden)
Fabrizio Russo
2004-09-01
Full Text Available A novel technique for the sharpening of noisy images is presented. The proposed enhancement system adopts a simple piecewise linear (PWL function in order to sharpen the image edges and to reduce the noise. Such effects can easily be controlled by varying two parameters only. The noise sensitivity of the operator is further decreased by means of an additional filtering step, which resorts to a nonlinear model too. Results of computer simulations show that the proposed sharpening system is simple and effective. The application of the method to contrast enhancement of color images is also discussed.
Directory of Open Access Journals (Sweden)
Ying-Ying Wang
2015-06-01
Full Text Available The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm.
Application Research of a DC Motor System Based on Piecewise Fuzzy Control%分段模糊控制在直流调速系统中的应用研究
Institute of Scientific and Technical Information of China (English)
董子文; 朱张青
2011-01-01
基于常规模糊控制理论,结合双闭环直流调速系统的具体应用环境,设计了一种分段模糊控制器,在调速范围广、调速性能要求高的场合,通过对调速范围分段而采用与调速大小相适应的常规模糊控制规则,从而进一步改善了控制性能.最后,通过Matlab软件将其与常规模糊控制对比仿真,验证了分段模糊控制器的优点.%A piecewise fuzzy controller which based on the common fuzzy theory is designed in this paper. The dual closed loop controller of DC motor systems with this piecewise fuzzy controller can have an improved result in the situation of changing rotate speeds in long range and requiring high control performance by using the feat fuzzy control rule. Finally, this paper uses Matlab to prove the piecewise fuzzy controllers' advantages mentioned above.
Notes on Piecewise-Koszul Algebras
Institute of Scientific and Technical Information of China (English)
Jia Feng L(U); Xiao Lan YU
2011-01-01
The relationships between piecewise-Koszul algebras and other "Koszul-type" algebras are discussed.. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary "period" and piecewise-Koszul algebras with arbitrary "jump-degree".
Subband Affine Projection Algorithm for Acoustic Echo Cancellation System
Directory of Open Access Journals (Sweden)
Choi Hun
2007-01-01
Full Text Available We present a new subband affine projection (SAP algorithm for the adaptive acoustic echo cancellation with long echo path delay. Generally, the acoustic echo canceller suffers from the long echo path and large computational complexity. To solve this problem, the proposed algorithm combines merits of the affine projection (AP algorithm and the subband filtering. Convergence speed of the proposed algorithm is improved by the signal-decorrelating property of the orthogonal subband filtering and the weight updating with the prewhitened input signal of the AP algorithm. Moreover, in the proposed algorithms, as applying the polyphase decomposition, the noble identity, and the critical decimation to subband the adaptive filter, the sufficiently decomposed SAP updates the weights of adaptive subfilters without a matrix inversion. Therefore, computational complexity of the proposed method is considerably reduced. In the SAP, the derived weight updating formula for the subband adaptive filter has a simple form as ever compared with the normalized least-mean-square (NLMS algorithm. The efficiency of the proposed algorithm for the colored signal and speech signal was evaluated experimentally.
Stable piecewise polynomial vector fields
Directory of Open Access Journals (Sweden)
Claudio Pessoa
2012-09-01
Full Text Available Let $N={y>0}$ and $S={y<0}$ be the semi-planes of $mathbb{R}^2$ having as common boundary the line $D={y=0}$. Let $X$ and $Y$ be polynomial vector fields defined in $N$ and $S$, respectively, leading to a discontinuous piecewise polynomial vector field $Z=(X,Y$. This work pursues the stability and the transition analysis of solutions of $Z$ between $N$ and $S$, started by Filippov (1988 and Kozlova (1984 and reformulated by Sotomayor-Teixeira (1995 in terms of the regularization method. This method consists in analyzing a one parameter family of continuous vector fields $Z_{epsilon}$, defined by averaging $X$ and $Y$. This family approaches $Z$ when the parameter goes to zero. The results of Sotomayor-Teixeira and Sotomayor-Machado (2002 providing conditions on $(X,Y$ for the regularized vector fields to be structurally stable on planar compact connected regions are extended to discontinuous piecewise polynomial vector fields on $mathbb{R}^2$. Pertinent genericity results for vector fields satisfying the above stability conditions are also extended to the present case. A procedure for the study of discontinuous piecewise vector fields at infinity through a compactification is proposed here.
Piecewise-adaptive decomposition methods
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n, 29013 Malaga (Spain)], E-mail: jirs@lcc.uma.es
2009-05-30
Piecewise-adaptive decomposition methods are developed for the solution of nonlinear ordinary differential equations. These methods are based on some theorems that show that Adomian's decomposition method is a homotopy perturbation technique and coincides with Taylor's series expansions for autonomous ordinary differential equations. Piecewise-decomposition methods provide series solutions in intervals which are subject to continuity conditions at the end points of each interval, and their adaption is based on the use of either a fixed number of approximants and a variable step size, a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size. It is shown that the appearance of noise terms in the decomposition method is related to both the differential equation and the manner in which the homotopy parameter is introduced, especially for the Lane-Emden equation. It is also shown that, in order to avoid the use of numerical quadrature, there is a simple way of introducing the homotopy parameter in the two first-order ordinary differential equations that correspond to the second-order Thomas-Fermi equation. It is also shown that the piecewise homotopy perturbation methods presented here provide more accurate results than a modified Adomian decomposition technique which makes use of Pade approximants and the homotopy analysis method, for the Thomas-Fermi equation.
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL CONTROLLABILITY OF A CLASS OF AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yimin SUN; Shengwei MEI; Qiang LU
2007-01-01
In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n - 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore,we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure.Finally, we will give three examples to show the applications of our results.
Smoothing a Piecewise-Smooth: An Example from Plankton Population Dynamics
DEFF Research Database (Denmark)
Piltz, Sofia Helena
2016-01-01
In this work we discuss a piecewise-smooth dynamical system inspired by plankton observations and constructed for one predator switching its diet between two different types of prey. We then discuss two smooth formulations of the piecewise-smooth model obtained by using a hyperbolic tangent...
An Analysis of a Transport System Using Non-Affine Transformations
Directory of Open Access Journals (Sweden)
Péter Ficzer
2011-09-01
Full Text Available The authors investigated the transformation possibilities and particularly the usage of non-affine transformations of maps in order to analyse the current status and development possibilities of the Hungarian railway system. In the introduction, the authors overview the theoretical background of map transformations and then present the detailed description of the non-parameter affine transformations and their applicability to the evaluation of railway networks.
Barbero-Liñán, María
2011-01-01
Affine connection control systems are mechanical control systems that model a wide range of real systems such as robotic legs, hovercrafts, planar rigid bodies, rolling pennies, snakeboards and so on. In 1997 the accessibility and a particular notion of controllability was intrinsically described by A. D. Lewis and R. Murray at points of zero velocity. Here, we present a novel generalization of the description of accessibility algebra for those systems at some points with nonzero velocity as long as the affine connection restricts to the distribution given by the symmetric closure. The results are used to describe the accessibility algebra of different mechanical control systems.
Smoothing of Piecewise Linear Paths
Directory of Open Access Journals (Sweden)
Michel Waringo
2008-11-01
Full Text Available We present an anytime-capable fast deterministic greedy algorithm for smoothing piecewise linear paths consisting of connected linear segments. With this method, path points with only a small influence on path geometry (i.e. aligned or nearly aligned points are successively removed. Due to the removal of less important path points, the computational and memory requirements of the paths are reduced and traversing the path is accelerated. Our algorithm can be used in many different applications, e.g. sweeping, path finding, programming-by-demonstration in a virtual environment, or 6D CNC milling. The algorithm handles points with positional and orientational coordinates of arbitrary dimension.
On the dynamic analysis of piecewise-linear networks
Heemels, WPMH; Camlibel, MK; Schumacher, JM
2002-01-01
Piecewise-linear (PL) modeling is often used to approximate the behavior of nonlinear circuits. One of the possible PL modeling methodologies is based on the linear complementarity problem, and this approach has already been used extensively in the circuits and systems community for static networks.
Safety Verification of Piecewise-Deterministic Markov Processes
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer; Bujorianu, Manuela
2016-01-01
We consider the safety problem of piecewise-deterministic Markov processes (PDMP). These are systems that have deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. Specifically, we solve a p-safety problem, where we identify the set...
Adjoint affine fusion and tadpoles
Urichuk, Andrew; Walton, Mark A.
2016-06-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Adjoint affine fusion and tadpoles
Urichuk, Andrew
2016-01-01
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows, and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Adjoint affine fusion and tadpoles
Energy Technology Data Exchange (ETDEWEB)
Urichuk, Andrew, E-mail: andrew.urichuk@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Walton, Mark A., E-mail: walton@uleth.ca [Physics and Astronomy Department, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy)
2016-06-15
We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.
Cubic systems with invariant affine straight lines of total parallel multiplicity seven
Directory of Open Access Journals (Sweden)
Alexandru Suba
2013-12-01
Full Text Available In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 different topological phase portraits in the Poincar\\'e disc associated to this family of cubic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and rescaling of the time variable.
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
DEFF Research Database (Denmark)
Gravesen, Jens
2005-01-01
t is shown that a closed polygon with an odd number of vertices is the median of exactly one piecewise planar cylinder and one piecewise planar Möbius band, intersecting each other orthogonally. A closed polygon with an even number of vertices is in the generic case neither the median of a piecew...
Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
loop is preserved. The RB is realized by a virtual actuator and a reference model. Using notions of incremental and input-to-state stability (ISS), it is shown that ISS of the closed-loop reconfigured system can be achieved by the separate design of the virtual actuator. The proposed method does...... not need any knowledge of the nominal controller and only assumes that the nominal closed-loop system is ISS. The method is demonstrated on a dynamic positioning system for an offshore supply vessel, where the virtual actuator is designed using backstepping....
Verification of Mixed-Signal Systems with Affine Arithmetic Assertions
Directory of Open Access Journals (Sweden)
Carna Radojicic
2013-01-01
Full Text Available Embedded systems include an increasing share of analog/mixed-signal components that are tightly interwoven with functionality of digital HW/SW systems. A challenge for verification is that even small deviations in analog components can lead to significant changes in system properties. In this paper we propose the combination of range-based, semisymbolic simulation with assertion checking. We show that this approach combines advantages, but as well some limitations, of multirun simulations with formal techniques. The efficiency of the proposed method is demonstrated by several examples.
A representation result for rate-independent systems
Klein, Olaf
2016-04-01
The representation formula for hysteresis operators acting on scalar-valued continuous input functions being piecewise monotone that was derived in Brokate and Sprekels (1996) [1] has been extended to results for hysteresis operators acting on vectorial input function, see Klein (2012, 2014) [2-5]. In the current paper, the representation result is extended to rate-independent systems, as considered for example in Mielke (2005) [9]. The input functions are requested to be continuous and to be piecewise strictly monotaffine, i.e. to be piecewise the composition of a strictly monotone increasing function with an affine function, the strictly monotone function being applied first.
A representation result for rate-independent systems
Energy Technology Data Exchange (ETDEWEB)
Klein, Olaf, E-mail: olaf.klein@wias-berlin.de
2016-04-01
The representation formula for hysteresis operators acting on scalar-valued continuous input functions being piecewise monotone that was derived in Brokate and Sprekels (1996) [1] has been extended to results for hysteresis operators acting on vectorial input function, see Klein (2012, 2014) [2–5]. In the current paper, the representation result is extended to rate-independent systems, as considered for example in Mielke (2005) [9]. The input functions are requested to be continuous and to be piecewise strictly monotaffine, i.e. to be piecewise the composition of a strictly monotone increasing function with an affine function, the strictly monotone function being applied first.
Structured Control of Affine Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure to design structured controllers for discrete-time afﬁne linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, ﬁxed order output feedback, simultaneous plant-control design, among others. A parametervarying...
Wang, Weizhi; Huang, Yanyan; Jin, Yulong; Liu, Guoquan; Chen, Yi; Ma, Huimin; Zhao, Rui
2013-05-21
A novel integrated microfluidic system was designed and fabricated for affinity peptide screening with in situ detection. A tetra-layer microfluidic hybrid chip containing two top eccentric diffluent layers, an inter-layer and a bottom screening layer, was developed as the core device of the system. The eccentric diffluent layers were ingeniously invented for the vertical sample delivery from 2 top-inlets into 12 bottom-inlets, which eliminated the use of excessive accessories and complicated pipelines currently used in other systems. By using six pH gradient generators, the magnetic bead-based screening in 36 parallel chambers was simultaneously carried out under 6 different pH conditions from 5.4 to 8.2. This allowed simultaneous screening of 6 compounds and each under 6 different pH conditions. The fabricated chip system was applied to screening of affinity peptides towards β-endorphin antibody. The affinities of the peptide ligands to the antibody were assessed by on-chip confocal detection. The results from the screening study using this system indicated that the pentapeptide with the sequence of YGGFL had the highest affinity towards β-endorphin antibody at pH 7.1, which was further confirmed by the ELISA assay using a 96-well plate format. This microfluidic screening system is automatic, low-cost and reusable for not only peptide screening but also other bioactive compounds screening towards target molecules.
Plant potassium channels are in general dual affinity uptake systems
Directory of Open Access Journals (Sweden)
Ingo Dreyer
2017-02-01
Full Text Available In plant science, we are currently at the dawn of an era, in which mathematical modeling and computational simulations will influence and boost tremendously the gain of new knowledge. However, for many plant scientists mathematical modeling is still rather dubious and is often negligently considered as an oversimplification of the real situation. The goal of this article is to provide a toolbox that allows first steps in the modeling of transport phenomena in plants. The provided framework is applied in the simulation of K+ uptake by cells via K+ channels. Historically, K+ uptake systems are divided into “high affinity” (e.g. H+-coupled K+ transporters and “low affinity” (K+ channels transporters. The computational cell biology studies presented here refute this separation. They show that K+ channels are in general uptake systems with “low” and “high affinity” components. The analyses clarify that constraints in wet-lab experiments usually mask the “high affinity” component. Consequently, the channels were widely assigned a “low affinity” component, only. The results presented here unmask the absurdity of the concept of “high- and low-affinity” transporters.
Institute of Scientific and Technical Information of China (English)
Chunxia Jia; Detong Zhu
2008-01-01
In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables.By employing the affine scaling conjugate gradient path search strategy,we obtain an iterative direction by solving the linearize model.By using the line search technique,we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing.The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions.Furthermore,the numerical results of the proposed algorithm indicate to be effective.
On global controllability of affine nonlinear systems with a triangular-like structure
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability,by using the techniques developed by Sun Yimin and Guo Lei recently.Furthermore,we will give two examples to illustrate its application.
Exposition on affine and elliptic root systems and elliptic Lie algebras
Azam, Saeid; Yousofzadeh, Malihe
2009-01-01
This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the isotropic root multiplicities of those elliptic Lie algebras.
Enhanced piecewise regression based on deterministic annealing
Institute of Scientific and Technical Information of China (English)
ZHANG JiangShe; YANG YuQian; CHEN XiaoWen; ZHOU ChengHu
2008-01-01
Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced piecewise regression algorithm by using "migration of prototypes" is proposed to eliminate "empty cell" in the annealing process. Numerical experiments on several benchmark datasets show that the new algo-rithm can remove redundancy and improve generalization of the piecewise regres-sion model.
Algebraic reconstruction of piecewise-smooth functions from integral measurements
Batenkov, Dmitry; Yomdin, Yosef
2011-01-01
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier coefficients, Radon transform, etc.). Our results concern reconstruction (from the moments or Fourier coefficients) of signals in two specific classes: linear combinations of shifts of a given function, and "piecewise $D$-finite functions" which satisfy on each continuity interval a linear differential equation with polynomial coefficients. In each case the problem is reduced to a solution of a certain type of non-linear algebraic system of equations ("Prony-type system"). We recall some known methods for explicitly solving such systems in one variable, and provide extensions to some multi-dimensional cases. Finally, we investigate the local stability of solving the Prony-type systems.
Piecewise Linear Analysis for Pseudo-elasticity of Shape Memory Alloy (SMA)
Institute of Scientific and Technical Information of China (English)
WANG Xiao-dong; DU Xiao-wei; SUN Guo-jun
2005-01-01
Based on the Brinson constitutive model of SMA, a piecewise linear model for the hysteresis loop of pseudo-elasticity is proposed and applied in the analysis of responses of an SMA-spring-mass system under initial velocity activation. The histories of displacement and velocity of the mass, and the response of stress of SMA are calculated with Brinson's model and the piecewise linear model. The difference of results of the two models is not significant. The calculation with piecewise-linear model needs no iteration and is highly efficient.
Robust control of a class of non-affine nonlinear systems by state and output feedback
Institute of Scientific and Technical Information of China (English)
陈贞丰; 章云
2014-01-01
Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers:the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded (UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.
Piecewise polynomial solutions to linear inverse problems
DEFF Research Database (Denmark)
Hansen, Per Christian; Mosegaard, K.
1996-01-01
We have presented a new algorithm PP-TSVD that computes piecewise polynomial solutions to ill-posed problems, without a priori knowledge about the positions of the break points. In particular, we can compute piecewise constant functions that describe layered models. Such solutions are useful, e.g.......g., in seismological problems, and the algorithm can also be used as a preprocessor for other methods where break points/discontinuities must be incorporated explicitly....
An affine-intuitionistic system of types and effects: confluence and termination
Amadio, Roberto; Madet, Antoine
2010-01-01
We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values such as references or channels are abstracted into a finite set of regions. We introduce a discipline of region usage that entails the confluence (and hence determinacy) of the typable programs. Further, we show that a discipline of region stratification guarantees termination.
EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM
Institute of Scientific and Technical Information of China (English)
XU Zi-xiang; ZHOU De-yun; DENG Zi-chen
2006-01-01
To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control,multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
Directory of Open Access Journals (Sweden)
Haiquan Zhao
2014-01-01
Full Text Available A new improved memorised improved proportionate affine projection algorithm (IMIPAPA is proposed to improve the convergence performance of sparse system identification, which incorporates l(0-norm as a measure of sparseness into a recently proposed MIPAPA algorithm. In addition, a simplified implementation of the IMIPAPA (SIMIPAPA with low-computational burden is presented while maintaining the consistent convergence performance. The simulation results demonstrate that the IMIPAPA and SIMIPAPA algorithms outperform the MIPAPA algorithm for sparse system identification.
Piecewise linear and Boolean models of chemical reaction networks
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-01-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. PMID:25412739
Piecewise linear and Boolean models of chemical reaction networks.
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-12-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [Formula: see text] is large. However, while the case of small constant [Formula: see text] appears in practice, it is not well understood. We provide a mathematical analysis of this limit and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed-form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator.
Real zeros of the zero-dimensional parametric piecewise algebraic variety
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi- algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and suffcient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and suffcient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex.
Institute of Scientific and Technical Information of China (English)
刘保军; 蔡理; 冯朝文
2012-01-01
研究了基于SETMOS构成的、参数未知的类双涡卷混沌系统与结构不同的简单分段线性混沌系统的广义自适应同步方法.通过分析混沌系统的特点和广义同步的定义,基于李雅普诺夫稳定性理论,提出了一种新颖的、结构简单的自适应控制器和参数更新律,来实现不同结构、驱动系统参数未知的混沌系统的广义同步.这种方法还可以应用于不同结构或相同结构的其他同步问题,如自适应广义反同步等,应用范围较广.仿真结果进一步证实了该方法的有效性和可行性.%The generalized synchronization of different structure chaotic systems based on SETMOS with unknown parameters,double-scroll-like chaotic system and simple piecewise linear chaotic system is investigated with respect to an assumed function. By analyzing characteristics of the chaotic systems and definition of the generalized synchronization,based on Lyapnuov stability theorem,novel and simple adaptive controllers and corresponding parameter update law are proposed for generalized synchronization of different chaotic systems with unknown parameters.Further,if the function is changed,the theory can also be applied for other synchronization for different structure chaotic systems,such as adaptive generalized anti-synchronization.Numerical simulation results are provided to show the effectiveness and feasibility of the proposed theory.
Liquid-liquid extraction of enzymes by affinity aqueous two-phase systems
Directory of Open Access Journals (Sweden)
Xu Yan
2003-12-01
Full Text Available From analytical to commercial scale, aqueous two-phase systems have their application in the purification, characterization and study of biomaterials. In order to improve the selectivity of the systems, the biospecific affinity ligands were introduced. In the affinity partitioning aqueous two-phase system, have many enzymes been purified. This review discusses the partitioning of some enzymes in the affinity aqueous two-phase systems in regard to the different ligands, including reactive dyes, metal ions and other ligands. Some integration of aqueous two-phase system with other techniques for more effective purification of enzymes are also presented.Tanto em escala de laboratório como industrial, os sistemas de duas fases aquosas podem ser utilizados para a purificação, caracterização e estudos de biomateriais. Para aumentar a seletividade desse sistema, ligantes de afinidade bioespecíficos podem ser utilizados. No sistema de duas fases aquosas por afinidade, muitas enzimas podem ser purificadas. Neste artigo de revisão, a partição de algumas enzimas por esse tipo de afinidade, utilizando diferentes ligantes como corantes e íons metálicos, são discutidas. Além disso, a integração desse sistema de duas fases aquosas com outras técnicas de purificação estão sendo apresentados, com o objetivo mostrar a melhoria da eficiência do processo.
Characterization of a genetically reconstituted high-affinity system for serotonin transport
Energy Technology Data Exchange (ETDEWEB)
Chang, A.S.S.; Lam, D.M.K. (Baylor College of Medicine, Woodlands, TX (USA) Baylor College of Medicine, Houston, TX (USA)); Frnka, J.V.; Chen, D. (Baylor College of Medicine, Woodlands, TX (USA))
1989-12-01
By transfecting mouse fibroblast L-M cells with human genomic DNA, the authors have established and identified several clonal cell lines that stably express a high-affinity serotonin (5-HT)-uptake mechanism absent in untransfected host cells. One such cell line, L-S1, possesses features of 5-({sup 3}H)HT uptake similar to those previously characterized in the central nervous system and blood platelets: (i) specificity for 5-HT; (ii) antagonism by imipramine, a known inhibitor of high-affinity 5-HT uptake; (iii) both Na{sup +} and temperature dependence; (iv) kinetic saturability; and (v) high affinity for 5-HT. This cell line can be used to compare the relative efficacies of known blockers of 5-HT uptake and thereby offers a rapid and reliable assay system for testing novel inhibitors of this system. Since L-S1 contains stably integrated human DNA in its genome, they postulate that the observed 5-HT-uptake system resulted from the expression of human gene(s) coding for the 5-HT transporter. Thus, cell lines such as L-S1 may represent novel means for screening and developing therapeutic agents specific for neutrotransmitter-uptake systems as well as substrate for the cloning and elucidation of the genes encoding the various neurotransmitter transporters.
Specificity residues determine binding affinity for two-component signal transduction systems.
Willett, Jonathan W; Tiwari, Nitija; Müller, Susanne; Hummels, Katherine R; Houtman, Jon C D; Fuentes, Ernesto J; Kirby, John R
2013-11-05
Two-component systems (TCS) comprise histidine kinases and their cognate response regulators and allow bacteria to sense and respond to a wide variety of signals. Histidine kinases (HKs) phosphorylate and dephosphorylate their cognate response regulators (RRs) in response to stimuli. In general, these reactions appear to be highly specific and require an appropriate association between the HK and RR proteins. The Myxococcus xanthus genome encodes one of the largest repertoires of signaling proteins in bacteria (685 open reading frames [ORFs]), including at least 127 HKs and at least 143 RRs. Of these, 27 are bona fide NtrC-family response regulators, 21 of which are encoded adjacent to their predicted cognate kinases. Using system-wide profiling methods, we determined that the HK-NtrC RR pairs display a kinetic preference during both phosphotransfer and phosphatase functions, thereby defining cognate signaling systems in M. xanthus. Isothermal titration calorimetry measurements indicated that cognate HK-RR pairs interact with dissociation constants (Kd) of approximately 1 µM, while noncognate pairs had no measurable binding. Lastly, a chimera generated between the histidine kinase, CrdS, and HK1190 revealed that residues conferring phosphotransfer and phosphatase specificity dictate binding affinity, thereby establishing discrete protein-protein interactions which prevent cross talk. The data indicate that binding affinity is a critical parameter governing system-wide signaling fidelity for bacterial signal transduction proteins. Using in vitro phosphotransfer and phosphatase profiling assays and isothermal titration calorimetry, we have taken a system-wide approach to demonstrate specificity for a family of two-component signaling proteins in Myxococcus xanthus. Our results demonstrate that previously identified specificity residues dictate binding affinity and that phosphatase specificity follows phosphotransfer specificity for cognate HK-RR pairs. The data
A Piecewise Linear Fitting Technique for Multivalued Two-dimensional Paths
Directory of Open Access Journals (Sweden)
V.M. Jimenez-Fernandez
2013-10-01
Full Text Available This paper presents a curve-fitting technique for multivalued two-dimensional piecewise-linear paths. The proposed method is based on a decomposed formulation of the canonical piecewise linear model description of Chua and Kang. The path is treated as a parametric system of two position equations (x(k, y(k, where k is an artificial parameter to map each variable (x and y into an independent k-domain.
A prototype piecewise-linear dynamic attenuator
Hsieh, Scott S.; Peng, Mark V.; May, Christopher A.; Shunhavanich, Picha; Fleischmann, Dominik; Pelc, Norbert J.
2016-07-01
The piecewise-linear dynamic attenuator has been proposed as a mechanism in CT scanning for personalizing the x-ray illumination on a patient- and application-specific basis. Previous simulations have shown benefits in image quality, scatter, and dose objectives. We report on the first prototype implementation. This prototype is reduced in scale and speed and is integrated into a tabletop CT system with a smaller field of view (25 cm) and longer scan time (42 s) compared to a clinical system. Stainless steel wedges were machined and affixed to linear actuators, which were in turn held secure by a frame built using rapid prototyping technologies. The actuators were computer-controlled, with characteristic noise of about 100 microns. Simulations suggest that in a clinical setting, the impact of actuator noise could lead to artifacts of only 1 HU. Ring artifacts were minimized by careful design of the wedges. A water beam hardening correction was applied and the scan was collimated to reduce scatter. We scanned a 16 cm water cylinder phantom as well as an anthropomorphic pediatric phantom. The artifacts present in reconstructed images are comparable to artifacts normally seen with this tabletop system. Compared to a flat-field reference scan, increased detectability at reduced dose is shown and streaking is reduced. Artifacts are modest in our images and further refinement is possible. Issues of mechanical speed and stability in the challenging clinical CT environment will be addressed in a future design.
Discretization of Fractional Differential Equations by a Piecewise Constant Approximation
Angstmann, Christopher N; McGann, Anna V
2016-01-01
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a dynamical systems analysis. Unfortunately, due to mistakes in the fundamental papers, the difference equations formulated through this process do not capture the dynamics of the fractional order equations. We show that the correct application of this nonstandard piecewise approximation leads to a one parameter family of fractional order differential equations that converges to the original equation as the parameter tends to zero. A closed formed solution exists for each member of this family and leads to the formulation of a difference equation that is of increasing order as time steps are taken. Whilst this does not lead to a simplified dynamical analysis it does lead to a numerical method for solving the fractional order differential equation. The method is shown to be eq...
Optimality of affine control system of several species in competition on a Sequential Batch Reactor
J. C. Rodriguez; Ramirez, Hector; Gajardo, Pedro; Rapaport, Alain
2014-01-01
International audience; In this paper we analyze the optimalty of affine control system of several species in competition for a single substrate on a Sequential Batch Reactors (SBR), with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which we apply different optim...
Piecewise polynomial representations of genomic tracks.
Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz
2012-01-01
Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.
Gravitational backreaction on piecewise linear cosmic string loops
Wachter, Jeremy M.; Olum, Ken D.
2017-01-01
We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational backreaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, backreaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop.
Gravitational back reaction on piecewise linear cosmic string loops
Wachter, Jeremy M
2016-01-01
We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational back reaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, back reaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" loop whose generators lie at right angles evaporates without changing shape, but in all other cases, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, the loop will evaporate before its kinks are significantly changed; if it is far from square, the opening out of the kinks is much faster than evaporation of the loop. In more realistic loops, the curvature of the straight segments due to gravitational back reaction may lead to cusps which did not exist in the original shape with the bending of the string concentrated at kinks.
Adaptive Neuro-fuzzy Controller Design for Non-affine Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
JIA Li; GE Shu-zhi; QIU Ming-sen
2008-01-01
An adaptive neuro-fuzzy control is investigated for a class of noa-affine nonlinear systems.To do so,rigorous description and quantification of the approximation error of the neuro-fuzzy controller are firstly discussed.Applying this result and Lyapunov stability theory,a novel updating algorithm to adapt the weights,centers,and widths of the neuro-fuzzy controller is presented.Consequently,the proposed design method is able to guaranteg the stability of the closed-loop system and the convergence of the tracking error.Simulation results illustrate the effectiveness of the proposed adaptive neuro-fuzzy control scheme.
Triangulations, Subdivisions, and Covers for Control of Affine Hypersurface Systems on Polytopes
Lin, Zhiyun
2009-01-01
This paper studies the problem for an affine hypersurface system to reach a polytopic target set starting from inside a polytope in the state space. We present an exhaustive solution which begins with a characterization of states which can reach the target by open-loop control and concludes with a systematic procedure to synthesize a feedback control. Our emphasis is on methods of subdivision, triangulation, and covers which explicitly account for the capabilities of the control system. In contrast with previous literature, the partition methods are guaranteed to yield a correct feedback synthesis, assuming the problem is solvable by open-loop control.
N(o)ther-type theorem of piecewise algebraic curves
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic curve is a generalization of the classical algebraic curve.This paper describes the improvement of the Nother-type theorem of piecewise algebraic curves on the star region.Moreover,the Nother-type theorem of piecewise algebraic curves on the cross-cut partition is discussed.
Methods for Fault Diagnosability Analysis of a Class of Affine Nonlinear Systems
Directory of Open Access Journals (Sweden)
Xiafu Peng
2015-01-01
Full Text Available The fault diagnosability analysis for a given model, before developing a diagnosis algorithm, can be used to answer questions like “can the fault fi be detected by observed states?” and “can it separate fault fi from fault fj by observed states?” If not, we should redesign the sensor placement. This paper deals with the problem of the evaluation of detectability and separability for the diagnosability analysis of affine nonlinear system. First, we used differential geometry theory to analyze the nonlinear system and proposed new detectability criterion and separability criterion. Second, the related matrix between the faults and outputs of the system and the fault separable matrix are designed for quantitative fault diagnosability calculation and fault separability calculation, respectively. Finally, we illustrate our approach to exemplify how to analyze diagnosability by a certain nonlinear system example, and the experiment results indicate the effectiveness of the fault evaluation methods.
Malinowska, Klara H; Nash, Michael A
2016-06-01
Enzyme-mediated polymerization and polymerization-based signal amplification have emerged as two closely related techniques that are broadly applicable in the nanobio sciences. We review recent progress on polymerization systems mediated by biological molecules (e.g., affinity molecules and enzymes), and highlight newly developed formats and configurations of these systems to perform such tasks as non-instrumented biodetection, synthesis of core-shell nanomaterials, isolation of rare cells, and high-throughput screening. We discuss useful features of biologically mediated polymerization systems, such as multiple mechanisms of amplification (e.g., enzymatic, radical chain propagation), and the ability to localize structures at interfaces and at cell surfaces with microscopic spatial confinement. We close with a perspective on desirable improvements that need to be addressed to adapt these molecular systems to future applications.
Contribution to the ergodic theory of piecewise monotone continuous maps
Faller, Bastien
2008-01-01
This thesis is devoted to the ergodic theory of the piecewise monotone continuous maps of the interval. The coding is a classical approach for these maps. Thanks to the coding, we get a symbolic dynamical system which is almost isomorphic to the initial dynamical system. The principle of the coding is very similar to the one of expansion of real numbers. We first define the coding in a perspective similar to the one of the expansions of real numbers; this perspective was already adopted by Ré...
Genetic evidence of a high-affinity cyanuric acid transport system in Pseudomonas sp. ADP.
Platero, Ana I; Santero, Eduardo; Govantes, Fernando
2014-03-01
The Pseudomonas sp. ADP plasmid pADP-1 encodes the activities involved in the hydrolytic degradation of the s-triazine herbicide atrazine. Here, we explore the presence of a specific transport system for the central intermediate of the atrazine utilization pathway, cyanuric acid, in Pseudomonas sp. ADP. Growth in fed-batch cultures containing limiting cyanuric acid concentrations is consistent with high-affinity transport of this substrate. Acquisition of the ability to grow at low cyanuric acid concentrations upon conjugal transfer of pADP1 to the nondegrading host Pseudomonas putida KT2442 suggests that all activities required for this phenotype are encoded in this plasmid. Co-expression of the pADP1-borne atzDEF and atzTUVW genes, encoding the cyanuric acid utilization pathway and the subunits of an ABC-type solute transport system, in P. putida KT2442 was sufficient to promote growth at cyanuric acid concentrations as low as 50 μM in batch culture. Taken together, our results strongly suggest that the atzTUVW gene products are involved in high-affinity transport of cyanuric acid.
Global behaviour of a predator-prey like model with piecewise constant arguments.
Kartal, Senol; Gurcan, Fuat
2015-01-01
The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle.
Integral Value Transformations: A Class of Affine Discrete Dynamical Systems and an Application
Hassan, Sk S; Nayak, B K; Ghosh, A; Banerjee, J
2011-01-01
In this paper, the notion of Integral Value Transformations (IVTs), a class of Discrete Dynamical Maps has been introduced. Then notion of Affine Discrete Dynamical System (ADDS) in the light of IVTs is defined and some rudimentary mathematical properties of the system are depicted. Collatz Conjecture is one of the most enigmatic problems in 20th Century. The Conjecture was posed by German Mathematician L. Collatz in 1937. There are much advancement in generalizing and defining analogous conjectures, but even to the date, there is no fruitful result for the advancement for the settlement of the conjecture. We have made an effort to make a Collatz type problem in the domain of IVTs and we have been able to solve the problem in 2011 [1]. Here mainly, we have focused and inquired on Collatz-like ADDS. Finally, we have designed the Optimal Distributed and Parallel Environment (ODPE) in the light of ADDS.
Piecewise flat embeddings for hyperspectral image analysis
Hayes, Tyler L.; Meinhold, Renee T.; Hamilton, John F.; Cahill, Nathan D.
2017-05-01
Graph-based dimensionality reduction techniques such as Laplacian Eigenmaps (LE), Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP), and Kernel Principal Components Analysis (KPCA) have been used in a variety of hyperspectral image analysis applications for generating smooth data embeddings. Recently, Piecewise Flat Embeddings (PFE) were introduced in the computer vision community as a technique for generating piecewise constant embeddings that make data clustering / image segmentation a straightforward process. In this paper, we show how PFE arises by modifying LE, yielding a constrained ℓ1-minimization problem that can be solved iteratively. Using publicly available data, we carry out experiments to illustrate the implications of applying PFE to pixel-based hyperspectral image clustering and classification.
Decomposed Implicit Models of Piecewise - Linear Networks
Directory of Open Access Journals (Sweden)
J. Brzobohaty
1992-05-01
Full Text Available The general matrix form of the implicit description of a piecewise-linear (PWL network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced.
MAP estimators for piecewise continuous inversion
Dunlop, M. M.; Stuart, A. M.
2016-10-01
We study the inverse problem of estimating a field u a from data comprising a finite set of nonlinear functionals of u a , subject to additive noise; we denote this observed data by y. Our interest is in the reconstruction of piecewise continuous fields u a in which the discontinuity set is described by a finite number of geometric parameters a. Natural applications include groundwater flow and electrical impedance tomography. We take a Bayesian approach, placing a prior distribution on u a and determining the conditional distribution on u a given the data y. It is then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP estimators can be characterised as minimisers of a generalised Onsager-Machlup functional, in the case where the prior measure is a Gaussian random field. We extend this theory to a more general class of prior distributions which allows for piecewise continuous fields. Specifically, the prior field is assumed to be piecewise Gaussian with random interfaces between the different Gaussians defined by a finite number of parameters. We also make connections with recent work on MAP estimators for linear problems and possibly non-Gaussian priors (Helin and Burger 2015 Inverse Problems 31 085009) which employs the notion of Fomin derivative. In showing applicability of our theory we focus on the groundwater flow and EIT models, though the theory holds more generally. Numerical experiments are implemented for the groundwater flow model, demonstrating the feasibility of determining MAP estimators for these piecewise continuous models, but also that the geometric formulation can lead to multiple nearby (local) MAP estimators. We relate these MAP estimators to the behaviour of output from MCMC samples of the posterior, obtained using a state-of-the-art function space Metropolis-Hastings method.
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-01-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), {\\em directly at the quantum level}. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. The present paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on \\textit{piecewise analytic paths}. The embedding is well-defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed, and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise-linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such hol...
Embedding loop quantum cosmology without piecewise linearity
Engle, Jonathan
2013-04-01
An important goal is to understand better the relation between full loop quantum gravity (LQG) and the simplified, reduced theory known as loop quantum cosmology (LQC), directly at the quantum level. Such a firmer understanding would increase confidence in the reduced theory as a tool for formulating predictions of the full theory, as well as permitting lessons from the reduced theory to guide further development in the full theory. This paper constructs an embedding of the usual state space of LQC into that of standard LQG, that is, LQG based on piecewise analytic paths. The embedding is well defined even prior to solving the diffeomorphism constraint, at no point is a graph fixed and at no point is the piecewise linear category used. This motivates for the first time a definition of operators in LQC corresponding to holonomies along non-piecewise linear paths, without changing the usual kinematics of LQC in any way. The new embedding intertwines all operators corresponding to such holonomies, and all elements in its image satisfy an operator equation which classically implies homogeneity and isotropy. The construction is made possible by a recent result proven by Fleischhack. Communicated by P Singh
Chaotic dynamics and diffusion in a piecewise linear equation.
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-03-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Chaotic dynamics and diffusion in a piecewise linear equation
Energy Technology Data Exchange (ETDEWEB)
Shahrear, Pabel, E-mail: pabelshahrear@yahoo.com [Department of Mathematics, Shah Jalal University of Science and Technology, Sylhet–3114 (Bangladesh); Glass, Leon, E-mail: glass@cnd.mcgill.ca [Department of Physiology, 3655 Promenade Sir William Osler, McGill University, Montreal, Quebec H3G 1Y6 (Canada); Edwards, Rod, E-mail: edwards@uvic.ca [Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, British Columbia V8W 2Y2 (Canada)
2015-03-15
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Regular and chaotic dynamics of a piecewise smooth bouncer
Energy Technology Data Exchange (ETDEWEB)
Langer, Cameron K., E-mail: c.k.langer@tcu.edu; Miller, Bruce N., E-mail: b.miller@tcu.edu [Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129 (United States)
2015-07-15
The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function. We confirm the existence of distinct unbounded orbits (Fermi acceleration) in the elastic model, and investigate regular and chaotic behavior in the inelastic cases. We also examine in the constant restitution model trajectories wherein the particle experiences an infinite number of collisions in a finite time, i.e., the phenomenon of inelastic collapse. We address these so-called “sticking solutions” and their relation to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally, we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. We find the non-smooth nature of the system produces novel bifurcation phenomena not seen in the sinusoidal model, including border-collision bifurcations. The analytical and numerical investigations reveal that although our piecewise linear bouncer is a simplified version of the sinusoidal model, the former not only captures essential features of the latter but also exhibits behavior unique to the discontinuous dynamics.
Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
Faggionato, A.; Gabrielli, D.; Ribezzi Crivellari, M.
2009-10-01
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states ( x, σ)∈Ω×Γ, Ω being a region in ℝ d or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601, 2001; J. Stat. Phys. 107(3-4):635-675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at http://www.arxiv.org/abs/0807.4457, 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti-Cohen-type symmetry relation with involution map different from time-reversal.
Yang, Qinmin; Jagannathan, Sarangapani
2012-04-01
In this paper, reinforcement learning state- and output-feedback-based adaptive critic controller designs are proposed by using the online approximators (OLAs) for a general multi-input and multioutput affine unknown nonlinear discretetime systems in the presence of bounded disturbances. The proposed controller design has two entities, an action network that is designed to produce optimal signal and a critic network that evaluates the performance of the action network. The critic estimates the cost-to-go function which is tuned online using recursive equations derived from heuristic dynamic programming. Here, neural networks (NNs) are used both for the action and critic whereas any OLAs, such as radial basis functions, splines, fuzzy logic, etc., can be utilized. For the output-feedback counterpart, an additional NN is designated as the observer to estimate the unavailable system states, and thus, separation principle is not required. The NN weight tuning laws for the controller schemes are also derived while ensuring uniform ultimate boundedness of the closed-loop system using Lyapunov theory. Finally, the effectiveness of the two controllers is tested in simulation on a pendulum balancing system and a two-link robotic arm system.
Lin, Zhe
This research is motivated by gain scheduling, a technique which has been successfully applied to many nonlinear control problems. In flight controls, the wide variations in the characteristics of the aircraft dynamics throughout the flight envelope make gain scheduling a particularly suitable design strategy. This research consists of two parts: (1) aircraft pitch attitude scheduling scheme designs, and (2) control of a class of linear parametrically varying (LPV) systems. In the first part, the classical gain scheduling technique and the single quadratic Lyapunov function (SQLF) based LPV technique are investigated. In the classical gain scheduling design, the Hinfinity mixed sensitivity GS/T method is chosen for local linear time invariant (LTI) designs to provide robustness to unmodeled dynamics and parametric uncertainties. Following a model reduction procedure that exploits the optimal controller structure, LTI controllers designed at the selected equilibrium points are reduced to second order controllers and realized in a feedback path configuration. Such controllers are shown to retain the superior robust performance at each flight condition, while having a low order that is amenable to scheduling. A gain-scheduling law is developed and simulation results verify that the closed-loop performance specifications are met. In the LPV design, the mixed sensitivity S/KS/T design setup is used. An approximation to the original LPV controller using the linear fractional transformation (LFT) representation is constructed. Our design exhibits potential applications of the LPV technique to commercial aircraft gain scheduling designs. In the second part, we consider a class of discrete, affine, linear parametrically varying (DALPV) systems. For this type of systems, the parameters are assumed to vary in a polytope and the state space matrices are assumed to depend affinely on the varying parameters. A sufficient condition is derived to analyze the stability and the
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2017-03-01
This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
Relative binding affinity of steroids for the corticosterone receptor system in rat hippocampus
De Kloet, E R; Veldhuis, H D; Wagenaars, J L; Bergink, E W
1984-01-01
In cytosol of the hippocampus corticosterone displays highest affinity for the sites that remain available for binding in the presence of excess RU 26988, which is shown to be a "pure" glucocorticoid. A rather high affinity (greater than or equal to 25%) was found for 11 beta-hydroxyprogesterone, 21
Directory of Open Access Journals (Sweden)
D. A. Fetisov
2015-01-01
Full Text Available The controllability conditions are well known if we speak about linear stationary systems: a linear stationary system is controllable if and only if the dimension of the state vector is equal to the rank of the controllability matrix. The concept of the controllability matrix is extended to affine systems, but relations between affine systems controllability and properties of this matrix are more complicated. Various controllability conditions are set for affine systems, but they deal as usual either with systems of some special form or with controllability in some small neighborhood of the concerned point. An affine system is known to be controllable if the system is equivalent to a system of a canonical form, which is defined and regular in the whole space of states. In this case, the system is said to be feedback linearizable in the space of states. However there are examples, which illustrate that a system can be controllable even if it is not feedback linearizable in any open subset in the space of states. In this article we deal with such systems.Affine systems with two-dimensional control are considered. The system in question is assumed to be equivalent to a system of a quasicanonical form with two-dimensional zero dynamics which is defined and regular in the whole space of states. Therefore the controllability of the original system is equivalent to the controllability of the received system of a quasicanonical form. In this article the sufficient condition for an available solution of the terminal problem is proven for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. The condition is valid in the case of an arbitrary time interval and arbitrary initial and finite states of the system. Therefore the controllability condition is set for systems of a quasicanonical form with two-dimensional control and two-dimensional zero dynamics. An example is given which illustrates how the proved
Institute of Scientific and Technical Information of China (English)
卫洪涛; 孔宪仁; 王本利; 张相盟
2011-01-01
基于振型转换的思想,提出了一种求解分段线性边界条件,以及可将其他非线性边界条件转化为分段线性边界条件的连续体振动问题的方法——相对振型转换法(Relative Mode Transfer Method,RMTM),用该法研究了端点带双阻挡悬臂梁的非线性振动.利用相对振型转换法处理了梁的接触振型与非接触振型的振动转换,与Moon于1983年所提方法进行了相互印证,通过时程图与幅频响应图,将两种方法得到的梁端点响应的结果进行对比,证实了相对振型转换法的正确性；并研究了一类边界条件梁的非线性振动,通过梁端点的幅值响应的分岔图,讨论了振型之间的耦合、模态阻尼及端点弹簧刚度对梁端点响应的影响.结果表明,弹簧刚度、阻尼、激励力等不同的参数组合可以导致梁的单周期运动、多周期运动以及混沌运动,得到了上述复杂非线性响应在激励力频域上存在的区域.%A new approach named the relative mode transfer method (RMTM) is developed in this study to solve the vibration problem of continuous systems with piecewise-linear boundary conditions or other nonlinear boundary conditions which can be transformed into piecewise-linear boundary conditions based on the mode transfer principle. The nonlinear vibration of a cantilever with double stops on the tip is investigated. The transfer between the contact states and non-contact states is dealt with using the new method, and its validity is proved by contrasting the results of a case studied both by the new approach and Moon's method which was proposed in 1983. The problem represented by the case is studied through the bifurcation response of the cantilever tip, and a discussion of the effects of the coupling between modes, modal damping, and stop stiffness. It is found that different combinations of the parameters of stop stiffness, damping ratio, driving force, etc., can lead to period-one, period-n and
Optimal Piecewise-Linear Approximation of the Quadratic Chaotic Dynamics
Directory of Open Access Journals (Sweden)
J. Petrzela
2012-04-01
Full Text Available This paper shows the influence of piecewise-linear approximation on the global dynamics associated with autonomous third-order dynamical systems with the quadratic vector fields. The novel method for optimal nonlinear function approximation preserving the system behavior is proposed and experimentally verified. This approach is based on the calculation of the state attractor metric dimension inside a stochastic optimization routine. The approximated systems are compared to the original by means of the numerical integration. Real electronic circuits representing individual dynamical systems are derived using classical as well as integrator-based synthesis and verified by time-domain analysis in Orcad Pspice simulator. The universality of the proposed method is briefly discussed, especially from the viewpoint of the higher-order dynamical systems. Future topics and perspectives are also provided
最小二乘法分段拟合红外测距系统%Least Square Piecewise Fitting Infrared Ranging System
Institute of Scientific and Technical Information of China (English)
朱杰; 何凌霄; 林凡强; 苟乔欣
2014-01-01
In order to improve the accuracy of infrared distance measurement, we use MSP430F149 single chip microcomputer as control core, infrared receiving module as sensor for launch. The distance was measured by measuring the infrared intense of the reflected light which was emitted by infrared transmitting tube. This system will measure the light intensity to convert it into voltage signal,and form a corresponding relationship between the voltage signal and the distance. From the subsection fitting of the least square method,the relationship between the voltage signal and the distance gets for the distance measurement. Our method makes the error of the infrared distance measurement system reache to 1 mm. The system can be used widely to measure distance at close range and for automotive anti-collision system.%为了提高测距的红外测距的精度,提出了以MSP430F149单片机为控制核心,红外线发射接收模块为传感器,通过测量红外发射管发出的红外线反射的光线强度来测量距离。此系统将测量的光线强度转换为电压信号,并测得电压信号和距离的对应关系,最后通过最小二乘法进行分段拟合,得到电压信号和距离的关系式以实现测距。该红外测距系统误差达到1 mm,可以广泛近距离测距和汽车防撞系统中。
Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho
2015-05-01
This paper focuses on a class of reinforcement learning (RL) algorithms, named integral RL (I-RL), that solve continuous-time (CT) nonlinear optimal control problems with input-affine system dynamics. First, we extend the concepts of exploration, integral temporal difference, and invariant admissibility to the target CT nonlinear system that is governed by a control policy plus a probing signal called an exploration. Then, we show input-to-state stability (ISS) and invariant admissibility of the closed-loop systems with the policies generated by integral policy iteration (I-PI) or invariantly admissible PI (IA-PI) method. Based on these, three online I-RL algorithms named explorized I-PI and integral Q -learning I, II are proposed, all of which generate the same convergent sequences as I-PI and IA-PI under the required excitation condition on the exploration. All the proposed methods are partially or completely model free, and can simultaneously explore the state space in a stable manner during the online learning processes. ISS, invariant admissibility, and convergence properties of the proposed methods are also investigated, and related with these, we show the design principles of the exploration for safe learning. Neural-network-based implementation methods for the proposed schemes are also presented in this paper. Finally, several numerical simulations are carried out to verify the effectiveness of the proposed methods.
Piecewise multivariate modelling of sequential metabolic profiling data
Directory of Open Access Journals (Sweden)
Nicholson Jeremy K
2008-02-01
Full Text Available Abstract Background Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints. Results A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted. Conclusion The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA for modelling and analysis of short time-series data.
[Optimizing algorithm design of piecewise linear classifier for spectra].
Lan, Tian-Ge; Fang, Yong-Hua; Xiong, Wei; Kong, Chao; Li, Da-Cheng; Dong, Da-Ming
2008-11-01
Being able to identify pollutant gases quickly and accurately is a basic request of spectroscopic technique for envirment monitoring for spectral classifier. Piecewise linear classifier is simple needs less computational time and approachs nonlinear boundary beautifully. Combining piecewise linear classifier and linear support vector machine which is based on the principle of maximizing margin, an optimizing algorithm for single side piecewise linear classifier was devised. Experimental results indicate that the piecewise linear classifier trained by the optimizing algorithm proposed in this paper can approach nonolinear boundary with fewer super_planes and has higher veracity for classification and recognition.
Gene Structure and Expression of the High-affinity Nitrate Transport System in Rice Roots
Institute of Scientific and Technical Information of China (English)
Chao Cai; Jun-Yi Wang; Yong-Guan Zhu; Qi-Rong Shen; Bin Li; Yi-Ping Tong; Zhen-Sheng Li
2008-01-01
Rice has a preference for uptake of ammonium over nitrate and can use ammonium-N efficiently. Consequently, transporters mediating ammonium uptake have been extensively studied, but nitrate transporters have been largely ignored. Recently,some reports have shown that rice also has high capacity to acquire nitrate from growth medium, so understanding the nitrate transport system in rice roots is very important for improving N use efficiency in rice. The present study identified four putative NRT2 and two putative NAR2 genes that encode components of the high-affinity nitrate transport system (HATS) in the rice (Oryza sativa L. subsp, japonica cv. Nipponbare) genome. OsNRT2.1 and OsNRT2.2 share an identical coding region sequence, and their deduced proteins are closely related to those from monocotyledonous plants. The two NAR2 proteins are closely related to those from mono-cotyledonous plants as well. However, OsNRT2.3 and OsNRT2.4 are more closely related to Arabidopsis NRT2 proteins. Relative quantitative reverse tranecdption-polymerase chain reaction analysis showed that all of the six genes were rapidly upregulated and then downregulated in the roots of N-starved rice plants after they were re-supplied with 0.2 mM nitrate, but the response to nitrate differed among gene members.The results from phylogenetic tree, gene structure and expression analysis implied the divergent roles for the individual members of the rice NRT2 and NAR2 families. High-affinity nitrate influx rates associated with nitrate induction in rice roots were investigated and were found to be regulated by external pH. Compared with the nitrate influx rates at pH 6.5, alkaline pH (pH 8.0) inhibited nitrate Influx, and acidic pH (pH 5.0) enhanced the nitrate influx In I h nitrate induced roots, but did not significantly affect that in 4 to 8 h nitrate induced roots.
Piecewise Silence in Discrete Cosmological Models
Clifton, Timothy; Rosquist, Kjell
2014-01-01
We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon "piecewise silence".
Bayesian regression of piecewise homogeneous Poisson processes
Directory of Open Access Journals (Sweden)
Diego Sevilla
2015-12-01
Full Text Available In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is valuable for detecting breaking points in the count rate of time series for Poisson processes. Received: 2 November 2015, Accepted: 27 November 2015; Edited by: R. Dickman; Reviewed by: M. Hutter, Australian National University, Canberra, Australia.; DOI: http://dx.doi.org/10.4279/PIP.070018 Cite as: D J R Sevilla, Papers in Physics 7, 070018 (2015
Designer protein delivery: From natural to engineered affinity-controlled release systems.
Pakulska, Malgosia M; Miersch, Shane; Shoichet, Molly S
2016-03-18
Exploiting binding affinities between molecules is an established practice in many fields, including biochemical separations, diagnostics, and drug development; however, using these affinities to control biomolecule release is a more recent strategy. Affinity-controlled release takes advantage of the reversible nature of noncovalent interactions between a therapeutic protein and a binding partner to slow the diffusive release of the protein from a vehicle. This process, in contrast to degradation-controlled sustained-release formulations such as poly(lactic-co-glycolic acid) microspheres, is controlled through the strength of the binding interaction, the binding kinetics, and the concentration of binding partners. In the context of affinity-controlled release--and specifically the discovery or design of binding partners--we review advances in in vitro selection and directed evolution of proteins, peptides, and oligonucleotides (aptamers), aided by computational design.
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-22
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-01
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Piecewise power laws in individual learning curves.
Donner, Yoni; Hardy, Joseph L
2015-10-01
The notion that human learning follows a smooth power law (PL) of diminishing gains is well-established in psychology. This characteristic is observed when multiple curves are averaged, potentially masking more complex dynamics underpinning the curves of individual learners. Here, we analyzed 25,280 individual learning curves, each comprising 500 measurements of cognitive performance taken from four cognitive tasks. A piecewise PL (PPL) model explained the individual learning curves significantly better than a single PL, controlling for model complexity. The PPL model allows for multiple PLs connected at different points in the learning process. We also explored the transition dynamics between PL curve component pieces. Performance in later pieces typically surpassed that in earlier pieces, after a brief drop in performance at the transition point. The transition rate was negatively associated with age, even after controlling for overall performance. Our results suggest at least two processes at work in individual learning curves: locally, a gradual, smooth improvement, with diminishing gains within a specific strategy, which is modeled well as a PL; and globally, a discrete sequence of strategy shifts, in which each strategy is better in the long term than the ones preceding it. The piecewise extension of the classic PL of practice has implications for both individual skill acquisition and theories of learning.
Renormalizable two-parameter piecewise isometries.
Lowenstein, J H; Vivaldi, F
2016-06-01
We exhibit two distinct renormalization scenarios for two-parameter piecewise isometries, based on 2π/5 rotations of a rhombus and parameter-dependent translations. Both scenarios rely on the recently established renormalizability of a one-parameter triangle map, which takes place if and only if the parameter belongs to the algebraic number field K=Q(5) associated with the rotation matrix. With two parameters, features emerge which have no counterpart in the single-parameter model. In the first scenario, we show that renormalizability is no longer rigid: whereas one of the two parameters is restricted to K, the second parameter can vary continuously over a real interval without destroying self-similarity. The mechanism involves neighbouring atoms which recombine after traversing distinct return paths. We show that this phenomenon also occurs in the simpler context of Rauzy-Veech renormalization of interval exchange transformations, here regarded as parametric piecewise isometries on a real interval. We explore this analogy in some detail. In the second scenario, which involves two-parameter deformations of a three-parameter rhombus map, we exhibit a weak form of rigidity. The phase space splits into several (non-convex) invariant components, on each of which the renormalization still has a free parameter. However, the foliations of the different components are transversal in parameter space; as a result, simultaneous self-similarity of the component maps requires that both of the original parameters belong to the field K.
Piecewise-Planar Parabolic Reflectarray Antenna
Hodges, Richard; Zawadzki, Mark
2009-01-01
The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.
Energy Technology Data Exchange (ETDEWEB)
Biessen, E.A.L; Horn, A.S.; Robillard, G.T. (Univ. of Groningen (Netherlands))
1990-04-03
This paper describes a procedure for the synthesis and application of a citalopram-derived affinity resin in purifying the 5HT-reuptake system from human blood platelets. A two-step scheme has been developed for partial purification, based on wheat germ agglutinin-lectin (WGA) affinity and citalopram affinity chromatographies. Upon solubilization of the carrier with 1% digitonin, a 50-70-fold increase in specific ({sup 3}H) imipramine binding activity with a 70% recovery could be accomplished through WGA-lectin chromatography. The WGA pool was then subjected to affinity chromatography on citalopram-agarose. At least 90% of the binding capacity adsorbed to the column. Specific elution using 10 {mu}M citalopram resulted in a 22% recovery of binding activity. A 10,000-fold overall purification was obtained by using this two-step procedure. Analysis of the fractions on SDS-PAGE after {sup 125}I labeling revealed specific elution of 78- and 55-kDa proteins concomitant with the appearance of ({sup 3}H) imipramine binding activity. The pharmacological profile of the partially purified reuptake system correlated well with that derived from the crude membrane-bound reuptake system, suggesting a copurification of the 5HT binding activity and ({sup 3}H)imipramine binding activity.
An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm
Directory of Open Access Journals (Sweden)
Yuping Hu
2014-01-01
Full Text Available An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack.
An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm
Hu, Yuping; Wang, Zhijian
2014-01-01
An image encryption algorithm based on improved piecewise linear chaotic map (MPWLCM) model was proposed. The algorithm uses the MPWLCM to permute and diffuse plain image simultaneously. Due to the sensitivity to initial key values, system parameters, and ergodicity in chaotic system, two pseudorandom sequences are designed and used in the processes of permutation and diffusion. The order of processing pixels is not in accordance with the index of pixels, but it is from beginning or end alternately. The cipher feedback was introduced in diffusion process. Test results and security analysis show that not only the scheme can achieve good encryption results but also its key space is large enough to resist against brute attack. PMID:24592159
Ballatori, N; Dutczak, W J
1994-08-05
Driving forces and substrate specificity for transport of reduced glutathione (GSH) across rat liver cell canalicular membrane were examined in vesicles isolated from this plasma membrane domain. In contrast to previous studies indicating a single saturable component of canalicular GSH transport, the present results demonstrate the presence of both high and low affinity components with apparent Km values of 0.24 +/- 0.04 and 17.4 +/- 2.1 mM and Vmax values of 0.09 +/- 0.01 and 2.3 +/- 0.3 nmol.mg-1.20 s-1, respectively. The Km values in two previously published reports are discordant, 0.33 versus 16 mM, but are comparable with the two transport components identified in the present study. To further characterize these GSH transport mechanisms, [3H]GSH uptake by canalicular vesicles was measured at concentrations of 50 microM, where transport is expected to occur largely on the high affinity component, and at 5 mM, where the low affinity system should predominate. Neither component of GSH transport was affected by ATP or a Na+ gradient, but both were stimulated by a valinomycin-induced membrane potential, indicating electrogenic transport pathways. The high affinity component was cis-inhibited by glutathione S-conjugates (1 mM), other gamma-glutamyl compounds (5 mM), and 4,4'-diisothiocyanatostilbene-2,2'-disulfonic acid (0.1 mM), whereas these agents had no effect on the low affinity component at similar inhibitor concentrations. Sulfobromophthalein (BSP, 0.1 mM) inhibited both GSH transport components. However, neither component was affected by taurocholate (0.5 mM) or L-glutamate (10 mM). The inhibition by S-butylglutathione, the GSH analogue ophthalmic acid, and by BSP was competitive in nature, although BSP also produced a slight decrease in Vmax, suggesting a mixed type of inhibition. Ophthalmic acid and some glutathione S-conjugates were also able to trans-stimulate high affinity GSH uptake. These results indicate the presence of at least two ATP
Li, Haiyan; Ge, Jingwen; Guo, Tao; Yang, Shuo; He, Zhonggui; York, Peter; Sun, Lixin; Xu, Xu; Zhang, Jiwen
2013-08-30
It is challenging and extremely difficult to measure the kinetics of supramolecular systems with extensive, weak binding (Kahigh performance affinity chromatography (HPAC) was established to determine the dissociation rate constant of cyclodextrin supramolecular systems. The interactions of β-cyclodextrin with acetaminophen and sertraline were used to exemplify the method. The retention times, variances and the plate heights of the peaks for acetaminophen or sertraline, conventional non-retained substance (H2O) on the β-cyclodextrin bonded column and a control column were determined at four flow rates under linear elution conditions. Then, plate heights for the theoretical non-retained substance were estimated by the modified HPAC method, in consideration of the diffusion and stagnant mobile phase mass transfer. As a result, apparent dissociation rate constants of 1.82 (±0.01)s(-1) and 3.55 (±0.37)s(-1) were estimated for acetaminophen and sertraline respectively at pH 6.8 and 25°C with multiple flow rates. Following subtraction of the non-specific binding with the support, dissociation rate constants were estimated as 1.78 (±0.00) and 1.91 (±0.02)s(-1) for acetaminophen and sertraline, respectively. These results for acetaminophen and sertraline were in good agreement with the magnitude of the rate constants for other drugs determined by capillary electrophoresis reported in the literature and the peak fitting method we performed. The method described in this work is thought to be suitable for other supramolecules, with relatively weak, fast and extensive interactions.
The piecewise constant method in gait design through optimization
Institute of Scientific and Technical Information of China (English)
Yizhen Wei
2014-01-01
The objective of this paper is to introduce the piecewise constant method in gait design of a planar, under actuated, five-link biped robot model and to discuss the advantages and disadvantages. The piecewise constant method transforms the dynamic optimal control problem into a static problem.
Using piecewise sinusoidal basis functions to blanket multiple wire segments
CSIR Research Space (South Africa)
Lysko, AA
2009-06-01
Full Text Available This paper discusses application of the piecewise sinusoidal (PWS) basis function (BF) over a chain of several wire segments, for example as a multiple domain basis function. The usage of PWS BF is compared to results based on the piecewise linear...
Directory of Open Access Journals (Sweden)
André M. Lopes
2008-01-01
Full Text Available In this work, we provide an investigation of the role and strength of affinity interactions on the partitioning of the glucose-6-phosphate dehydrogenase in aqueous two-phase micellar systems. These systems are constituted of micellar surfactant solutions and offer both hydrophobic and hydrophilic environments, providing selectivity to biomolecules. We studied G6PD partitioning in systems composed of the nonionic surfactants, separately, in the presence and absence of affinity ligands. We observed that G6PD partitions to the micelle-poor phase, owing to the strength of excluded-volume interactions in these systems that drive the protein to the micelle-poor phase, where there is more free volume available.
Autocalibrating Tiled Projectors on Piecewise Smooth Vertically Extruded Surfaces.
Sajadi, Behzad; Majumder, Aditi
2011-09-01
In this paper, we present a novel technique to calibrate multiple casually aligned projectors on fiducial-free piecewise smooth vertically extruded surfaces using a single camera. Such surfaces include cylindrical displays and CAVEs, common in immersive virtual reality systems. We impose two priors to the display surface. We assume the surface is a piecewise smooth vertically extruded surface for which the aspect ratio of the rectangle formed by the four corners of the surface is known and the boundary is visible and segmentable. Using these priors, we can estimate the display's 3D geometry and camera extrinsic parameters using a nonlinear optimization technique from a single image without any explicit display to camera correspondences. Using the estimated camera and display properties, the intrinsic and extrinsic parameters of each projector are recovered using a single projected pattern seen by the camera. This in turn is used to register the images on the display from any arbitrary viewpoint making it appropriate for virtual reality systems. The fast convergence and robustness of this method is achieved via a novel dimension reduction technique for camera parameter estimation and a novel deterministic technique for projector property estimation. This simplicity, efficiency, and robustness of our method enable several coveted features for nonplanar projection-based displays. First, it allows fast recalibration in the face of projector, display or camera movements and even change in display shape. Second, this opens up, for the first time, the possibility of allowing multiple projectors to overlap on the corners of the CAVE-a popular immersive VR display system. Finally, this opens up the possibility of easily deploying multiprojector displays on aesthetic novel shapes for edutainment and digital signage applications.
Affine connection form of Regge calculus
Khatsymovsky, V M
2015-01-01
Regge action is represented analogously to how the Palatini action for general relativity (GR) as some functional of the metric and a general connection as independent variables represents the Einstein-Hilbert action. The piecewise flat (or simplicial) spacetime of Regge calculus is equipped with some world coordinates and some piecewise affine metric which is completely defined by the set of edge lengths and the world coordinates of the vertices. The conjugate variables are the general nondegenerate matrices on the 3-simplices which play a role of a general discrete connection. Our previous result on some representation of the Regge calculus action in terms of the local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as independent variables is somewhat modified for the considered case of the general linear group GL(4,R) of the connection matrices. As a result, we have some action invariant w. r. t. arbitrary change of coordinates of the vertices (and related GL(4,R) transformations in...
Affine Maps of the Polarization Vector for Quantum Systems of Arbitrary Dimension
Byrd, Mark S; Ou, Yong-Cheng
2010-01-01
The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density matrix in terms of the polarization vector representation. This has been thoroughly explored for qubits since the components of the polarization vector are measurable quantities (corresponding to expectation values of Hermitian operators) and also because it enables the description of map domains geometrically. Here we extend the OS-affine map correspondence to qudits, briefly discuss general properties of the map, the form for particular important cases, and provide several explicit results for qutrit maps. We use the affine map and a singular-value-like decomposition, to find positivity constraints that provide a symmetry for small polarization vector magnitudes (states which are closer to the maximally mixed state) which is broken as the polarization vector increases in ...
Complete parameterization of piecewise-polynomial interpolation kernels.
Blu, Thierry; Thévenaz, Philippe; Unser, Michael
2003-01-01
Every now and then, a new design of an interpolation kernel appears in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. We propose to ease this burden by providing an explicit formula that can generate every possible piecewise-polynomial kernel given its degree, its support, its regularity, and its order of approximation. This formula contains a set of coefficients that can be chosen freely and do not interfere with the four main design parameters; it is thus easy to tune the design to achieve any additional constraints that the designer may care for.
Affine and quasi-affine frames for rational dilations
DEFF Research Database (Denmark)
Bownik, Marcin; Lemvig, Jakob
2011-01-01
, the corresponding family of quasi-affine systems are frames with uniform frame bounds. We also prove a similar equivalence result between pairs of dual affine frames and dual quasi-affine frames. Finally, we uncover some fundamental differences between the integer and rational settings by exhibiting an example......In this paper we extend the investigation of quasi-affine systems, which were originally introduced by Ron and Shen [J. Funct. Anal. 148 (1997), 408-447] for integer, expansive dilations, to the class of rational, expansive dilations. We show that an affine system is a frame if, and only if...
Piecewise deterministic processes in biological models
Rudnicki, Ryszard
2017-01-01
This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models. Further, it presents examples of biological phenomena, such as gene activity and population growth, where different types of PDMPs appear: continuous time Markov chains, deterministic processes with jumps, processes with switching dynamics, and point processes. Subsequent chapters present the necessary tools from the theory of stochastic processes and semigroups of linear operators, as well as theoretical results concerning the long-time behaviour of stochastic semigroups induced by PDMPs and their applications to biological models. As such, the book offers a valuable resource for mathematicians and biologists alike. The first group will find new biological models that lead to interesting and often new mathematical questions, while the second can observe how to include seemingly disparate biological processes into a unified mathematical theory, and...
Incompressible flows with piecewise constant density
Danchin, Raphaël
2012-01-01
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness holds in any dimension and for a wider class of velocity fields. Let us emphasize that all those results are true for piecewise constant densities with arbitrarily large jumps. Global results are established in dimension two if the density is close enough to a positive constant, and in n-dimension if, in addition, the initial velocity is small. The Lagrangian formula- tion for describing the flow plays a key role in the analysis that is proposed in the present paper.
Robust Hinf control of uncertain switched systems defined on polyhedral sets with Filippov solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Carathe ́odory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions...... with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov...... solutions. Subsequently, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed Hinf performance are presented. Furthermore, these results has been generalized to the case of piecewise affine systems. Finally, a V–K iteration algorithm is proposed to deal...
Characterization of the low affinity transport system for NO(3)(-) uptake by Citrus roots.
Cerezo, M; Flors, V; Legaz, F; García-Agustín, P
2000-12-07
Three-month old citrange Troyer (hybrid of Citrus sinensis x Poncirus trifoliata) seedlings were grown hydroponically and, after a period of NO(3)(-) starvation, plants were transferred to solutions enriched with K(15)NO(3) (96% atoms 15N excess) to measure 15NO(3)(-) uptake rates as a function of external 15NO(3)(-) concentrations. Two different NO(3)(-) uptake systems were found. Between 1 and 50 mM 15NO(3)(-) in the uptake solution medium, the uptake rate increased linearly due to the low affinity transport system (LATS). Nitrate reductase activity showed the same response to external [NO(3)(-)], and also appears to be regulated by the rate of nitrate uptake. Nitrate pre-treatments had a represive effect on NO(3)(-) uptake rate measured at 5 or 30 mM external [15NO(3)(-)]. The extent of the inhibition depended on the [NO(3)(-)] during the pre-treatment and in the uptake solution. These results suggest that the LATS of Citrus seedlings is under feedback control by the N status of the plant. Accordingly, addition of amino acids (Glu, Asp, Asn, Gln) to the uptake solution resulted in a decrease in 15NO(3)(-) uptake rate. However, the inactivation of nitrate reductase activity after treatment of the seedlings with either 100 or 500 µM WO(4)(2-) did not affect the activity of the LATS. Metabolic uncouplers, 2,4-DNP and KCN, reduced the uptake rate by 43.3% and 41.4% respectively at 5mM external [15NO(3)(-)]. However, these compounds had little effect when 15NO(3)(-) uptake was assayed at 30 mM external concentration. The ATPase inhibitors DCCD and DES reduced 15NO(3)(-) uptake by 68.8%-35.6%, at both external [15NO(3)(-)]. Nitrate uptake by the LATS declined with the increase of the solution pH beyond pH 4. The data presented are discussed in the context of the kinetics, energy dependence and regulation of NO(3)(-) uptake.
Stability Analysis of Periodic Orbits in a Class of Duffing-Like Piecewise Linear Vibrators
El Aroudi, A.
2014-09-01
In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.
Estimation of the Bezout number for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
WANG; Renhong(王仁宏); XU; Zhiqiang(许志强)
2003-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method, an upperbound of the Bezout number defined as the maximum finite number of intersection points of two piecewisealgebraic curves is presented.
Landsman, Zinoviy
2008-10-01
We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see sciencedirect.com/science/journal/03770427>, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.
Cao, YY; Lam, J.
2001-01-01
This paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via perio...
Oscillation region of a piecewise-smooth model of the vocal folds
Lucero, Jorge C.; Gajo, Cristiane A.
2006-01-01
The two-mass model of the vocal folds is a popular representation of their dynamical structure used in phonation studies. This paper presents an analysis of a recent piecewise-smooth version of the model. This version has two equilibrium positions, and in one of them (the initial prephonatory position) the system is nondifferentiable. Standard methods of stability analysis do not apply for that position, because they require smoothness of the system. A geometrical approac...
Directory of Open Access Journals (Sweden)
Koki Tsukamoto
2009-01-01
Full Text Available Koki Tsukamoto1, Tatsuya Yoshikawa1,2, Kiyonobu Yokota1, Yuichiro Hourai1, Kazuhiko Fukui11Computational Biology Research Center (CBRC, National Institute of Advanced Industrial Science and Technology (AIST, Koto-ku, Tokyo, Japan; 2Department of Bioinformatic Engineering, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, JapanAbstract: A system was developed to evaluate and predict the interaction between protein pairs by using the widely used shape complementarity search method as the algorithm for docking simulations between the proteins. We used this system, which we call the affinity evaluation and prediction (AEP system, to evaluate the interaction between 20 protein pairs. The system first executes a “round robin” shape complementarity search of the target protein group, and evaluates the interaction between the complex structures obtained by the search. These complex structures are selected by using a statistical procedure that we developed called ‘grouping’. At a prevalence of 5.0%, our AEP system predicted protein–protein interactions with a 50.0% recall, 55.6% precision, 95.5% accuracy, and an F-measure of 0.526. By optimizing the grouping process, our AEP system successfully predicted 10 protein pairs (among 20 pairs that were biologically relevant combinations. Our ultimate goal is to construct an affinity database that will provide cell biologists and drug designers with crucial information obtained using our AEP system.Keywords: protein–protein interaction, affinity analysis, protein–protein docking, FFT, massive parallel computing
DEFF Research Database (Denmark)
Guglielmi, Michel; Johannesen, Hl
2004-01-01
This paper will introduce a project sourced by an ideas competition called Landmark East England. It was open to anyone with the ability to develop and deliver a visionary idea for a landmark. A sustainable icon representing a new region in England, which comprises Bedfordshire, Cambridgeshire......, Essex, Hertfordshire, Norfolk and Suffolk. Research found that there was a lack of identity or sense of belonging and nothing anchoring people to the region as a whole. Common affinity is somehow forced to the people of East England and thereby we came to the conclusion that a single landmark...... or a series of landmarks would do little to achieve true affinity. Therefore, we based our design strategy in trying to elaborate an alternatereality based on fabulation, virtualization and narratives that we subtly interweaved into architectonic structures (fabric) of the real. We have created plots...
Directory of Open Access Journals (Sweden)
Brian H. Carrick
2016-03-01
Full Text Available Isolation of endogenous proteins from Saccharomyces cerevisiae has been facilitated by inserting encoding polypeptide affinity tags at the C-termini of chromosomal open reading frames (ORFs using homologous recombination of DNA fragments. Tagged protein isolation is limited by a number of factors, including high cost of affinity resins for bulk isolation and low concentration of ligands on the resin surface, leading to low isolation efficiencies and trapping of contaminants. To address this, we have created a recombinant “CelTag” DNA construct from which PCR fragments can be created to easily tag C-termini of S. cerevisiae ORFs using selection for a nat1 marker. The tag has a C-terminal cellulose binding module to be used in the first affinity step. Microgranular cellulose is very inexpensive and has an effectively continuous ligand on its surface, allowing rapid, highly efficient purification with minimal background. Cellulose-bound proteins are released by specific cleavage of an included site for TEV protease, giving nearly pure product. The tag can be lifted from the recombinant DNA construct either with or without a 13x myc epitope tag between the target ORF and the TEV protease site. Binding of CelTag protein fusions to cellulose is stable to high salt, nonionic detergents, and 1 M urea, allowing stringent washing conditions to remove loosely associated components, as needed, before specific elution. It is anticipated that this reagent could allow isolation of protein complexes from large quantities of yeast extract, including soluble, membrane-bound, or nucleic acid-associated assemblies.
Carrick, Brian H; Hao, Linxuan; Smaldino, Philip J; Engelke, David R
2015-12-29
Isolation of endogenous proteins from Saccharomyces cerevisiae has been facilitated by inserting encoding polypeptide affinity tags at the C-termini of chromosomal open reading frames (ORFs) using homologous recombination of DNA fragments. Tagged protein isolation is limited by a number of factors, including high cost of affinity resins for bulk isolation and low concentration of ligands on the resin surface, leading to low isolation efficiencies and trapping of contaminants. To address this, we have created a recombinant "CelTag" DNA construct from which PCR fragments can be created to easily tag C-termini of S. cerevisiae ORFs using selection for a nat1 marker. The tag has a C-terminal cellulose binding module to be used in the first affinity step. Microgranular cellulose is very inexpensive and has an effectively continuous ligand on its surface, allowing rapid, highly efficient purification with minimal background. Cellulose-bound proteins are released by specific cleavage of an included site for TEV protease, giving nearly pure product. The tag can be lifted from the recombinant DNA construct either with or without a 13x myc epitope tag between the target ORF and the TEV protease site. Binding of CelTag protein fusions to cellulose is stable to high salt, nonionic detergents, and 1 M urea, allowing stringent washing conditions to remove loosely associated components, as needed, before specific elution. It is anticipated that this reagent could allow isolation of protein complexes from large quantities of yeast extract, including soluble, membrane-bound, or nucleic acid-associated assemblies.
Directory of Open Access Journals (Sweden)
Essam R. El-Zahar
2016-01-01
Full Text Available A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM. First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term.
A new BODIPY/nanoparticle/Ni affinity system for binding of cytochrome c
Energy Technology Data Exchange (ETDEWEB)
Maltas, Esra, E-mail: maltasesra@gmail.com [Selcuk University, Faculty of Science, Department of Chemistry, 42075 Konya (Turkey); Selcuk University, Faculty of Science, Department of Biochemistry, 42075 Konya (Turkey); Kursunlu, Ahmed Nuri [Selcuk University, Faculty of Science, Department of Chemistry, 42075 Konya (Turkey); Arslan, Gulsin [Selcuk University, Faculty of Science, Department of Biochemistry, 42075 Konya (Turkey); Selcuk University, Advanced Research Technology and Application Center, 42075 Konya (Turkey); Ozmen, Mustafa [Selcuk University, Faculty of Science, Department of Chemistry, 42075 Konya (Turkey); Selcuk University, Advanced Research Technology and Application Center, 42075 Konya (Turkey)
2015-09-15
Highlights: • BODIPY was synthesized, and then attached to magnetic nanoparticles. • Ni(II) ions were chelated on prepared material. • The binding of cytochrome c to obtained material was studied. - Abstract: In this study, 3,5-{Bis[4,4-difluoro, 8-(2,6-diethyl, 1,3,5,7-tetramethyl-4-bora-3a,4a-diaza-s-indacene)]}benzoylchloride (BODIPY) was synthesized for the improving of a new immobilized metal affinity supporting material. Firstly, the synthesized BODIPY was immobilized on iron oxide superparamagnetic nanoparticles (SPIONs) and then, Ni(II) ions were chelated with the active terminals of BODIPY on nanoparticles surfaces to prepare an immobilized metal affinity (IMA) adsorbent for protein adsorption. The amount of BODIPY coated on SPIONs was about 29.7 μM at 10 mg nanoparticles. 738 μmol of Ni(II) ions were loaded to 10 mg of the SPIONs/BODIPY. The binding amount of cytochrome c was found to be 170 μg to the SPIONs/BODIPY/Ni at pH 7.4. The binding amount of the molecules on SPIONs was analyzed by using UV–vis, fluorescence and atomic absorption spectroscopy. The characterization of the prepared surfaces was performed by FT-IR, SEM and TEM.
The Diffusion Coefficient For Piecewise Expanding Maps Of The Interval With Metastable States
Dolgopyat, Dmitry
2010-01-01
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the subintervals lose their invariance in such a way that there is a unique ACIM, we show how to approximate the diffusion coefficient for an observable of bounded variation by the diffusion coefficient of a related continuous time Markov chain.
Jiang, Zhi-Guo; Zhang, Hai-De; Wang, Wei-Tao
2015-05-01
A simple and inexpensive aqueous two-phase affinity partitioning system using metal ligands was introduced to improve the selectivity of commercial papain extraction. Polyethylene glycol 4000 was first activated using epichlorohydrin, then it was covalently linked to iminodiacetic acid. Finally, the specific metal ligand Cu(2+) was attached to the polyethylene glycol-iminodiacetic acid. The chelated Cu(2+) content was measured by atomic absorption spectrometry as 0.88 mol/mol (polyethylene glycol). The effects on the purification at different conditions, including polyethylene glycol molecular weight (2000, 4000, and 6000), concentration of phase-forming components (polyethylene glycol 12-20% w/w and sodium sulfate 12-20%, w/w), metal ligand type, and concentration, system pH and the commercial papain loading on papain extraction, were systematically studied. Under optimum conditions of the system, i.e. 18% w/w sodium sulfate, 18% w/w polyethylene glycol 4000, 1% w/w polyethylene glycol-iminodiacetic acid-Cu(2+) and pH 7, a maximum yield of 90.3% and a degree of purification of 3.6-fold were obtained. Compared to aqueous two phase extraction without ligands, affinity partitioning was found to be an effective technique for the purification of commercial papain with higher extraction efficiency and degree of purification.
Directory of Open Access Journals (Sweden)
Elaheh Saeedi
2014-07-01
Full Text Available In this paper, a decentralized adaptive controller with using wavelet neural network is used for a class of large-scale nonlinear systems with time- delay unknown nonlinear non- affine subsystems. The entered interruptions in subsystems are considered nonlinear with time delay, this is closer the reality, compared with the case in which the delay is not considered for interruptions. In this paper, the output weights of wavelet neural network and the other parameters of wavelet are adjusted online. The stability of close loop system is guaranteed with using the Lyapanov- Krasovskii method. Moreover the stability of close loop systems, guaranteed tracking error is converging to neighborhood zero and also all of the signals in the close loop system are bounded. Finally, the proposed method, simulated and applied for the control of two inverted pendulums that connected by a spring and the computer results, show that the efficiency of suggested method in this paper.
Breaking the continuity of a piecewise linear map
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Schenke Björn
2012-08-01
Full Text Available Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear map in the generic form, which can be used as a normal form for these bifurcations in other 1D discontinuous maps with one discontinuity. These organizing centers appear when the continuity of the system function is broken in a fixed point. The type of an organizing center depends on the slopes of the piecewise-linear map. The organizing centers that occur if the slopes have an absolute value smaller than one were already described in previous works, so we concentrate on presenting the organizing centers that occur if one or both slopes have absolute values larger than one. By doing this, we also show that the behavior for each organizing center can be explained using four basic bifurcation scenarios: the period incrementing and the period adding scenarios in the periodic domain, as well as the bandcount incrementing and the bandcount adding scenarios in the chaotic domain. Les connaissances sur le comportement d’applications linéaires par morceaux discontinues sont importantes pour de nombreuses applications. Une méthode puissante pour étudier la structure de bifurcation dans les espaces de paramètre 2D de telles applications est de détecter des points de bifurcation spécifiques de codimension 2, appelés centres organisateurs, et de décrire la structure de bifurcation dans leur voisinage. Dans ce travail, nous présentons les centres organisateurs pour une application linéaire par morceaux discontinue 1D sous forme générique, ce qui peut être utilisé comme une forme normale pour ces
Interactive seismic interpretation with piecewise global energy minimization
Hollt, Thomas
2011-03-01
Increasing demands in world-wide energy consumption and oil depletion of large reservoirs have resulted in the need for exploring smaller and more complex oil reservoirs. Planning of the reservoir valorization usually starts with creating a model of the subsurface structures, including seismic faults and horizons. However, seismic interpretation and horizon tracing is a difficult and error-prone task, often resulting in hours of work needing to be manually repeated. In this paper, we propose a novel, interactive workflow for horizon interpretation based on well positions, which include additional geological and geophysical data captured by actual drillings. Instead of interpreting the volume slice-by-slice in 2D, we propose 3D seismic interpretation based on well positions. We introduce a combination of 2D and 3D minimal cost path and minimal cost surface tracing for extracting horizons with very little user input. By processing the volume based on well positions rather than slice-based, we are able to create a piecewise optimal horizon surface at interactive rates. We have integrated our system into a visual analysis platform which supports multiple linked views for fast verification, exploration and analysis of the extracted horizons. The system is currently being evaluated by our collaborating domain experts. © 2011 IEEE.
Fassò, Francesco; Sansonetto, Nicola
2016-04-01
Energy is in general not conserved for mechanical nonholonomic systems with affine constraints. In this article we point out that, nevertheless, in certain cases, there is a modification of the energy that is conserved. Such a function is the pull-back of the energy of the system written in a system of time-dependent coordinates in which the constraint is linear, and for this reason will be called a `moving' energy. After giving sufficient conditions for the existence of a conserved, time-independent moving energy, we point out the role of symmetry in this mechanism. Lastly, we apply these ideas to prove that the motions of a heavy homogeneous solid sphere that rolls inside a convex surface of revolution in uniform rotation about its vertical figure axis, are (at least for certain parameter values and in open regions of the phase space) quasi-periodic on tori of dimension up to three.
Dynamical zeta functions for piecewise monotone maps of the interval
Ruelle, David
2004-01-01
Consider a space M, a map f:M\\to M, and a function g:M \\to {\\mathbb C}. The formal power series \\zeta (z) = \\exp \\sum ^\\infty _{m=1} \\frac {z^m}{m} \\sum _{x \\in \\mathrm {Fix}\\,f^m} \\prod ^{m-1}_{k=0} g (f^kx) yields an example of a dynamical zeta function. Such functions have unexpected analytic properties and interesting relations to the theory of dynamical systems, statistical mechanics, and the spectral theory of certain operators (transfer operators). The first part of this monograph presents a general introduction to this subject. The second part is a detailed study of the zeta functions associated with piecewise monotone maps of the interval [0,1]. In particular, Ruelle gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of \\zeta (z) and the eigenvalues of the transfer operator. He also proves a theorem expressing the largest eigenvalue of the transfer operator in terms of the ergodic properties of (M,f,g).
Weak-noise limit of a piecewise-smooth stochastic differential equation.
Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram
2013-11-01
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.
Trushin, Egor; Betzinger, Markus; Blügel, Stefan; Görling, Andreas
2016-08-01
An approach to calculate fundamental band gaps, ionization energies, and electron affinities of periodic electron systems is explored. Starting from total energies obtained with the help of the adiabatic-connection fluctuation-dissipation (ACFD) theorem, these physical observables are calculated according to their basic definition by differences of the total energies of the N -, (N -1 ) -, and (N +1 ) -electron system. The response functions entering the ACFD theorem are approximated here by the direct random phase approximation (dRPA). For a set of prototypical semiconductors and insulators it is shown that even with this quite drastic approximation the resulting band gaps are very close to experiment and of a similar quality to those from the computationally more involved G W approximation. By going beyond the dRPA in the future the accuracy of the calculated band gaps may be significantly improved further.
Zhang, Tian-Ping; Zhu, Qing; Yang, Yue-Quan
2012-04-01
In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.
Piecewise Filter of Infrared Image Based on Moment Theory
Institute of Scientific and Technical Information of China (English)
GAO Yang; LI Yan-jun; ZHANG Ke
2007-01-01
The disadvantages of IR images mostly include high noise, blurry edge and so on. The characteristics make the existent smoothing methods ineffective in preserving edge. To solve this problem, a piecewise moment filter (PMF) is put forward. By using moment and piecewise linear theory, the filter can preserve edge. Based on the statistical model of random noise, a related-coefficient method is presented to estimate the variance of noise. The edge region and model are then detected by the estimated variance. The expectation of first-order derivatives is used in getting the reliable offset of edge.At last, a fast moment filter of double-stair edge model is used to gain the piecewise smoothing results and reduce the calculation. The experimental result shows that the new method has a better capability than other methods in suppressing noise and preserving edge.
RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD
Institute of Scientific and Technical Information of China (English)
Hongwei Li; Xuecheng Tai; Sigurd Ivar Aanonsen
2008-01-01
We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.
Piecewise-linearized methods for oscillators with limit cycles
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)] e-mail: jirs@lcc.uma.es
2006-03-01
A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.
An analogue of Polya's theorem for piecewise holomorphic functions
Buslaev, V. I.
2015-12-01
A well-known result due to Polya for a function given by its holomorphic germ at z=∞ is extended to the case of a piecewise holomorphic function on an arbitrary compact set in \\overline{ C}. This result is applied to the problem of the existence of compact sets that have the minimum transfinite diameter in the external field of the logarithmic potential of a negative unit charge among all compact sets such that a certain multivalued analytic function is single-valued and piecewise holomorphic on their complement. Bibliography: 13 titles.
Hamdy, M; Hamdan, I
2015-07-01
In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study.
ASIFT: An Algorithm for Fully Affine Invariant Comparison
Directory of Open Access Journals (Sweden)
Guoshen Yu
2011-02-01
Full Text Available If a physical object has a smooth or piecewise smooth boundary, its images obtained by cameras in varying positions undergo smooth apparent deformations. These deformations are locally well approximated by affine transforms of the image plane. In consequence the solid object recognition problem has often been led back to the computation of affine invariant image local features. The similarity invariance (invariance to translation, rotation, and zoom is dealt with rigorously by the SIFT method The method illustrated and demonstrated in this work, Affine-SIFT (ASIFT, simulates a set of sample views of the initial images, obtainable by varying the two camera axis orientation parameters, namely the latitude and the longitude angles, which are not treated by the SIFT method. Then it applies the SIFT method itself to all images thus generated. Thus, ASIFT covers effectively all six parameters of the affine transform.
Affinity partitioning of human antibodies in aqueous two-phase systems
Rosa, P. A. J.; Azevedo, A. M.; Ferreira, I. F.; de Vries, J.; Korporaal, R.; Verhoef, H. J.; Visser, T. J.; Aires-Barros, M. R.
2007-01-01
The partitioning of human immunoglobulin (IgG) in a polymer-polymer and polymer-salt aqueous two-phase system (ATPS) in the presence of several functionalised polyethylene glycols (PEGs) was studied. As a first approach, the partition studies were performed with pure IgG using systems in which the t
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Ciepliński Krzysztof
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions of the functional equation , , where are closed intervals, and , are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
A family of quantization based piecewise linear filter networks
DEFF Research Database (Denmark)
Sørensen, John Aasted
1992-01-01
A family of quantization-based piecewise linear filter networks is proposed. For stationary signals, a filter network from this family is a generalization of the classical Wiener filter with an input signal and a desired response. The construction of the filter network is based on quantization of...
Data-based fault-tolerant control for affine nonlinear systems with actuator faults.
Xie, Chun-Hua; Yang, Guang-Hong
2016-09-01
This paper investigates the fault-tolerant control (FTC) problem for unknown nonlinear systems with actuator faults including stuck, outage, bias and loss of effectiveness. The upper bounds of stuck faults, bias faults and loss of effectiveness faults are unknown. A new data-based FTC scheme is proposed. It consists of the online estimations of the bounds and a state-dependent function. The estimations are adjusted online to compensate automatically the actuator faults. The state-dependent function solved by using real system data helps to stabilize the system. Furthermore, all signals in the resulting closed-loop system are uniformly bounded and the states converge asymptotically to zero. Compared with the existing results, the proposed approach is data-based. Finally, two simulation examples are provided to show the effectiveness of the proposed approach.
Energy Technology Data Exchange (ETDEWEB)
Qu, Yi; Wu, Si; Zhao, Rui; Zink, Erika M.; Orton, Daniel J.; Moore, Ronald J.; Meng, Da; Clauss, Therese RW; Aldrich, Joshua T.; Lipton, Mary S.; Pasa-Tolic, Ljiljana
2013-06-05
Enrichment of bacterial phosphopeptides is an essential step prior to bottom-up mass spectrometry-based analysis of the phosphoproteome, which is fundamental to understanding the role of phosphoproteins in cell signaling and regulation of protein activity. We developed an automated IMAC system to enrich strong cation exchange-fractionated phosphopeptides from the soluble proteome of Escherichia coli MG1655 grown on minimal medium. Initial demonstration of the system resulted in identification of 75 phosphopeptides covering 52 phosphoproteins. Consistent with previous studies, many of these phosphoproteins are involved in the carbohydrate portion of central metabolism. The automated system utilizes a large capacity IMAC column that can effectively enrich phosphopeptides from a bacterial sample by increasing peptide loading and reducing the wash time. An additional benefit of the automated IMAC system is reduced labor and associated costs.
On the Convergence of Piecewise Linear Strategic Interaction Dynamics on Networks
Gharesifard, Bahman
2015-09-11
We prove that the piecewise linear best-response dynamical systems of strategic interactions are asymptotically convergent to their set of equilibria on any weighted undirected graph. We study various features of these dynamical systems, including the uniqueness and abundance properties of the set of equilibria and the emergence of unstable equilibria. We also introduce the novel notions of social equivalence and social dominance on directed graphs, and demonstrate some of their interesting implications, including their correspondence to consensus and chromatic number of partite graphs. Examples illustrate our results.
Energy Technology Data Exchange (ETDEWEB)
Vereshchagin, D.A. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation); Leble, S.B. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation) and Theoretical Physics and Mathematical Methods Department, Gdansk University of Technology, ul. Narutowicza 11/12, Gdansk (Poland)]. E-mail: leble@mifgate.pg.gda.pl; Solovchuk, M.A. [Theoretical Physics Department, Kaliningrad State University, A. Nevsky st. 14, Kaliningrad (Russian Federation)]. E-mail: solovchuk@yandex.ru
2006-01-02
The system of hydrodynamic-type equations for a stratified gas in gravity field is derived from BGK equation by method of piecewise continuous distribution function. The obtained system of the equations generalizes the Navier-Stokes one at arbitrary Knudsen numbers. The problem of a wave disturbance propagation in a rarefied gas is explored. The verification of the model is made for a limiting case of a homogeneous medium. The phase velocity and attenuation coefficient values are in an agreement with former fluid mechanics theories; the attenuation behavior reproduces experiment and kinetics-based results at more wide range of the Knudsen numbers.
Directory of Open Access Journals (Sweden)
Bahita Mohamed
2011-01-01
Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.
Controllability of affine right-invariant systems on solvable Lie groups
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Yuri L. Sachkov
1997-12-01
Full Text Available The aim of this paper is to present some recent results on controllability of right-invariant systems on Lie groups. From the Lie-theoretical point of view, we study conditions under which subsemigroups generated by half-planes in the Lie algebra of a Lie group coincide with the whole Lie group.
Low affinity of heterotrophic bacteria to loose deposits in drinking water distribution systems
Poças, A.; Napier, V.; Neto, C.; Ferreira, E.; Benoliel, M.J.; Rietveld, L.C.; Vreeburg, J.; Menaia, J.
2015-01-01
Loose deposits (LD) accumulate in drinking water distribution systems (DWDS) and may lead to tap water discoloration incidents upon resuspension. While inconvenient for the consumers and the water companies, discoloration may be accompanied by degradation of the microbiological quality of the wat
Tatsumi, Kasumi; Sakashita, Gyosuke; Nariai, Yuko; Okazaki, Kosuke; Kato, Hiroaki; Obayashi, Eiji; Yoshida, Hisashi; Sugiyama, Kanako; Park, Sam-Yong; Sekine, Joji; Urano, Takeshi
2017-01-01
The recognition specificity of monoclonal antibodies (mAbs) has made mAbs among the most frequently used tools in both basic science research and in clinical diagnosis and therapies. Precise determination of the epitope allows the development of epitope tag systems to be used with recombinant proteins for various purposes. Here we describe a new family of tag derived from the epitope recognized by a highly specific mAb G196. The minimal epitope was identified as the five amino acid sequence Asp-Leu-Val-Pro-Arg. Permutation analysis was used to characterize the binding requirements of mAb G196, and the variable regions of the mAb G196 were identified and structurally analyzed by X-ray crystallography. Isothermal titration calorimetry revealed the high affinity (Kd = 1.25 nM) of the mAb G196/G196-epitope peptide interaction, and G196-tag was used to detect several recombinant cytosolic and nuclear proteins in human and yeast cells. mAb G196 is valuable for developing a new peptide tagging system for cell biology and biochemistry research. PMID:28266535
Venkatesh, P. R.; Venkatesan, A.
2016-10-01
We report the occurrence of vibrational resonance in piecewise-linear non-autonomous system. Especially, we show that an optimal amplitude of the high frequency second harmonic driving enhances the response of a piece-wise linear non-autonomous Murali-Lakshmanan-Chua (MLC) system to a low frequency first harmonic signal. This phenomenon is illustrated with the analytical solutions of circuit equations characterising the system and finally compared with the numerical method. Further, it has been enunciated explicitly, the implementation of the fundamental NOR/NAND gate via vibrational resonance, both by numerical and analytical solutions. In addition, these logical behaviours (AND/NAND/OR/NOR) can be decided by the amplitude of the input square waves without altering the system parameters.
Multi-input sliding mode control of nonlinear uncertain affine systems
Bartolini, Giorgio; Punta, Elisabetta; Zolezzi, Tullio
2011-05-01
In the extension to multi-input nonlinear uncertain systems of the sliding mode methodology, a crucial role is played by the matrix pre-multiplying the control in the dynamic equation of the sliding output. If this matrix is perfectly known and invertible, it is possible to transform a multi-input sliding mode control problem in an almost decoupled set of single-input problems. If this matrix is uncertain then nothing can be done in general, and the investigation is oriented to find conditions ensuring the feasibility of control strategies in a progressively more general set of uncertain matrices. In the case of uncertain and constant matrices, it is possible, in principle, to manage the case in which the matrix in question is invertible. The corresponding adaptive or switching strategy suffers from the curse of dimensionality of the so-called unmixing set. In this article the case of time- and state-varying uncertain matrix is dealt with. A more general class of such a matrices for which there is, at least locally, a solution of the problem is found. The introduction of artificial integrators in the output channel (the integral sliding mode control methodology) allows the practical implementation of the control law without requiring the a priori knowledge of parameters featured by the solution of a relevant nonlinear Lyapunov equation.
Goreac, D
2010-01-01
We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook's model for haploinssuficiency, and a stochastic model for bacteriophage lambda.
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
Affine connection form of Regge calculus
Khatsymovsky, V. M.
2016-12-01
Regge action is represented analogously to how the Palatini action for general relativity (GR) as some functional of the metric and a general connection as independent variables represents the Einstein-Hilbert action. The piecewise flat (or simplicial) spacetime of Regge calculus is equipped with some world coordinates and some piecewise affine metric which is completely defined by the set of edge lengths and the world coordinates of the vertices. The conjugate variables are the general nondegenerate matrices on the three-simplices which play the role of a general discrete connection. Our previous result on some representation of the Regge calculus action in terms of the local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as independent variables is somewhat modified for the considered case of the general linear group GL(4, R) of the connection matrices. As a result, we have some action invariant w.r.t. arbitrary change of coordinates of the vertices (and related GL(4, R) transformations in the four-simplices). Excluding GL(4, R) connection from this action via the equations of motion we have exactly the Regge action for the considered spacetime.
Saito, Asaki; Yasutomi, Shin-ichi; Tamura, Jun-ichi; Ito, Shunji
2015-06-01
We introduce a true orbit generation method enabling exact simulations of dynamical systems defined by arbitrary-dimensional piecewise linear fractional maps, including piecewise linear maps, with rational coefficients. This method can generate sufficiently long true orbits which reproduce typical behaviors (inherent behaviors) of these systems, by properly selecting algebraic numbers in accordance with the dimension of the target system, and involving only integer arithmetic. By applying our method to three dynamical systems—that is, the baker's transformation, the map associated with a modified Jacobi-Perron algorithm, and an open flow system—we demonstrate that it can reproduce their typical behaviors that have been very difficult to reproduce with conventional simulation methods. In particular, for the first two maps, we show that we can generate true orbits displaying the same statistical properties as typical orbits, by estimating the marginal densities of their invariant measures. For the open flow system, we show that an obtained true orbit correctly converges to the stable period-1 orbit, which is inherently possessed by the system.
Institute of Scientific and Technical Information of China (English)
Chao Cai; Xue-Qiang Zhao; Yong-Guan Zhu; Bin Li; Yi-Ping Tong; Zhen-Sheng Li
2007-01-01
Nitrate is a major nitrogen (N) source for most crops.Nitrate uptake by root cells is a key step of nitrogen metabolism and has been widely studied at the physiological and molecular levels.Understanding how nitrate uptake is regulated will help us engineer crops with improved nitrate uptake efficiency.The present study investigated the regulation of the high-affinity nitrate transport system (HATS) by exogenous abscisic acid (ABA) and glutamine (Gin) in wheat (Triticum aestivum L.) roots.Wheat seedlings grown in nutrient solution containing 2 mmollL nitrate as the only nitrogen source for 2 weeks were deprived of N for 4d and were then transferred to nutrient solution containing 50 μmol/L ABA, and 1 mmol/L Gin in the presence or absence of 2 mmol/L nitrate for 0, 0.5, 1, 2, 4, and 8 h.Treated wheat plants were then divided into two groups.One group of plants was used to investigate the mRNA levels of the HATS components NRT2 and NAR2 genes in roots through semi-quantitative RT-PCR approach, and the other set of plants were used to measure high-affinity nitrate influx rates in a nutrient solution containing 0.2 mmol/L 15 N-labeled nitrate.The results showed that exogenous ABA induced the expression of the TaNRT2.1, TaNRT2.2, TaNRT2.3, TaNAR2.1, and TaNAR2.2 genes in roots when nitrate was not present in the nutrient solution, but did not further enhance the induction of these genes by nitrate.Glutamine, which has been shown to inhibit the expression of NRT2 genes when nitrate is present in the growth media, did not inhibit this induction.When Gin was supplied to a nitrate-free nutrient solution, the expression of these five genes in roots was induced.These results imply that the inhibition by Gin of NRT2 expression occurs only when nitrate is present in the growth media.Although exogenous ABA and Gin induced HATS genes in the roots of wheat, they did not induce nitrate influx.
Spectral analysis and an area-preserving extension of a piecewise linear intermittent map
Miyaguchi, Tomoshige; Aizawa, Yoji
2007-06-01
We investigate the spectral properties of a one-dimensional piecewise linear intermittent map, which has not only a marginal fixed point but also a singular structure suppressing injections of the orbits into neighborhoods of the marginal fixed point. We explicitly derive generalized eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map for classes of observables and piecewise constant initial densities, and it is found that the Frobenius-Perron operator has two simple real eigenvalues 1 and λdɛ(-1,0) and a continuous spectrum on the real line [0,1]. From these spectral properties, we also found that this system exhibits a power law decay of correlations. This analytical result is found to be in a good agreement with numerical simulations. Moreover, the system can be extended to an area-preserving invertible map defined on the unit square. This extended system is similar to the baker transformation, but does not satisfy hyperbolicity. A relation between this area-preserving map and a billiard system is also discussed.
Makarska-Bialokoz, Magdalena
2017-09-01
The binding affinity between vitamin B12 (VitB12) and bovine serum albumin (BSA) has been investigated in aqueous solution at pH = 7.4, employing UV-vis absorption and steady-state, synchronous and three-dimensional fluorescence spectra techniques. Representative effects noted for BSA intrinsic fluorescence resulting from the interactions with VitB12 confirm the formation of π-π stacked non-covalent and non-fluorescent complexes in the system VitB12-BSA. All the determined parameters, the binding, fluorescence quenching and bimolecular quenching rate constants (of the order of 104 L mol- 1, 103 L mol- 1 and 1011 L mol- 1 s- 1, respectively), as well as Förster resonance energy transfer parameters validate the mechanism of static quenching. The interaction with VitB12 induces folding of the polypeptide chains around Trp residues of BSA, resulting in a more hydrophobic surrounding. Presented outcomes suggest that the addition of VitB12 can lead to the more organized BSA conformation and its more folded tertiary structure, what could influence the physiological functions of bovine serum albumin, notably in case of its overuse or abnormal metabolism.
Piecewise quartic polynomial curves with a local shape parameter
Han, Xuli
2006-10-01
Piecewise quartic polynomial curves with a local shape parameter are presented in this paper. The given blending function is an extension of the cubic uniform B-splines. The changes of a local shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. The given curves possess satisfying shape-preserving properties. The given curve can also be used to interpolate locally the control points with GC2 continuity. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. As an application, the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter. The given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse. Some computing examples for curve design are given.
A 3D Facial Expression Tracking Method Using Piecewise Deformations
Directory of Open Access Journals (Sweden)
Jing Chi
2013-02-01
Full Text Available We present a new fast method for 3D facial expression tracking based on piecewise non-rigid deformations. Our method takes as input a video-rate sequence of face meshes that record the shape and time-varying expressions of a human face, and deforms a source mesh to match each input mesh to output a new mesh sequence with the same connectivity that reflects the facial shape and expressional variations. In mesh matching, we automatically segment the source mesh and estimate a non-rigid transformation for each segment to approximate the input mesh closely. Piecewise non-rigid transformation significantly reduces computational complexity and improves tracking speed because it greatly decreases the unknowns to be estimated. Our method can also achieve desired tracking accuracy because segmentation can be adjusted automatically and flexibly to approximate arbitrary deformations on the input mesh. Experiments demonstrate the efficiency of our method.
Border Collision Bifurcations in Two Dimensional Piecewise Smooth Maps
Banerjee, S; Banerjee, Soumitro; Grebogi, Celso
1999-01-01
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the theoretical problem: the development of a theory and classification of the new type of bifurcations resulting from border collision. We then present a systematic analysis of such bifurcations by deriving a normal form --- the piecewise linear approximation in the neighborhood of the border. We show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all syst...
Convergence of the natural approximations of piecewise monotone interval maps.
Haydn, Nicolai
2004-06-01
We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which is Lipshitz continuous and for which the densities converge in the bounded variation norm at a logarithmic rate. This shows that in general one cannot expect exponential convergence in the bounded variation norm. Here we prove that if the derivative of the interval map is Holder continuous and its variation is well approximable (gamma-uniform variation for gamma>0), then the densities converge exponentially fast in the norm.
Dose reduction using a dynamic, piecewise-linear attenuator
Energy Technology Data Exchange (ETDEWEB)
Hsieh, Scott S., E-mail: sshsieh@stanford.edu [Department of Radiology, Stanford University, Stanford, California 94305 and Department of Electrical Engineering, Stanford University, Stanford, California 94305 (United States); Fleischmann, Dominik [Department of Radiology, Stanford University, Stanford, California 94305 (United States); Pelc, Norbert J. [Department of Radiology, Stanford University, Stanford, California 94305 and Department of Bioengineering, Stanford University, Stanford, California 94305 (United States)
2014-02-15
Purpose: The authors recently proposed a dynamic, prepatient x-ray attenuator capable of producing a piecewise-linear attenuation profile customized to each patient and viewing angle. This attenuator was intended to reduce scatter-to-primary ratio (SPR), dynamic range, and dose by redistributing flux. In this work the authors tested the ability of the attenuator to reduce dose and SPR in simulations. Methods: The authors selected four clinical applications, including routine full field-of-view scans of the thorax and abdomen, and targeted reconstruction tasks for an abdominal aortic aneurysm and the pancreas. Raw data were estimated by forward projection of the image volume datasets. The dynamic attenuator was controlled to reduce dose while maintaining peak variance by solving a convex optimization problem, assuminga priori knowledge of the patient anatomy. In targeted reconstruction tasks, the noise in specific regions was given increased weighting. A system with a standard attenuator (or “bowtie filter”) was used as a reference, and used either convex optimized tube current modulation (TCM) or a standard TCM heuristic. The noise of the scan was determined analytically while the dose was estimated using Monte Carlo simulations. Scatter was also estimated using Monte Carlo simulations. The sensitivity of the dynamic attenuator to patient centering was also examined by shifting the abdomen in 2 cm intervals. Results: Compared to a reference system with optimized TCM, use of the dynamic attenuator reduced dose by about 30% in routine scans and 50% in targeted scans. Compared to the TCM heuristics which are typically used withouta priori knowledge, the dose reduction is about 50% for routine scans. The dynamic attenuator gives the ability to redistribute noise and variance and produces more uniform noise profiles than systems with a conventional bowtie filter. The SPR was also modestly reduced by 10% in the thorax and 24% in the abdomen. Imaging with the dynamic
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
Goulden, I. P.; Guay-Paquet, Mathieu; Novak, Jonathan
2016-04-01
This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil.
On Uniqueness of Conjugacy of Continuous and Piecewise Monotone Functions
Directory of Open Access Journals (Sweden)
Krzysztof Ciepliński
2009-01-01
Full Text Available We investigate the existence and uniqueness of solutions φ:I→J of the functional equation φ(f(x=F(φ(x, x∈I, where I,J are closed intervals, and f:I→I, F:J→J are some continuous piecewise monotone functions. A fixed point principle plays a crucial role in the proof of our main result.
Rectification of aerial images using piecewise linear transformation
Liew, L. H.; Lee, B. Y.; Wang, Y. C.; Cheah, W. S.
2014-02-01
Aerial images are widely used in various activities by providing visual records. This type of remotely sensed image is helpful in generating digital maps, managing ecology, monitoring crop growth and region surveying. Such images could provide insight into areas of interest that have lower altitude, particularly in regions where optical satellite imaging is prevented due to cloudiness. Aerial images captured using a non-metric cameras contain real details of the images as well as unexpected distortions. Distortions would affect the actual length, direction and shape of objects in the images. There are many sources that could cause distortions such as lens, earth curvature, topographic relief and the attitude of the aircraft that is used to carry the camera. These distortions occur differently, collectively and irregularly in the entire image. Image rectification is an essential image pre-processing step to eliminate or at least reduce the effect of distortions. In this paper, a non-parametric approach with piecewise linear transformation is investigated in rectifying distorted aerial images. The non-parametric approach requires a set of corresponding control points obtained from a reference image and a distorted image. The corresponding control points are then applied with piecewise linear transformation as geometric transformation. Piecewise linear transformation divides the image into regions by triangulation. Different linear transformations are employed separately to triangular regions instead of using a single transformation as the rectification model for the entire image. The result of rectification is evaluated using total root mean square error (RMSE). Experiments show that piecewise linear transformation could assist in improving the limitation of using global transformation to rectify images.
A spectral gap for transer operators of piecewise expanding maps
Thomine, Damien
2010-01-01
We provide a simplified proof of the existence, under some assumptions, of a spectral gap for the Perron-Frobenius operator of piecewise uniformly expanding maps on Riemannian manifolds when acting on some Sobolev spaces. Its consequences include, among others, the existence of invariant physical measures, and an exponential decay of correlations for suitable observables. These features are then adapted to different function spaces (functions with bounded variation or bounded oscillation), so as to give a new insight of - and generalize - earlier results.
Considerations Related to Interpolation of Experimental Data Using Piecewise Functions
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Stelian Alaci
2016-12-01
Full Text Available The paper presents a method for experimental data interpolation by means of a piecewise function, the points where the form of the function changes being found simultaneously with the other parameters utilized in an optimization criterion. The optimization process is based on defining the interpolation function using a single expression founded on the Heaviside function and regarding the optimization function as a generalised infinitely derivable function. The exemplification of the methodology is made via a tangible example.
Numeric Function Generators Using Piecewise Arithmetic Expressions
2011-05-01
Hiroshima City University, Hiroshima, JAPAN †Dept. of Computer Science and Electronics , Kyushu Institute of Technology, Iizuka, JAPAN ‡Dept. of... IEICE Trans. on Information and Systems, Vol. E93-D, No. 8, pp. 2059–2067, Aug. 2010. [12] B.-G. Nam, H. Kim, and H.-J. Yoo, “Power and area- efficient...unified computation of vector and elementary functions for handheld 3D graphics systems,” IEEE Transactions on Computers, Vol. 57, No. 4, pp. 490– 503
具有分片线性NCP函数的QP-Free可行域方法%Piecewise Linear NCP Function for QP-Free Feasible Method
Institute of Scientific and Technical Information of China (English)
濮定国; 周岩
2006-01-01
In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piecewise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising.
De-synchronization of the Distributed Refrigeration System
DEFF Research Database (Denmark)
Chen, Liang; Wisniewski, Rafal
2010-01-01
The supermarket refrigeration system typically has a distributed control structure, which simple and flexible, however, neglects interactions between its subsystems. Practice shows that these interactions lead to a synchronous operation of the display cases. It causes excessive wear...... on the compressors and increased energy consumption. The paper focuses on the synchronization analysis and de-synchronization control. The supermarket refrigeration system is modeled as a piecewise-affine switched system. The system behavior is decomposed such that synchronization analysis can be completed by using...... performance and can deal with the large scale refrigeration system with different system parameters in the display cases....
Tatsii, R. M.; Pazen, O. Yu.
2016-03-01
A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.
GRMHD Simulations of Binary Neutron Star Mergers with Piecewise Polytropic Equations of State
Giacomazzo, Bruno
2015-04-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. Our new simulations consider both equal and unequal-mass systems and describe the NS matter via piecewise polytropic equations of state (EOSs). BNS mergers are powerful sources of gravitational waves (GWs) that can be detected by ground based detectors, such as advanced Virgo and LIGO, and they are also thought to be behind the central engine powering short gamma-ray bursts. In our simulations we therefore focus both on the GW emission and on the dynamics of matter and magnetic fields, both in the case a black hole is promptly formed and in the case of the formation of a long-lived magnetized NS. Since the EOS has an important role in both GW emission and matter dynamics, our simulations employ piecewise polytropic EOSs composed by seven pieces, four for the low-density regions (including the crust) and three for the core, in order to more accurately match physically motivated EOSs. Thermal effects are also included in order to more properly describe the post-merger dynamics.
Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics.
Cao, Qingjie; Wiercigroch, Marian; Pavlovskaia, Ekaterina E; Thompson, J Michael T; Grebogi, Celso
2008-02-28
In a recent paper we examined a model of an arch bridge with viscous damping subjected to a sinusoidally varying central load. We showed how this yields a useful archetypal oscillator which can be used to study the transition from smooth to discontinuous dynamics as a parameter, alpha, tends to zero. Decreasing this smoothness parameter (a non-dimensional measure of the span of the arch) changes the smooth load-deflection curve associated with snap-buckling into a discontinuous sawtooth. The smooth snap-buckling curve is not amenable to closed-form theoretical analysis, so we here introduce a piecewise linearization that correctly fits the sawtooth in the limit at alpha=0. Using a Hamiltonian formulation of this linearization, we derive an analytical expression for the unperturbed homoclinic orbit, and make a Melnikov analysis to detect the homoclinic tangling under the perturbation of damping and driving. Finally, a semi-analytical method is used to examine the full nonlinear dynamics of the perturbed piecewise linear system. A chaotic attractor located at alpha=0.2 compares extremely well with that exhibited by the original arch model: the topological structures are the same, and Lyapunov exponents (and dimensions) are in good agreement.
Gardini, Laura; Fournier-Prunaret, Danièle; Chargé, Pascal
2011-06-01
In recent years, the study of chaotic and complex phenomena in electronic circuits has been widely developed due to the increasing number of applications. In these studies, associated with the use of chaotic sequences, chaos is required to be robust (not occurring only in a set of zero measure and persistent to perturbations of the system). These properties are not easy to be proved, and numerical simulations are often used. In this work, we consider a simple electronic switching circuit, proposed as chaos generator. The object of our study is to determine the ranges of the parameters at which the dynamics are chaotic, rigorously proving that chaos is robust. This is obtained showing that the model can be studied via a two-dimensional piecewise smooth map in triangular form and associated with a one-dimensional piecewise linear map. The bifurcations in the parameter space are determined analytically. These are the border collision bifurcation curves, the degenerate flip bifurcations, which only are allowed to occur to destabilize the stable cycles, and the homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in 1-piece.
A piecewise-integration method for simulating the influence of external forcing on climate
Institute of Scientific and Technical Information of China (English)
Zhifu Zhang; Chongjian Qiu; Chenghai Wang
2008-01-01
Climate drift occurs in most general circulation models (GCMs) as a result of incomplete physical and numerical representation of the complex climate system,which may cause large uncertainty in sensitivity experiments evaluating climate response to changes in external forcing.To solve this problem,we propose a piecewise-integration method to reduce the systematic error in climate sensitivity studies.The observations are firstly assimilated into a numerical model by using the dynamic relaxation technique to relax to the current state of atmosphere,and then the assimilated fields are continuously used to reinitialize the simulation to reduce the error of climate simulation.When the numerical model is integrated with changed external forcing,the results can be split into two parts,background and perturbation fields,and the background is the state before the external forcing is changed.The piecewise-integration method is used to continuously reinitialize the model with the assimilated field,instead of the background.Therefore,the simulation error of the model with the external forcing can be reduced.In this way,the accuracy of climate sensitivity experiments is greatly improved.Tests with a simple low-order spectral model show that this approach can significantly reduce the uncertainty of climate sensitivity experiments.
Nther-type theorem of piecewise algebraic curves on triangulation
Institute of Scientific and Technical Information of China (English)
2007-01-01
The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space.In this paper,using the properties of bivariate splines,the Nther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.
N(o)ther-type theorem of piecewise algebraic curves on triangulation
Institute of Scientific and Technical Information of China (English)
Chun-gang ZHU; Ren-hong WANG
2007-01-01
The piecewise algebraic curve is a kind generalization of the classical algebraic curve.N(o)ther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the N(o)ther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented.
The Cayley-Bacharach Theorem for Continuous Piecewise Algebraic Curves over Cross-cut Triangulations
Institute of Scientific and Technical Information of China (English)
Renhong WANG; Shaofan WANG
2011-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper,we propose the Cayley-Bacharach theorem for continuous piecewise algebraic curves over cross-cut triangulations.We show that,if two continuous piecewise algebraic curves of degrees m and n respectively meet at mnT distinct points over a cross-cut triangulation,where T denotes the number of cells of the triangulation,then any continuous piecewise algebraic curve of degree m + n - 2 containing all but one point of them also contains the last point.
Collisions in piecewise flat gravity in 3+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Van de Meent, Maarten, E-mail: M.vandeMeent@uu.n [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, PO Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-21
We consider the (3 + 1)-dimensional locally finite gravity model proposed by 't Hooft (2008 Found. Phys. 38 733-57). In particular we revisit the problem of resolving collisions of string defects. We provide a new geometric description of the configurations of strings using piecewise flat manifolds and use it to resolve a more general class of collisions. We argue that beyond certain bounds for the deficiency/surplus angles no resolutions may be found that satisfy the imposed causality conditions.
Guidance law based on piecewise constant control for hypersonic gliders
Hull, David G.; Seguin, Jean-Marie
A midcourse guidance law is developed for the descent of a hypersonic glider to a fixed target on the ground. It is based on an optimal piecewise constant control (N intervals) obtained from an approximate physical model (flat earth, exponential atmosphere, parabolic drag polar, etc). The resulting optimal control equations can be integrated either analytically or by quadrature, and the guidance algorithm requires the solution of 2N+1 nonlinear algebraic equations. The guidance law is implemented in a realistic glider simulation, the intercept is achieved, and final velocities within 14 percent of the true values are obtained for the downrange and crossranges considered.
Mixing with piecewise isometries on a hemispherical shell
Park, Paul P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2016-07-01
We introduce mixing with piecewise isometries (PWIs) on a hemispherical shell, which mimics features of mixing by cutting and shuffling in spherical shells half-filled with granular media. For each PWI, there is an inherent structure on the hemispherical shell known as the exceptional set E, and a particular subset of E, E+, provides insight into how the structure affects mixing. Computer simulations of PWIs are used to visualize mixing and approximations of E+ to demonstrate their connection. While initial conditions of unmixed materials add a layer of complexity, the inherent structure of E+ defines fundamental aspects of mixing by cutting and shuffling.
Piecewise-linear maps and their application to financial markets
Directory of Open Access Journals (Sweden)
Fabio Tramontana
2016-08-01
Full Text Available The goal of this paper is to review some work on agent-based financial market models in which the dynamics is driven by piecewise-linear maps. As we will see, such models allow deep analytical insights into the functioning of financial markets, may give rise to unexpected dynamics effects, allow explaining a number of important stylized facts of financial markets, and offer novel policy recommendations. However, much remains to be done in this rather new research field. We hope that our paper attracts more scientists to this area.
A Parallel Encryption Algorithm Based on Piecewise Linear Chaotic Map
Directory of Open Access Journals (Sweden)
Xizhong Wang
2013-01-01
Full Text Available We introduce a parallel chaos-based encryption algorithm for taking advantage of multicore processors. The chaotic cryptosystem is generated by the piecewise linear chaotic map (PWLCM. The parallel algorithm is designed with a master/slave communication model with the Message Passing Interface (MPI. The algorithm is suitable not only for multicore processors but also for the single-processor architecture. The experimental results show that the chaos-based cryptosystem possesses good statistical properties. The parallel algorithm provides much better performance than the serial ones and would be useful to apply in encryption/decryption file with large size or multimedia.
Lower Bounds of the Discretization for Piecewise Polynomials
Lin, Qun; Xu, Jinchao
2011-01-01
Assume that $V_h$ is a space of piecewise polynomials of degree less than $r\\geq 1$ on a family of quasi-uniform triangulation of size $h$. Then the following well-known upper bound holds for a sufficiently smooth function $u$ and $p\\in [1, \\infty]$ $$ \\inf_{v_h\\in V_h}\\|u-v_h\\|_{j,p,\\Omega,h} \\le C h^{r-j} |u|_{r,p,\\Omega},\\quad 0\\le j\\le r. $$ In this paper, we prove that, roughly speaking, if $u\
Bifurcation Structures in a Bimodal Piecewise Linear Map
Directory of Open Access Journals (Sweden)
Anastasiia Panchuk
2017-05-01
Full Text Available In this paper we present an overview of the results concerning dynamics of a piecewise linear bimodal map. The organizing principles of the bifurcation structures in both regular and chaotic domains of the parameter space of the map are discussed. In addition to the previously reported structures, a family of regions closely related to the so-called U-sequence is described. The boundaries of distinct regions belonging to these structures are obtained analytically using the skew tent map and the map replacement technique.
An I(2) cointegration model with piecewise linear trends
DEFF Research Database (Denmark)
Kurita, Takamitsu; Bohn Nielsen, Heino; Rahbæk, Anders
2011-01-01
This paper presents likelihood analysis of the I(2) cointegrated vector autoregression which allows for piecewise linear deterministic terms. Limiting behaviour of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio...... statistic for the cointegration ranks, extending Nielsen and Rahbek. The provided asymptotic theory extends also the results in Johansen et al. where asymptotic inference is discussed in detail for one of the cointegration parameters. An empirical analysis of US consumption, income and wealth, 1965...
Piecewise linear manifolds: Einstein metrics and Ricci flows
Schrader, Robert
2016-05-01
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. Dedicated to Ludwig Faddeev on the occasion of his 80th birthday.
Ultra-high-frequency piecewise-linear chaos using delayed feedback loops
Cohen, Seth D.; Rontani, Damien; Gauthier, Daniel J.
2012-12-01
We report on an ultra-high-frequency (>1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar.
Mohanty, B. P.; Bowman, R. S.; Hendrickx, J. M. H.; van Genuchten, M. T.
Modeling water flow in macroporous field soils near saturation has been a major challenge in vadose zone hydrology. Using in situ and laboratory measurements, we developed new piecewise-continuous soil water retention and hydraulic conductivity functions to describe preferential flow in tile drains under a flood-irrigated agricultural field in Las Nutrias, New Mexico. After incorporation into a two-dimensional numerical flow code, CHAIN_2D, the performance of the new piecewise-continuous hydraulic functions was compared with that of the unimodal van Genuchten-Mualem model and with measured tile-flow data at the field site during a number of irrigation events. Model parameters were collected/estimated by site characterization (e.g., soil texture, surface/subsurface saturated/unsaturated soil hydraulic property measurements), as well as by local and regional-scale hydrologic monitoring (including the use of groundwater monitoring wells, piezometers, and different surface-irrigation and subsurface-drainage measurement systems). Comparison of numerical simulation results with the observed tile flow indicated that the new piecewise-continuous hydraulic functions generally predicted preferential flow in the tile drain reasonably well following all irrigation events at the field site. Also, the new bimodal soil water retention and hydraulic conductivity functions performed better than the unimodal van Genuchten-Mualem functions in terms of describing the observed flow regime at the field site.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-01
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan
2016-12-28
The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.
Gortler, Steven J; Liu, Ligang; Thurston, Dylan P
2010-01-01
We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.
Directory of Open Access Journals (Sweden)
Steven J. Gortler
2013-12-01
Full Text Available We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding. Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1-vertex-connected. We also show neighborhood affine rigidity of a graph implies universal rigidity of its squared graph. Our results, and affine rigidity more generally, have natural applications in point registration and localization, as well as connections to manifold learning.
Video Enhancement Using Adaptive Spatio-Temporal Connective Filter and Piecewise Mapping
Directory of Open Access Journals (Sweden)
Wang Chao
2008-01-01
Full Text Available This paper presents a novel video enhancement system based on an adaptive spatio-temporal connective (ASTC noise filter and an adaptive piecewise mapping function (APMF. For ill-exposed videos or those with much noise, we first introduce a novel local image statistic to identify impulse noise pixels, and then incorporate it into the classical bilateral filter to form ASTC, aiming to reduce the mixture of the most two common types of noises—Gaussian and impulse noises in spatial and temporal directions. After noise removal, we enhance the video contrast with APMF based on the statistical information of frame segmentation results. The experiment results demonstrate that, for diverse low-quality videos corrupted by mixed noise, underexposure, overexposure, or any mixture of the above, the proposed system can automatically produce satisfactory results.
Video Enhancement Using Adaptive Spatio-Temporal Connective Filter and Piecewise Mapping
Directory of Open Access Journals (Sweden)
Shi-Qiang Yang
2008-06-01
Full Text Available This paper presents a novel video enhancement system based on an adaptive spatio-temporal connective (ASTC noise filter and an adaptive piecewise mapping function (APMF. For ill-exposed videos or those with much noise, we first introduce a novel local image statistic to identify impulse noise pixels, and then incorporate it into the classical bilateral filter to form ASTC, aiming to reduce the mixture of the most two common types of noisesÃ¢Â€Â”Gaussian and impulse noises in spatial and temporal directions. After noise removal, we enhance the video contrast with APMF based on the statistical information of frame segmentation results. The experiment results demonstrate that, for diverse low-quality videos corrupted by mixed noise, underexposure, overexposure, or any mixture of the above, the proposed system can automatically produce satisfactory results.
Liu, Xuele
2016-01-01
Finding new phase is a fundamental task in physics. Landau's theory explained the deep connection between symmetry breaking and phase transition commonly occurring in magnetic, superconducting and super uid systems. The discovery of the quantum Hall effect led to Z topological phases which could be different for same symmetry and are characterized by the discrete values of the Berry phases. By studying 1D trimer lattices we report new phases characterized by Berry phases which are piecewise continuous rather than discrete numbers. The phase transition occurs at the discontinuity point. With time-dependent changes, trimer lattices also give a 2D phases characterized by very specific 2D Berry phases of half period. These Berry phases change smoothly within a phase while change discontinuously at the transition point. We further demonstrate the existence of adiabatic pumping for each phase and gain assisted enhanced pumping. The non-reciprocity of the pumping process makes the system a good optical diode.
Structure of classical affine and classical affine fractional W-algebras
Energy Technology Data Exchange (ETDEWEB)
Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr [Department of Mathematical Sciences, Seoul National University, GwanAkRo 1, Gwanak-Gu, Seoul 151-747 (Korea, Republic of)
2015-01-15
We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.
High resolution A/D conversion based on piecewise conversion at lower resolution
Terwilliger, Steve
2012-06-05
Piecewise conversion of an analog input signal is performed utilizing a plurality of relatively lower bit resolution A/D conversions. The results of this piecewise conversion are interpreted to achieve a relatively higher bit resolution A/D conversion without sampling frequency penalty.
Piecewise Linear-Linear Latent Growth Mixture Models with Unknown Knots
Kohli, Nidhi; Harring, Jeffrey R.; Hancock, Gregory R.
2013-01-01
Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of…
Digital architecture for a piecewise-linear arbitrary-waveform generator
Indian Academy of Sciences (India)
VICTOR M JIMENEZ-FERNANDEZ; HECTOR VAZQUEZ-LEAL; PABLO S LUNA-LOZANO; J L VAZQUEZ-BELTRAN; G GARCIA-SANTIAGO; E VALDES-ORTEGA
2016-08-01
In this paper a digital architecture for generating piecewise-linear arbitrary waveforms is presented. The proposed design is able to generate a piecewise-linear periodic signal by only using a minimum number of input data (breakpoints). The generator circuit implements a hybrid scheme which takes advantage of two methods: the purely piecewise-linear interpolation and the lookup-table structure. From the piecewise-linear method exploits the characteristic of a reduced memory requirement as well as the capability of automatically construct a waveform by repetitive (iterative) function evaluations. From lookup-table makes use of the simplicity in hardware implementation and the higher processing speed. In order to verify the performance of thisproposal, three piecewise-linear waveforms have been successfully implemented in a ATMEGA32 microcontroller. Experimental results show a fast execution speed and a reduced memory demand in the proposed circuit realization.
Some Researches on Real Piecewise Algebraic Curves%实分片代数曲线的某些研究
Institute of Scientific and Technical Information of China (English)
朱春钢; 王仁宏
2008-01-01
The piecewise algebraic curve,defined by a bivariate spline,is a generalization of the classical algebraic curve.In this palper,we present some researches on real piecewise algebraic curves using elementary algebra.A real piecewise algebraic curve is studied according to the fact that a real spline for the curve is indefinite,definite or semidefinite(nondefinite).Moreover,the isolated points of a real piecewise algebraic curve is also discussed.
Directory of Open Access Journals (Sweden)
Hwanyub Joo
2015-01-01
Full Text Available This paper addresses the output regulation problem of synchronous buck converters with piecewise-constant load fluctuations via linear parameter varying (LPV control scheme. To this end, an output-error state-space model is first derived in the form of LPV systems so that it can involve a mismatch error that temporally arises from the process of generating a feedforward control. Then, to attenuate the mismatch error in parallel with improving the transient behavior of the converter, this paper proposes an LMI-based stabilization condition capable of achieving both H∞ and pole-placement objectives. Finally, the simulation and experimental results are provided to show the validity of our approach.
Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression
Bressloff, Paul C.
2011-01-01
We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary. © 2011 Society for Industrial and Applied Mathematics.
Gultekin, Kemal
2015-01-01
In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schroedinger, we construct and analyze different affine gravities based on determinants of the Ricci tensor, torsion tensor, Riemann tensor and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to construction of the affine connection in terms of curvature and torsion tensors. Our solutions of the dynamical equations show that curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor.
Yao, Weigang; Liou, Meng-Sing
2016-08-01
To preserve nonlinearity of a full-order system over a range of parameters of interest, we propose an accurate and robust nonlinear modeling approach by assembling a set of piecewise linear local solutions expanded about some sampling states. The work by Rewienski and White [1] on micromachined devices inspired our use of piecewise linear local solutions to study nonlinear unsteady aerodynamics. These local approximations are assembled via nonlinear weights of radial basis functions. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving with different pitching motions, specifically AGARD's CT2 and CT5 problems [27], in which the flows exhibit different nonlinear behaviors. Furthermore, application of the developed aerodynamic model to a two-dimensional aero-elastic system proves the approach is capable of predicting limit cycle oscillations (LCOs) by using AGARD's CT6 [28] as a benchmark test. All results, based on inviscid solutions, confirm that our nonlinear model is stable and accurate, against the full model solutions and measurements, and for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robust for inputs that considerably depart from the base trajectory in form and magnitude. This modeling provides a very efficient way for predicting unsteady flowfields with varying parameters because it needs only a tiny fraction of the cost of a full-order modeling for each new condition-the more cases studied, the more savings rendered. Hence, the present approach is especially useful for parametric studies, such as in the case of design optimization and exploration of flow phenomena.
Detecting ecological breakpoints: a new tool for piecewise regression
Directory of Open Access Journals (Sweden)
Alessandro Ferrarini
2011-06-01
Full Text Available Simple linear regression tries to determine a linear relationship between a given variable X (predictor and a dependent variable Y. Since most of the environmental problems involve complex relationships, X-Y relationship is often better modeled through a regression where, instead of fitting a single straight line to the data, the algorithm allows the fitting to bend. Piecewise regressions just do it, since they allow emphasize local, instead of global, rules connecting predictor and dependent variables. In this work, a tool called RolReg is proposed as an implementation of Krummel's method to detect breakpoints in regression models. RolReg, which is freely available upon request from the author, could useful to detect proper breakpoints in ecological laws.
The Piecewise Cubic Method (PCM) for computational fluid dynamics
Lee, Dongwook; Faller, Hugues; Reyes, Adam
2017-07-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges at fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme on a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
The Piecewise Cubic Method (PCM) for Computational Fluid Dynamics
Lee, Dongwook; Reyes, Adam
2016-01-01
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed solutions are evolved in time with a fourth-order accuracy by tracing the characteristics of the cubic polynomials. As a result, our temporal update scheme provides a significantly simpler and computationally more efficient approach in achieving fourth order accuracy in time, relative to the comparable fourth-order Runge-Kutta method. We demonstrate that the solutions of PCM converges in fifth-order in solving 1D smooth flows described by hyperbolic conservation laws. We test the new scheme in a range of numerical experiments, including both gas dynamics and magnetohydrodynamics applications in multiple spatial dimensions.
A new approach to piecewise linear Wilson lines
Van der Veken, Frederik F
2014-01-01
Wilson lines are key objects in many QCD calculations. They are parallel transporters of the gauge field that can be used to render non-local operator products gauge invariant, which is especially useful for calculations concerning validation of factorization schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their Wilson segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their color structure. This framework allows one to easily switch results between different Wilson line structures, which is helpful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.
Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?
Dubey, Awadhesh K; Procaccia, Itamar; Shor, Carmel A B Z; Singh, Murari
2016-02-26
Quasistatic strain-controlled measurements of stress versus strain curves in macroscopic amorphous solids result in a nonlinear-looking curve that ends up either in mechanical collapse or in a steady state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress versus strain curves and propose that a useful description of the mechanical response is given by a stress (or strain) -dependent shear modulus for which a theoretical evaluation exists. The elastic response is piecewise linear rather than nonlinear.
Piecewise Mapping in HEVC Lossless Intra-prediction Coding.
Sanchez, Victor; Auli-Llinas, Francesc; Serra-Sagrista, Joan
2016-05-19
The lossless intra-prediction coding modality of the High Efficiency Video Coding (HEVC) standard provides high coding performance while allowing frame-by-frame basis access to the coded data. This is of interest in many professional applications such as medical imaging, automotive vision and digital preservation in libraries and archives. Various improvements to lossless intra-prediction coding have been proposed recently, most of them based on sample-wise prediction using Differential Pulse Code Modulation (DPCM). Other recent proposals aim at further reducing the energy of intra-predicted residual blocks. However, the energy reduction achieved is frequently minimal due to the difficulty of correctly predicting the sign and magnitude of residual values. In this paper, we pursue a novel approach to this energy-reduction problem using piecewise mapping (pwm) functions. Specifically, we analyze the range of values in residual blocks and apply accordingly a pwm function to map specific residual values to unique lower values. We encode appropriate parameters associated with the pwm functions at the encoder, so that the corresponding inverse pwm functions at the decoder can map values back to the same residual values. These residual values are then used to reconstruct the original signal. This mapping is, therefore, reversible and introduces no losses. We evaluate the pwm functions on 4×4 residual blocks computed after DPCM-based prediction for lossless coding of a variety of camera-captured and screen content sequences. Evaluation results show that the pwm functions can attain maximum bit-rate reductions of 5.54% and 28.33% for screen content material compared to DPCM-based and block-wise intra-prediction, respectively. Compared to Intra- Block Copy, piecewise mapping can attain maximum bit-rate reductions of 11.48% for camera-captured material.
DEFF Research Database (Denmark)
Buchardt, Kristian
2016-01-01
Affine processes possess the property that expectations of exponential affine transformations are given by a set of Riccati differential equations, which is the main feature of this popular class of processes. In this paper we generalise these results for expectations of more general transformati...
Schwer, Petra N.
2009-01-01
We prove equivalence of certain axiom sets for affine buildings. Along the lines a purely combinatorial proof of the existence of a spherical building at infinity is given. As a corollary we obtain that ``being an affine building'' is independent of the metric structure of the space.
Interior region-of-interest reconstruction using a small, nearly piecewise constant subregion.
Taguchi, Katsuyuki; Xu, Jingyan; Srivastava, Somesh; Tsui, Benjamin M W; Cammin, Jochen; Tang, Qiulin
2011-03-01
To develop a method to reconstruct an interior region-of-interest (ROI) image with sufficient accuracy that uses differentiated backprojection (DBP) projection onto convex sets (POCS) [H. Kudo et al., "Tiny a priori knowledge solves the interior problem in computed tomography," Phys. Med. Biol. 53, 2207-2231 (2008)] and a tiny knowledge that there exists a nearly piecewise constant subregion. The proposed method first employs filtered backprojection to reconstruct an image on which a tiny region P with a small variation in the pixel values is identified inside the ROI. Total variation minimization [H. Yu and G. Wang, "Compressed sensing based interior tomography," Phys. Med. Biol. 54, 2791-2805 (2009); W. Han et al., "A general total variation minimization theorem for compressed sensing based interior tomography," Int. J. Biomed. Imaging 2009, Article 125871 (2009)] is then employed to obtain pixel values in the subregion P, which serve as a priori knowledge in the next step. Finally, DBP-POCS is performed to reconstruct f(x,y) inside the ROI. Clinical data and the reconstructed image obtained by an x-ray computed tomography system (SOMATOM Definition; Siemens Healthcare) were used to validate the proposed method. The detector covers an object with a diameter of approximately 500 mm. The projection data were truncated either moderately to limit the detector coverage to Ø 350 mm of the object or severely to cover Ø199 mm. Images were reconstructed using the proposed method. The proposed method provided ROI images with correct pixel values in all areas except near the edge of the ROI. The coefficient of variation, i.e., the root mean square error divided by the mean pixel values, was less than 2.0% or 4.5% with the moderate or severe truncation cases, respectively, except near the boundary of the ROI. The proposed method allows for reconstructing interior ROI images with sufficient accuracy with a tiny knowledge that there exists a nearly piecewise constant
Institute of Scientific and Technical Information of China (English)
Lifeng XI
2008-01-01
In this paper,it is proved that any self-affine set satisfying the strong separation condition is uniformly porous.The author constructs a self-affine set which is not porous,although the open set condition holds.Besides,the author also gives a C1 iterated function system such that its invariant set is not porous.
Nther-type theorem of piecewise algebraic curves on quasi-cross-cut partition
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Nther’s theorem of algebraic curves plays an important role in classical algebraic geometry. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nther-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nther-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.
N(o)ther-type theorem of piecewise algebraic curves on quasi-cross-cut partition
Institute of Scientific and Technical Information of China (English)
ZHU ChunGang; WANG RenHong
2009-01-01
Nother's theorem of algebraic curves plays an important role in classical algebraic geome-try. As the zero set of a bivariate spline, the piecewise algebraic curve is a generalization of the classical algebraic curve. Nother-type theorem of piecewise algebraic curves is very important to construct the Lagrange interpolation sets for bivariate spline spaces. In this paper, using the characteristics of quasi-cross-cut partition, properties of bivariate splines and results in algebraic geometry, the Nother-type theorem of piecewise algebraic curves on the quasi-cross-cut is presented.
Zhang, Lijun; Zhao, Jiemei; Qi, Xue; Jia, Heming
2013-06-01
The problem of tracking control for a class of uncertain non-affine discrete-time nonlinear systems with internal dynamics is addressed. The fixed point theorem is first employed to ensure the control problem in question is solvable and well-defined. Based on it, an adaptive output feedback control scheme based on neural network (NN) is presented. The proposed control algorithm consists of two parts: a dynamic compensator is introduced to stabilise the linear portion of the tracking error system; a single-hidden-layer neural network (SHL NN) approximation mechanism is introduced to cancel the uncertainties resulting from the non-affine function, where the recursive weight update rules of NN estimation are derived from the discrete-time version of Lyapunov control theory. Ultimate boundedness of the error signals is shown through Lyapunov's direct method and the discrete-time version of input-to-state stability (ISS) theory. Finally, a model of automatical underwater vehicle (AUV) is considered to show the effectiveness of the proposed control scheme.
Energy Technology Data Exchange (ETDEWEB)
Woodward, P. R.
2003-03-26
This report summarizes the results of the project entitled, ''Piecewise-Parabolic Methods for Parallel Computation with Applications to Unstable Fluid Flow in 2 and 3 Dimensions'' This project covers a span of many years, beginning in early 1987. It has provided over that considerable period the core funding to my research activities in scientific computation at the University of Minnesota. It has supported numerical algorithm development, application of those algorithms to fundamental fluid dynamics problems in order to demonstrate their effectiveness, and the development of scientific visualization software and systems to extract scientific understanding from those applications.
Energy Technology Data Exchange (ETDEWEB)
Woodward, P. R.
2003-03-26
This report summarizes the results of the project entitled, ''Piecewise-Parabolic Methods for Parallel Computation with Applications to Unstable Fluid Flow in 2 and 3 Dimensions'' This project covers a span of many years, beginning in early 1987. It has provided over that considerable period the core funding to my research activities in scientific computation at the University of Minnesota. It has supported numerical algorithm development, application of those algorithms to fundamental fluid dynamics problems in order to demonstrate their effectiveness, and the development of scientific visualization software and systems to extract scientific understanding from those applications.
Fraschini, F; Stankov, B
1994-01-01
Currently, the melatonin receptor is depicted as a membrane-associated protein, linked to a guanine nucleotide-binding protein (G-protein), and thus the melatonin receptor represents a member of a receptor superfamily, acting through G-proteins in the first step of their signal-transduction pathways. Although on a number of occasions specific binding of radioactive melatonin has been demonstrated in a wide variety of tissues and organs, to date, high affinity G-protein-regulated melatonin binding sites, suggestive for a functional melatonin receptor, have been convincingly confirmed in the brain only. There is a significant species variation in the distribution of the melatonin receptor in the vertebrate brain. The limited number of studies prevents any definitive conclusion in terms of phylogeny, though generally speaking, the lower vertebrates' brains tend to express melatonin receptors with wider distribution. Two sites have been consistently found to express high density of melatonin receptors: the pars tuberalis of the adenohypophysis and the hypothalamic suprachiasmatic nuclei (SCN). It must be pointed out, however, that there are some exceptions. Binding in the human pars tuberalis has not been reported, and apparently, the sheep and the mustelids' suprachiasmatic nuclei do not express detectable binding. The function of melatonin in pars tuberalis is unclear, and the control of the synthesis (and release) of paracrine factors that act at site(s) distant from the melatonin target cells, have been suggested.(ABSTRACT TRUNCATED AT 250 WORDS)
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Heegaard, Niels H H
2009-06-01
The journal Electrophoresis has greatly influenced my approaches to biomolecular affinity studies. The methods that I have chosen as my main tools to study interacting biomolecules--native gel and later capillary zone electrophoresis--have been the topic of numerous articles in Electrophoresis. Below, the role of the journal in the development and dissemination of these techniques and applications reviewed. Many exhaustive reviews on affinity electrophoresis and affinity CE have been published in the last few years and are not in any way replaced by the present deliberations that are focused on papers published by the journal.
Affine density in wavelet analysis
Kutyniok, Gitta
2007-01-01
In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems. This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
El Aroudi, Abdelali
2014-05-01
Recently, nonlinearities have been shown to play an important role in increasing the extracted energy of vibration-based energy harvesting systems. In this paper, we study the dynamical behavior of a piecewise linear (PWL) spring-mass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. Different configurations of the PWL model and their corresponding state-space regions are derived. Then, from this PWL model, extensive numerical simulations are carried out by computing time-domain waveforms, state-space trajectories and frequency responses under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Filippov method, Poincaré map modeling and finite difference method (FDM). The Floquet multipliers are calculated using these three approaches and a good concordance is obtained among them. The performance of the system in terms of the harvested energy is studied by considering both purely harmonic excitation and a noisy vibrational source. A frequency-domain analysis shows that the harvested energy could be larger at low frequencies as compared to an equivalent linear system, in particular, for relatively low excitation intensities. This could be an advantage for potential use of this system in low frequency ambient vibrational-based energy harvesting applications. © 2014 World Scientific Publishing Company.
Wu, Ailong; Liu, Ling; Huang, Tingwen; Zeng, Zhigang
2017-01-01
Neurodynamic system is an emerging research field. To understand the essential motivational representations of neural activity, neurodynamics is an important question in cognitive system research. This paper is to investigate Mittag-Leffler stability of a class of fractional-order neural networks in the presence of generalized piecewise constant arguments. To identify neural types of computational principles in mathematical and computational analysis, the existence and uniqueness of the solution of neurodynamic system is the first prerequisite. We prove that the existence and uniqueness of the solution of the network holds when some conditions are satisfied. In addition, self-active neurodynamic system demands stable internal dynamical states (equilibria). The main emphasis will be then on several sufficient conditions to guarantee a unique equilibrium point. Furthermore, to provide deeper explanations of neurodynamic process, Mittag-Leffler stability is studied in detail. The established results are based on the theories of fractional differential equation and differential equation with generalized piecewise constant arguments. The derived criteria improve and extend the existing related results.
Energy Technology Data Exchange (ETDEWEB)
Gueltekin, Kemal [Izmir Institute of Technology, Department of Physics, Izmir (Turkey)
2016-03-15
In this study, we give a thorough analysis of a general affine gravity with torsion. After a brief exposition of the affine gravities considered by Eddington and Schroedinger, we construct and analyze different affine gravities based on the determinants of the Ricci tensor, the torsion tensor, the Riemann tensor, and their combinations. In each case we reduce equations of motion to their simplest forms and give a detailed analysis of their solutions. Our analyses lead to the construction of the affine connection in terms of the curvature and torsion tensors. Our solutions of the dynamical equations show that the curvature tensors at different points are correlated via non-local, exponential rescaling factors determined by the torsion tensor. (orig.)
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Zhang, Yiwei
2011-01-01
We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\\mathbb{R}^d$. This class of maps unifies piecewise isometries (PWIs) and piecewise hyperbolic maps where Lebesgue measure is locally preserved. In particular for PWIs, we use a functional approach to explore the relationship between topological transitivity and uniqueness of ACIPs, especially those measures with bounded variation densities. Our results "partially" answer one of the fundamental questions posed in \\cite{Goetz03} - determine all invariant non-atomic probability Borel measures in piecewise rotations. When reducing to interval exchange transformations (IETs), we demonstrate that for non-uniquely ergodic IETs with two or more ACIPs, these ACIPs have very irregular densities (namely of unbounded variation and discontinuous everywhere) and intermingle with each other.
Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes
Herencia-Zapana, Heber; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.
Directory of Open Access Journals (Sweden)
Cheryl M Vahling-Armstrong
Full Text Available The Znu system, encoded for by znuABC, can be found in multiple genera of bacteria and has been shown to be responsible for the import of zinc under low zinc conditions. Although this high-affinity uptake system is known to be important for both growth and/or pathogenesis in bacteria, it has not been functionally characterized in a plant-associated bacterium. A single homologue of this system has been identified in the plant endosymbiont, Sinorhizobium meliloti, while two homologous systems were found in the destructive citrus pathogen, Candidatus Liberibacter asiaticus. To understand the role of these protein homologues, a complementation assay was devised allowing the individual genes that comprise the system to be assayed independently for their ability to reinstate a partially-inactivated Znu system. Results from the assays have demonstrated that although all of the genes from S. meliloti were able to restore activity, only one of the two Ca. Liberibacter asiaticus encoded gene clusters contained genes that were able to functionally complement the system. Additional analysis of the gene clusters reveals that distinct modes of regulation may also exist between the Ca. Liberibacter asiaticus and S. meliloti import systems despite the intracellular-plant niche common to both of these bacteria.
Caneco, Acilina; Rocha, Jose; Gracio, Clara
2009-01-01
In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupl...
Decomposition of piecewise-polynomial model of a predistorter for power amplifier
2015-01-01
Decomposition of piecewise-polynomial model of a predistorter has been performed taking into account the alteration dynamics of the complex envelope’s magnitude for the signal, which is converted by an amplifier. Decomposition model provides higher accuracy of nonlinear distortions compensation for signals in the amplifier compared with piecewise-polynomial model of a predistorter. Comparative analysis of predistorters’ models has been carried out for the linearization of the Wiener–Hammerste...
Wavelets centered on a knot sequence: piecewise polynomial wavelets on a quasi-crystal lattice
Atkinson, Bruce W; Geronimo, Jeffrey S; Hardin, Douglas P
2011-01-01
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\\tau$-integers where $\\tau$ is the golden-mean. The resulting spaces then generate a multiresolution analysis of $L^2(\\mathbf{R})$ with scaling factor $\\tau$.
Optimal Piecewise Linear Basis Functions in Two Dimensions
Energy Technology Data Exchange (ETDEWEB)
Brooks III, E D; Szoke, A
2009-01-26
We use a variational approach to optimize the center point coefficients associated with the piecewise linear basis functions introduced by Stone and Adams [1], for polygonal zones in two Cartesian dimensions. Our strategy provides optimal center point coefficients, as a function of the location of the center point, by minimizing the error induced when the basis function interpolation is used for the solution of the time independent diffusion equation within the polygonal zone. By using optimal center point coefficients, one expects to minimize the errors that occur when these basis functions are used to discretize diffusion equations, or transport equations in optically thick zones (where they approach the solution of the diffusion equation). Our optimal center point coefficients satisfy the requirements placed upon the basis functions for any location of the center point. We also find that the location of the center point can be optimized, but this requires numerical calculations. Curiously, the optimum center point location is independent of the values of the dependent variable on the corners only for quadrilaterals.
Piecewise linear hypersurfaces using the marching cubes algorithm
Roberts, Jonathan C.; Hill, Steve
1999-03-01
Surface visualization is very important within scientific visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specified objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects. These surfaces (or contours) are often formed from a set of connected triangles (or lines). These piecewise segments represent the simplest non-degenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3- simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n-1 dimensional simplices. This lattice of connected simplices may be calculated over a set of adjacent n dimensional cubes, via for example the Marching Cubes Algorithm. We propose that the methods of this local-cell tiling method may be usefully- applied to four dimensions and potentially to N-dimensions. Thus, we organize the large number of traversal cases and major cases; introduce the notion of a sub-case (that enables the large number of cases to be further reduced); and describe three methods for implementing the Marching Cubes lookup table in four-dimensions.
Piecewise linear models for the quasiperiodic transition to chaos
Campbell, D K; Tresser, C; Uherka, D J; Campbell, David K; Galeeva, Roza; Tresser, Charles; Uherka, David J
1995-01-01
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on mode...
Piecewise linear mapping algorithm for SAR raw data compression
Institute of Scientific and Technical Information of China (English)
QI HaiMing; YU WeiDong; CHEN Xi
2008-01-01
When the saturation degree (SD) of space-borne SAR raw data is high, the performance of conventional block adaptive quantization (BAQ) deteriorates obviously. In order to overcome the drawback, this paper studies the mapping between the average signal magnitude (ASM) and the standard deviation of the input signal (SDIS) to the A/D from the original reference. Then, it points out the mistake of the mapping and introduces the concept of the standard deviation of the output signal (SDOS) from the A/D. After that, this paper educes the mapping between the ASM and SDOS from the A/D. Monte-Carlo experiment shows that none of the above two mappings is the optimal in the whole set of SD. Thus, this paper proposes the concept of piecewise linear mapping and the searching algorithm in the whole set of SD. According to the linear part, this paper gives the certification and analytical value of k and for nonlinear part, and utilizes the searching algorithm mentioned above to search the corresponding value of k. Experimental results based on simulated data and real data show that the performance of new algorithm is better than conventional BAQ when raw data is in heavy SD.
One Line or Two? Perspectives on Piecewise Regression
Energy Technology Data Exchange (ETDEWEB)
R.P. Ewing; D.W. Meek
2006-10-12
Sometimes we are faced with data that could reasonably be represented either as a single line, or as two or more line segments. How do we identify the best breakpoint(s), and decide how many segments are ''really'' present? Most of us are taught to distrust piecewise regression, because it can be easily abused. The best method for identifying the breakpoint varies according to specifics of the data; for example, the minimum sum of squares method excels for ''well-behaved'' data. In some cases, hidden Markov methods are more likely to succeed than are more ''obvious'' methods. Likewise, the most appropriate method for deciding between one or two lines depends on your expectations and understanding of the data: an unexpected break requires more justification than an expected one, and some decision criteria (e.g., the Akaike Information Criterion) are less strict than others (e.g., the Bayesian Information Criterion). This presentation will review some options and make specific, practical recommendations.
Affine and degenerate affine BMW algebras: Actions on tensor space
Daugherty, Zajj; Virk, Rahbar
2012-01-01
The affine and degenerate affine Birman-Murakami-Wenzl (BMW) algebras arise naturally in the context of Schur-Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine and cyclotomic Hecke algebras, and their degenerate versions are quotients. In this paper we explain how the affine and degenerate affine BMW algebras are tantalizers (tensor power centralizer algebras) by defining actions of the affine braid group and the degenerate affine braid algebra on tensor space and showing that, in important cases, these actions induce actions of the affine and degenerate affine BMW algebras. We then exploit the connection to quantum groups and Lie algebras to determine universal parameters for the affine and degenerate affine BMW algebras. Finally, we show that the universal parameters are central elements--the higher Casimir elements for orthogonal and symplectic enveloping algebras and quantum groups.
The N(o)ther and Riemann-Roch type theorems for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
Yi-sheng LAI; Ren-hong WANG
2007-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, the N(o)ther type theorems for Cμ piecewise algebraic curves are obtained.The theory of the linear series of sets of places on the piecewise algebraic curve is also established.In this theory, singular cycles are put into the linear series, and a complete series of the piecewise algebraic curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the algebraic curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions,and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cμ piecewise algebraic curves and the degree, the genus and the smoothness of the curves, hence the Riemann-Roch type theorem of the Cμpiecewise algebraic curve is established.
The Nother and Riemann-Roch type theorems for piecewise algebraic curve
Institute of Scientific and Technical Information of China (English)
2007-01-01
A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. In this paper, the Nother type theorems for Cμpiecewise algebraic curves are obtained. The theory of the linear series of sets of places on the piecewise algebraic curve is also established. In this theory, singular cycles are put into the linear series, and a complete series of the piecewise algebraic curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the algebraic curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions, and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cμpiecewise algebraic curves and the degree, the genus and the smoothness of the curves, hence the Riemann-Roch type theorem of the Cμpiecewise algebraic curve is established.
Schumacher, R.; Wahl, S.A.
2015-01-01
The design of microbial production processes relies on rational choices for metabolic engineering of the production host and the process conditions. These require a systematic and quantitative understanding of cellular regulation. Therefore, a novel method for dynamic flux identification using quant
分片旋转的Sigma-Delta模型的全局吸引子%Global Attraction in the Piecewise Rotation of the Sigma-Delta Modulator
Institute of Scientific and Technical Information of China (English)
余荣忠; 傅新楚; 袁利国
2005-01-01
This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise rotation, and by geometric analysis,the authors give a simpler and more sufficient proof of the conjecture, than the one presented by Deane and published in Dynamical Systems, 2002,17: 377 - 388.
On the Well-posedness of the PWM Control System
Institute of Scientific and Technical Information of China (English)
FAN Qi-fu; SHI Song-jiao
2006-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems.This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition lexicographic inequalities and the smooth continuation property of solutions.Furthermore,it is clear that when carrier signal h(t)=0,closed-loop pulse-width modulation (PWM) DC-DC converters are not well posed,and when some condition is satisfied,the closed-loop PWM DC-DC converters with a P controller are well posed.
Effect of stochastically moving border on basins of attraction in a class of piecewise smooth maps
Mandal, Dhrubajyoti; Banerjee, Soumitro
2017-07-01
Determination of the basin of attraction of an attractor plays an important role in understanding the dynamics of a system. In all the existing literature, the basin of attraction of any attractor has been described to be deterministic. In this paper we show the existence of a non-deterministic basin of attraction of an attractor. We have considered a piecewise smooth (PWS) one-dimensional map, having stochastically varying border, which is allowed to move in a small bounded region of the phase space while retaining the deterministic dynamics on each compartment of the phase space. In case of this type of systems there exists a region in the phase space with the property that orbits starting from a single point lying inside this region do not display the same property of convergence or divergence, i.e., one may converge while another may diverge. In other words, the convergence or divergence of an orbit starting from a point inside this region is a probabilistic event, and the probabilities of convergence and divergence are both non-zero. We also derive the upper and lower bounds of the corresponding probability curves. Since all physical systems contain noise, the occurrence of such non-deterministic basin of attraction is a definite possibility, if the noise affects the position of the border. This may lead to dangerous consequences, as a region of the basin of attraction of an attractor may become non-deterministic, with a non-zero probability of divergence of orbits starting inside it.
Theoretical proton affinity and fluoride affinity of nerve agent VX.
Bera, Narayan C; Maeda, Satoshi; Morokuma, Keiji; Viggiano, Al A
2010-12-23
Proton affinity and fluoride affinity of nerve agent VX at all of its possible sites were calculated at the RI-MP2/cc-pVTZ//B3LYP/6-31G* and RI-MP2/aug-cc-pVTZ//B3LYP/6-31+G* levels, respectively. The protonation leads to various unique structures, with H(+) attached to oxygen, nitrogen, and sulfur atoms; among which the nitrogen site possesses the highest proton affinity of -ΔE ∼ 251 kcal/mol, suggesting that this is likely to be the major product. In addition some H(2), CH(4) dissociation as well as destruction channels have been found, among which the CH(4) + [Et-O-P(═O)(Me)-S-(CH(2))(2)-N(+)(iPr)═CHMe] product and the destruction product forming Et-O-P(═O)(Me)-SMe + CH(2)═N(+)(iPr)(2) are only 9 kcal/mol less stable than the most stable N-protonated product. For fluoridization, the S-P destruction channel to give Et-O-P(═O)(Me)(F) + [S-(CH(2))(2)-N-(iPr)(2)](-) is energetically the most favorable, with a fluoride affinity of -ΔE ∼ 44 kcal. Various F(-) ion-molecule complexes are also found, with the one having F(-) interacting with two hydrogen atoms in different alkyl groups to be only 9 kcal/mol higher than the above destruction product. These results suggest VX behaves quite differently from surrogate systems.
Suzuki, Kimihiro; Kawamura, Masahide; Mineo, Midori; Shinohara, Tadashi; Kataharada, Koji; Okada, Makoto; Takada, Kunio; Miyawaki, Shoji; Ohsuzu, Fumitaka
2002-01-01
The aim of this study was to clarify the effects of anti-dsDNA antibodies on the titer and the nuclear staining pattern(s) in a fluorescent antinuclear antibody (FANA) assay using HEp-2 cells. Anti-dsDNA derived from 14 patients with systemic lupus erythematosus (SLE) was individually affinity-purified. The anti-dsDNA titer of the purified anti-dsDNA solution was measured by radioimmunoassay (RIA) or by enzyme-linked immunosorbent assay (ELISA). In the FANA assay, the anti-dsDNA solution was diluted in a stepwise manner and its titer was expressed by the endpoint dilution. The nuclear staining pattern in the anti-dsDNA solution was examined at the 1:5 and 1:20 dilutions and at the endpoint dilution. The anti-dsDNA titers of the affinity-purified anti-dsDNA solution were high enough (13 to 126 IU/ml) to be measured by RIA. However, the antinuclear antibody (ANA) titers of this solution were relatively low: 1:20 to 1:320. In the study of nuclear staining the peripheral pattern was observed in nine of the 14 cases at a 1:5 dilution. However, at the endpoint dilution, all cases exhibited the homogeneous pattern. These findings indicate that in the FANA assay using HEp-2 cells, 1) although serum samples show high anti-dsDNA titers by RIA or by ELISA, the antibodies' direct contribution to ANA titers is limited, and 2) when samples reveal a homogeneous staining pattern at the endpoint dilution, this suggests the presence of anti-dsDNA.
Energy Technology Data Exchange (ETDEWEB)
Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis, 02600 Arau, Perlis (Malaysia); Saaban, Azizan, E-mail: azizan.s@uum.edu.my [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu, E-mail: mohdnazari@perlis.uitm.edu.my [Faculty of Applied Science, Universiti Teknologi Mara, 02600 Arau, Perlis (Malaysia)
2015-12-11
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu
2015-12-01
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Lascola, Robert; O'Rourke, Patrick E; Kyser, Edward A
2017-01-01
We have developed a piecewise local (PL) partial least squares (PLS) analysis method for total plutonium measurements by absorption spectroscopy in nitric acid-based nuclear material processing streams. Instead of using a single PLS model that covers all expected solution conditions, the method selects one of several local models based on an assessment of solution absorbance, acidity, and Pu oxidation state distribution. The local models match the global model for accuracy against the calibration set, but were observed in several instances to be more robust to variations associated with measurements in the process. The improvements are attributed to the relative parsimony of the local models. Not all of the sources of spectral variation are uniformly present at each part of the calibration range. Thus, the global model is locally overfitting and susceptible to increased variance when presented with new samples. A second set of models quantifies the relative concentrations of Pu(III), (IV), and (VI). Standards containing a mixture of these species were not at equilibrium due to a disproportionation reaction. Therefore, a separate principal component analysis is used to estimate of the concentrations of the individual oxidation states in these standards in the absence of independent confirmatory analysis. The PL analysis approach is generalizable to other systems where the analysis of chemically complicated systems can be aided by rational division of the overall range of solution conditions into simpler sub-regions.
Canards in a minimal piecewise-linear square-wave burster
Desroches, M.; Fernández-García, S.; Krupa, M.
2016-07-01
We construct a piecewise-linear (PWL) approximation of the Hindmarsh-Rose (HR) neuron model that is minimal, in the sense that the vector field has the least number of linearity zones, in order to reproduce all the dynamics present in the original HR model with classical parameter values. This includes square-wave bursting and also special trajectories called canards, which possess long repelling segments and organise the transitions between stable bursting patterns with n and n + 1 spikes, also referred to as spike-adding canard explosions. We propose a first approximation of the smooth HR model, using a continuous PWL system, and show that its fast subsystem cannot possess a homoclinic bifurcation, which is necessary to obtain proper square-wave bursting. We then relax the assumption of continuity of the vector field across all zones, and we show that we can obtain a homoclinic bifurcation in the fast subsystem. We use the recently developed canard theory for PWL systems in order to reproduce the spike-adding canard explosion feature of the HR model as studied, e.g., in Desroches et al., Chaos 23(4), 046106 (2013).
Model Reduction of Hybrid Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
systems are derived in this thesis. The results are used for output feedback control of switched nonlinear systems. Model reduction of piecewise affine systems is also studied in this thesis. The proposed method is based on the reduction of linear subsystems inside the polytopes. The methods which......High-Technological solutions of today are characterized by complex dynamical models. A lot of these models have inherent hybrid/switching structure. Hybrid/switched systems are powerful models for distributed embedded systems design where discrete controls are applied to continuous processes...... of hybrid systems, designing controllers and implementations is very high so that the use of these models is limited in applications where the size of the state space is large. To cope with complexity, model reduction is a powerful technique. This thesis presents methods for model reduction and stability...
Lectin affinity chromatography of glycolipids
Energy Technology Data Exchange (ETDEWEB)
Torres, B.V.; Smith, D.F.
1987-05-01
Since glycolipids (GLs) are either insoluble or form mixed micelles in water, lectin affinity chromatography in aqueous systems has not been applied to their separation. They have overcome this problem by using tetrahydrofuran (THF) in the mobile phase during chromatography. Affinity columns prepared with the GalNAc-specific Helix pomatia agglutinin (HPA) and equilibrated in THF specifically bind the (/sup 3/H)oligosaccharide derived from Forssman GL indicating that the immobilized HPA retained its carbohydrate-binding specificity in this solvent. Intact Forssman GL was bound by the HPA-column equilibrated in THF and was specifically eluted with 0.1 mg/ml GalNAc in THF. Purification of the Forssman GL was achieved when a crude lipid extract of sheep erythrocyte membranes was applied to the HPA-column in THF. Non-specifically bound GLs were eluted from the column using a step gradient of aqueous buffer in THF, while the addition of GalNAc was required to elute the specifically bound GLs. Using this procedure the A-active GLs were purified from a crude lipid extract of type A human erythrocytes in a single chromatographic step. The use of solvents that maintain carbohydrate-binding specificity and lipid solubility will permit the application of affinity chromatography on immobilized carbohydrate-binding proteins to intact GLs.
Minguzzi, E.
2016-11-01
We investigate spacetimes whose light cones could be anisotropic. We prove the equivalence of the structures: (a) Lorentz-Finsler manifold for which the mean Cartan torsion vanishes, (b) Lorentz-Finsler manifold for which the indicatrix (observer space) at each point is a convex hyperbolic affine sphere centered on the zero section, and (c) pair given by a spacetime volume and a sharp convex cone distribution. The equivalence suggests to describe (affine sphere) spacetimes with this structure, so that no algebraic-metrical concept enters the definition. As a result, this work shows how the metric features of spacetime emerge from elementary concepts such as measure and order. Non-relativistic spacetimes are obtained replacing proper spheres with improper spheres, so the distinction does not call for group theoretical elements. In physical terms, in affine sphere spacetimes the light cone distribution and the spacetime measure determine the motion of massive and massless particles (hence the dispersion relation). Furthermore, it is shown that, more generally, for Lorentz-Finsler theories non-differentiable at the cone, the lightlike geodesics and the transport of the particle momentum over them are well defined, though the curve parametrization could be undefined. Causality theory is also well behaved. Several results for affine sphere spacetimes are presented. Some results in Finsler geometry, for instance in the characterization of Randers spaces, are also included.
D.F. Schrager
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing m
Nishimura, Tomohiro; Yagi, Risa; Usuda, Mariko; Oda, Kenji; Yamazaki, Mai; Suda, Sayaka; Takahashi, Yu; Okazaki, Fumiyasu; Sai, Yoshimichi; Higuchi, Kei; Maruyama, Tetsuo; Tomi, Masatoshi; Nakashima, Emi
2014-05-01
Betaine uptake is induced by hypertonic stress in a placental trophoblast cell line, and involvement of amino acid transport system A was proposed. Here, we aimed to identify the subtype(s) of system A that mediates hypertonicity-induced betaine uptake. Measurement of [(14)C]betaine uptake by HEK293 cells transiently transfected with human or rat sodium-coupled neutral amino acid transporters (SNATs), SNAT1, SNAT2 and SNAT4 revealed that only human and rat SNAT2 have betaine uptake activity. The Michaelis constants (Km) of betaine uptake by human and rat SNAT2 were estimated to be 5.3 mM and 4.6 mM, respectively. Betaine exclusively inhibited the uptake activity of SNAT2 among the rat system A subtypes. We found that rat SNAT1, SNAT2 and SNAT4 were expressed at the mRNA level under isotonic conditions, while expression of SNAT2 and SNAT4 was induced by hypertonicity in TR-TBT 18d-1 cells. Western blot analyses revealed that SNAT2 expression on plasma membrane of TR-TBT 18d-1 cells was more potently induced by hypertonicity than that in total cell lysate. Immunocytochemistry confirmed the induction of SNAT2 expression in TR-TBT 18d-1 cells exposed to hypertonic conditions and indicated that SNAT2 was localized on the plasma membrane in these cells. Our results indicate that SNAT2 transports betaine, and that tonicity-sensitive SNAT2 expression may be involved in regulation of betaine concentration in placental trophoblasts.
Piecewise compensation for the nonlinear error of fiber-optic gyroscope scale factor
Zhang, Yonggang; Wu, Xunfeng; Yuan, Shun; Wu, Lei
2013-08-01
Fiber-Optic Gyroscope (FOG) scale factor nonlinear error will result in errors in Strapdown Inertial Navigation System (SINS). In order to reduce nonlinear error of FOG scale factor in SINS, a compensation method is proposed in this paper based on curve piecewise fitting of FOG output. Firstly, reasons which can result in FOG scale factor error are introduced and the definition of nonlinear degree is provided. Then we introduce the method to divide the output range of FOG into several small pieces, and curve fitting is performed in each output range of FOG to obtain scale factor parameter. Different scale factor parameters of FOG are used in different pieces to improve FOG output precision. These parameters are identified by using three-axis turntable, and nonlinear error of FOG scale factor can be reduced. Finally, three-axis swing experiment of SINS verifies that the proposed method can reduce attitude output errors of SINS by compensating the nonlinear error of FOG scale factor and improve the precision of navigation. The results of experiments also demonstrate that the compensation scheme is easy to implement. It can effectively compensate the nonlinear error of FOG scale factor with slightly increased computation complexity. This method can be used in inertial technology based on FOG to improve precision.
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
Kilpatrick, Zachary P.
2010-06-01
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather. © 2010 Elsevier B.V. All rights reserved.
Akaishi, A.; Shudo, A.
2009-12-01
We investigate the stickiness of the two-dimensional piecewise linear map with a family of marginal unstable periodic orbits (FMUPOs), and show that a series of unstable periodic orbits accumulating to FMUPOs plays a significant role to give rise to the power law correlation of trajectories. We can explicitly specify the sticky zone in which unstable periodic orbits whose stability increases algebraically exist, and find that there exists a hierarchy in accumulating periodic orbits. In particular, the periodic orbits with linearly increasing stability play the role of fundamental cycles as in the hyperbolic systems, which allows us to apply the method of cycle expansion. We also study the recurrence time distribution, especially discussing the position and size of the recurrence region. Following the definition adopted in one-dimensional maps, we show that the recurrence time distribution has an exponential part in the short time regime and an asymptotic power law part. The analysis on the crossover time Tc∗ between these two regimes implies Tc∗˜-log[μ(R)] where μ(R) denotes the area of the recurrence region.
Petzold, Martin; Coghlan, Campbell J; Hearn, Milton T W
2014-07-18
This study describes the determination of the adsorption isotherms and binding kinetics of tagged recombinant proteins using a recently developed IMAC cassette system and employing automated robotic liquid handling procedures for IMAC resin screening. These results confirm that these new IMAC resins, generated from a variety of different metal-charged binuclear 1,4,7-triaza-cyclononane (tacn) ligands, interact with recombinant proteins containing a novel N-terminal metal binding tag, NT1A, with static binding capacities similar to those obtained with conventional hexa-His tagged proteins, but with significantly increased association constants. In addition, higher kinetic binding rates were observed with these new IMAC systems, an attribute that can be positively exploited to increase process productivity. The results from this investigation demonstrate that enhancements in binding capacities and affinities were achieved with these new IMAC resins and chosen NT1A tagged protein. Further, differences in the binding performances of the bis(tacn) xylenyl-bridged ligands were consistent with the distance between the metal binding centres of the two tacn moieties, the flexibility of the ligand and the potential contribution from the aromatic ring of the xylenyl group to undergo π/π stacking interactions with the tagged proteins.
仿射变换内点Levenberg-Marquardt法解KKT系统%Affine scaling interior Levenberg-Marquardt method for KKT systems
Institute of Scientific and Technical Information of China (English)
王云娟; 朱德通
2013-01-01
提供了一类新的结合非单调内点回代线搜索技术的仿射变换Levenberg-Marquardt法解Karush-Kuhn-Tucker (KKT)系统.基于由KKT系统转化得到的等价的部分变量具有非负约束的最小化问题,建立了Levenberg-Maxquardt方程.证明了算法不仅具有整体收敛性,而且在合理的假设条件下,算法具有超线性收敛速率.数值结果验证了算法的实际有效性.%We develop and analyze a new affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving Karush-KuhnTucker (KKT) system.By transforming the KKT system into an equivalent minimization problem with nonnegativity constraints on some of the variables,we establish the Levenberg-Marquardt equation based on this reformulation.Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergent rate under some reasonable conditions.The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
Postupalenko, Viktoriia; Desplancq, Dominique; Orlov, Igor; Arntz, Youri; Spehner, Danièle; Mely, Yves; Klaholz, Bruno P; Schultz, Patrick; Weiss, Etienne; Zuber, Guy
2015-09-01
Recombinant proteins with cytosolic or nuclear activities are emerging as tools for interfering with cellular functions. Because such tools rely on vehicles for crossing the plasma membrane we developed a protein delivery system consisting in the assembly of pyridylthiourea-grafted polyethylenimine (πPEI) with affinity-purified His-tagged proteins pre-organized onto a nickel-immobilized polymeric guide. The guide was prepared by functionalization of an ornithine polymer with nitrilotriacetic acid groups and shown to bind several His-tagged proteins. Superstructures were visualized by electron and atomic force microscopy using 2 nm His-tagged gold nanoparticles as probes. The whole system efficiently carried the green fluorescent protein, single-chain antibodies or caspase 3, into the cytosol of living cells. Transduction of the protease caspase 3 induced apoptosis in two cancer cell lines, demonstrating that this new protein delivery method could be used to interfere with cellular functions. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Affine and degenerate affine BMW algebras: The center
Daugherty, Zajj; Virk, Rahbar
2011-01-01
The degenerate affine and affine BMW algebras arise naturally in the context of Schur-Weyl duality for orthogonal and symplectic Lie algebras and quantum groups, respectively. Cyclotomic BMW algebras, affine Hecke algebras, cyclotomic Hecke algebras, and their degenerate versions are quotients. In this paper the theory is unified by treating the orthogonal and symplectic cases simultaneously; we make an exact parallel between the degenerate affine and affine cases via a new algebra which takes the role of the affine braid group for the degenerate setting. A main result of this paper is an identification of the centers of the affine and degenerate affine BMW algebras in terms of rings of symmetric functions which satisfy a "cancellation property" or "wheel condition" (in the degenerate case, a reformulation of a result of Nazarov). Miraculously, these same rings also arise in Schubert calculus, as the cohomology and K-theory of isotropic Grassmanians and symplectic loop Grassmanians. We also establish new inte...
Piecewise-homogeneous model for electron side injection into linear plasma waves
Energy Technology Data Exchange (ETDEWEB)
Golovanov, A.A., E-mail: agolovanov256@gmail.com; Kostyukov, I.Yu., E-mail: kost@appl.sci-nnov.ru
2016-09-01
An analytical piecewise-homogeneous model for electron side injection into linear plasma waves is developed. The dynamics of transverse betatron oscillations are studied. Based on the characteristics of the transversal motion the longitudinal motion of electrons is described. The electron parameters for which the electron trapping and subsequent acceleration are possible are estimated. The analytical results are verified by numerical simulations in the scope of the piecewise-homogeneous model. The results predicted by this model are also compared to the results given by a more realistic inhomogeneous model. - Highlights: • A piecewise-homogeneous model of side injection into a linear wakefield is developed. • The dynamics of betatron oscillations in the focusing phase is analytically studied. • The area of parameters for electron trapping is determined. • The model is compared to a more realistic inhomogeneous model.
Hierarchical Affinity Propagation
Givoni, Inmar; Frey, Brendan J
2012-01-01
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including biology, sensor networks and decision making in operational research. We derive an inference algorithm that operates by propagating information up and down the hierarchy, and is efficient despite the high-order potentials required for the graphical model formulation. We demonstrate that our method outperforms greedy techniques that cluster one layer at a time. We show that on an artificial dataset designed to mimic the HIV-strain mutation dynamics, our method outperforms related methods. For real HIV sequences, where the ground truth is not available, we show our method achieves better results, in terms of the underlying objective function, and show the results correspond meaningfully to geographi...
Affinity driven social networks
Ruyú, B.; Kuperman, M. N.
2007-04-01
In this work we present a model for evolving networks, where the driven force is related to the social affinity between individuals of a population. In the model, a set of individuals initially arranged on a regular ordered network and thus linked with their closest neighbors are allowed to rearrange their connections according to a dynamics closely related to that of the stable marriage problem. We show that the behavior of some topological properties of the resulting networks follows a non trivial pattern.
Skirzewski, Aureliano
2014-01-01
We develop a topological theory of gravity with torsion where metric has a dynamical rather than a kinematical origin. This approach towards gravity resembles pre-geometrical approaches in which a fundamental metric does not exist, but the affine connection gives place to a local inertial structure. Such feature reminds us of Mach's principle, that assumes the inertial forces should have dynamical origin. Additionally, a Newtonian gravitational force is obtained in the non-relativistic limit of the theory.
Hybrid control of the distributed refrigeration system
DEFF Research Database (Denmark)
Chen, L.; Wisniewski, R.
2010-01-01
The supermarket refrigeration system typically has a distributed control structure, which neglects interactions between its subsystems. These interactions from time to time lead to a synchronization operation of the display-cases which causes an inferior control performance and increased energy...... or a chaotic behavior, the system is considered away from the synchronization. Therefore, the paper proposes a concept that the system may be de-synchronized by making it chaotic. A de-synchronization scheme is developed. It includes a synchronization-early-monitoring detector by calculating the maximum...... consumption. The paper focuses on synchronization dynamics of the refrigeration system modeled as a piecewise-affine switched system. System behaviors are analyzed using chaos theory. The synchronization phenomenon is interpreted as a stable low-period orbit; if the system has a high-order periodic orbit...
Meneses, Domingos De Sousa; Rousseau, Benoit; Echegut, Patrick; Matzen, Guy
2007-06-01
A new expression of dielectric function model based on piecewise polynomials is introduced. Its association with spline and more recent shape preserving interpolation algorithms allows easy reproduction of every kind of experimental spectra and thus retrieval of all the linear optical functions of a material. Based on a pure mathematical framework, the expression of the model is always applicable and does not necessitate any knowledge of the microscopic mechanisms of absorption responsible for the optical response. The potential of piecewise polynomial dielectric functions is shown through synthetic examples and the analysis of experimental spectra.
The Cauchy Boundary Value Problems on Closed Piecewise Smooth Manifolds in Cn
Institute of Scientific and Technical Information of China (English)
Liang Yu LIN; Chun Hui QIU
2004-01-01
Suppose that D is a bounded domain with a piecewise C1 smooth boundary in Cn. Let ψ∈ C1+α((б)D). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Bochner-Martinelli kernel, which has integral density ψ. Moreover,by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauchy boundary value problem with the Bochner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.
On the Affine Isoperimetric Inequalities
Indian Academy of Sciences (India)
Wuyang Yu; Gangsong Leng
2011-11-01
We obtain an isoperimetric inequality which estimate the affine invariant -surface area measure on convex bodies. We also establish the reverse version of -Petty projection inequality and an affine isoperimetric inequality of $_{-p}K$.
Affine morphisms at zero level
Das, Paramita; Gupta, Ved Prakash
2010-01-01
Given a finite index subfactor, we show that the {\\em affine morphisms at zero level} in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a *-algebra.
Lang, Minglin; Fan, Qiangwang; Wang, Lei; Zheng, Yajun; Xiao, Guiran; Wang, Xiaoxi; Wang, Wei; Zhong, Yi; Zhou, Bing
2013-11-01
Disruption of copper homeostasis has been implicated in Alzheimer's disease (AD) during the last 2 decades; however, whether copper is a friend or a foe is controversial. Within a genetically tractable Drosophila AD model, we manipulated the expression of human high-affinity copper importer orthologous in Drosophila to explore the in vivo roles of copper ions in the development of AD. We found that inhibition of Ctr1C expression by RNAi in Aβ-expressing flies significantly reduced copper accumulation in the brains of the flies as well as ameliorating neurodegeneration, enhancing climbing ability, and prolonging lifespan. Interestingly, Ctr1C inhibition led to a significant increase in higher-molecular-weight Aβ42 forms in brain lysates, whereas it was accompanied by a trend of decreased expression of amyloid-β degradation proteases (including NEP1-3 and IDE) with age and reduced Cu-Aβ interaction-induced oxidative stress in Ctr1C RNAi flies. Similar results were obtained from inhibiting another copper importer Ctr1B and overexpressing a copper exporter DmATP7 in the nervous system of AD flies. These results imply that copper may play a causative role in developing AD, as either Aβ oligomers or aggregates were less toxic in a reduced copper environment or one with less copper binding. Early manipulation of brain copper uptake can have a great effect on Aβ pathology.
Directory of Open Access Journals (Sweden)
Youry Pii
2016-11-01
Full Text Available The induction, i.e. the rapid increase of nitrate (NO3- uptake following the exposure of roots to the anion, was studied integrating physiological and molecular levels in maize roots. Responses to NO3- treatment were characterized in terms of changes in NO3- uptake rate and plasma membrane (PM H+-ATPase activity and related to transcriptional and protein profiles of NRT2, NRT3 and PM H+-ATPase gene families. The behaviour of transcripts and proteins of ZmNRT2s and ZmNRT3s suggested that the regulation of the activity of inducible high-affinity transport system (iHATS is mainly based on the transcriptional/translational modulation of the accessory protein ZmNRT3.1A. Furthermore, ZmNRT2.1 and ZmNRT3.1A appear to be associated in a ∼ 150 kDa oligomer. The expression trend during the induction of the 11 identified PM H+-ATPase transcripts indicates that those mainly involved in the response to NO3- treatment are ZmHA2 and ZmHA4. Yet, partial correlation between the gene expression, protein levels and enzyme activity suggests an involvement of post-transcriptional and post-translational mechanisms of regulation. A nondenaturing Deriphat-PAGE approach allowed demonstrating for the first time that PM H+-ATPase can occur in vivo as hexameric complex together with the already described monomeric and dimeric forms.
Affine Patches on Positroid Varieties and Affine Pipe Dreams (Thesis)
Snider, Michelle
2010-01-01
The objects of interest in this thesis are positroid varieties in the Grassmannian, which are indexed by juggling patterns. In particular, we study affine patches on these positroid varieties. Our main result corresponds these affine patches to Kazhdan-Lusztig varieties in the affine Grassmannian. We develop a new term order and study how these spaces are related to subword complexes and Stanley-Reisner ideals. We define an extension of pipe dreams to the affine case and conclude by showing how our affine pipe dreams are generalizations of Cauchon and Le diagrams.
Directory of Open Access Journals (Sweden)
Haiyan Hu
1996-01-01
Full Text Available One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.
Wolf, Paul A; Schmidt, Taly G; Sidky, Emil Y
2012-01-01
A sparsity-exploiting algorithm intended for few-view Single Photon Emission Computed Tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true object in the noiseless case, projection data were generated from an object assuming this model and using the system matrix. Monte Carlo simulations were performed to provide more realistic data of a phantom with varying smoothness across the field of view. Reconstructions were performed across a sweep of two primary design parameters. The results demonstrate that the algorithm recovers the object in a noiseless simulation case. While the algorithm assumes a specific blurring model, the results suggest that the algorithm may provide high reconstruction accuracy even when the object does not match the assumed blurring model. Generally, increased values of the blurring parameter and TV weighting parameters reduced noi...
Directory of Open Access Journals (Sweden)
Zhinan Xia
2015-07-01
Full Text Available In this article, we show sufficient conditions for the existence, uniqueness and attractivity of piecewise weighted pseudo almost periodic classical solution of nonlinear impulsive integro-differential equations. The working tools are based on the fixed point theorem and fractional powers of operators. An application to impulsive integro-differential equations is presented.
Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries
Directory of Open Access Journals (Sweden)
Shay Kels
2010-07-01
Full Text Available The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with piecewise linear boundaries.
Moses, Tim
2013-01-01
The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of…
Directory of Open Access Journals (Sweden)
Pradeep Kumar
2013-10-01
Full Text Available The objective of this article is to prove the existence of piecewise continuous mild solutions to impulsive functional differential equation with iterated deviating arguments in a Banach space. The results are obtained by using the theory of analytic semigroups and fixed point theorems.
Institute of Scientific and Technical Information of China (English)
冯月才
2004-01-01
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.
Transitions from phase-locked dynamics to chaos in a piecewise-linear map
DEFF Research Database (Denmark)
Zhusubaliyev, Z.T.; Mosekilde, Erik; De, S.
2008-01-01
place via border-collision fold bifurcations. We examine the transition to chaos through torus destruction in such maps. Considering a piecewise-linear normal-form map we show that this transition, by virtue of the interplay of border-collision bifurcations with period-doubling and homoclinic...
Method of folding a piecewise polynomial function in the delta function integral representation
Energy Technology Data Exchange (ETDEWEB)
Lee, D.K.
1978-12-01
A simple procedure is presented for determining the folded form of a piecewise polynomial function in the delta function integral representation. The procedure is useful in evaluating the autocorrelation function by means of the algebraic convolution technique developed by Polge and Hasy (IEEE Trans. Comput. pp. 970-975, Nov 1973).
Pii, Youry; Alessandrini, Massimiliano; Dall’Osto, Luca; Guardini, Katia; Prinsi, Bhakti; Espen, Luca; Zamboni, Anita; Varanini, Zeno
2016-01-01
The induction, i.e., the rapid increase of nitrate (NO3–) uptake following the exposure of roots to the anion, was studied integrating physiological and molecular levels in maize roots. Responses to NO3– treatment were characterized in terms of changes in NO3– uptake rate and plasma membrane (PM) H+-ATPase activity and related to transcriptional and protein profiles of NRT2, NRT3, and PM H+-ATPase gene families. The behavior of transcripts and proteins of ZmNRT2s and ZmNRT3s suggested that the regulation of the activity of inducible high-affinity transport system (iHATS) is mainly based on the transcriptional/translational modulation of the accessory protein ZmNRT3.1A. Furthermore, ZmNRT2.1 and ZmNRT3.1A appear to be associated in a ∼150 kDa oligomer. The expression trend during the induction of the 11 identified PM H+-ATPase transcripts indicates that those mainly involved in the response to NO3– treatment are ZmHA2 and ZmHA4. Yet, partial correlation between the gene expression, protein levels and enzyme activity suggests an involvement of post-transcriptional and post-translational mechanisms of regulation. A non-denaturing Deriphat-PAGE approach allowed demonstrating for the first time that PM H+-ATPase can occur in vivo as hexameric complex together with the already described monomeric and dimeric forms. PMID:27877183
Pii, Youry; Alessandrini, Massimiliano; Dall'Osto, Luca; Guardini, Katia; Prinsi, Bhakti; Espen, Luca; Zamboni, Anita; Varanini, Zeno
2016-01-01
The induction, i.e., the rapid increase of nitrate ([Formula: see text]) uptake following the exposure of roots to the anion, was studied integrating physiological and molecular levels in maize roots. Responses to [Formula: see text] treatment were characterized in terms of changes in [Formula: see text] uptake rate and plasma membrane (PM) H(+)-ATPase activity and related to transcriptional and protein profiles of NRT2, NRT3, and PM H(+)-ATPase gene families. The behavior of transcripts and proteins of ZmNRT2s and ZmNRT3s suggested that the regulation of the activity of inducible high-affinity transport system (iHATS) is mainly based on the transcriptional/translational modulation of the accessory protein ZmNRT3.1A. Furthermore, ZmNRT2.1 and ZmNRT3.1A appear to be associated in a ∼150 kDa oligomer. The expression trend during the induction of the 11 identified PM H(+)-ATPase transcripts indicates that those mainly involved in the response to [Formula: see text] treatment are ZmHA2 and ZmHA4. Yet, partial correlation between the gene expression, protein levels and enzyme activity suggests an involvement of post-transcriptional and post-translational mechanisms of regulation. A non-denaturing Deriphat-PAGE approach allowed demonstrating for the first time that PM H(+)-ATPase can occur in vivo as hexameric complex together with the already described monomeric and dimeric forms.
Convenient Model for Systems with Hystereses-Control
DEFF Research Database (Denmark)
Wisniewski, Rafal; Leth, John-Josef
2011-01-01
We establish a model of a system with hystereses, which allows for standard stability analysis of fixed points and closed orbits. To this end, we represent a system with hystereses as a piecewise-affine switched system that consists of a family of dynamical systems defined on disjoint polyhedral...... sets. The discrete transitions are realized by reset maps defined on the facets of these polyhedral sets. We have shown that the state space of a resulting switched system is a smooth manifold, the Cartesian product of a torus with an Euclidean space. Additionally, we construct the charts explicitly....... Thereby, the analysis of a system with hystereses can be seen as the analysis of a dynamical system on a manifold, locally in chars. This dynamical system corresponds to a differential equation with discontinuous right hand side which solution is shown to exist and to be unique....
Modelling and simulation of affinity membrane adsorption.
Boi, Cristiana; Dimartino, Simone; Sarti, Giulio C
2007-08-24
A mathematical model for the adsorption of biomolecules on affinity membranes is presented. The model considers convection, diffusion and adsorption kinetics on the membrane module as well as the influence of dead end volumes and lag times; an analysis of flow distribution on the whole system is also included. The parameters used in the simulations were obtained from equilibrium and dynamic experimental data measured for the adsorption of human IgG on A2P-Sartoepoxy affinity membranes. The identification of a bi-Langmuir kinetic mechanisms for the experimental system investigated was paramount for a correct process description and the simulated breakthrough curves were in good agreement with the experimental data. The proposed model provides a new insight into the phenomena involved in the adsorption on affinity membranes and it is a valuable tool to assess the use of membrane adsorbers in large scale processes.
Affinity Purification of Insulin by Peptide-Ligand Affinity Chromatography
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The affinity heptapeptide (HWWWPAS) for insulin, selected from phage display library,was coupled to EAH Sepharose 4B gel and packed to a 1-mL column. The column was used for the affinity purification of insulin from protein mixture and commercial insulin preparation. It was observed that the minor impurity in the commercial insulin was removed by the affinity chromatography. Nearly 40 mg of insulin could be purified with the 1-mL affinity column. The results revealed the high specificity and capacity of the affinity column for insulin purification. Moreover, based on the analysis of the amino acids in the peptide sequence, shorter peptides were designed and synthesized for insulin chromatography. As a result, HWWPS was found to be a good alternative to HWWWPAS, while the other two peptides with three or four amino acids showed weak affinity for insulin. The results indicated that the peptide sequence of HWWWPAS was quite conservative for specific binding of insulin.
Jacobi Structures on Affine Bundles
Institute of Scientific and Technical Information of China (English)
J. GRABOWSKI; D. IGLESIAS; J. C. MARRERO; E. PADR(O)N; P. URBA(N)SKI
2007-01-01
We study affine Jacobi structures (brackets) on an affine bundle π: A→M, i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-to- one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A+=∪p∈M Aff(Ap, R) of affine functionals. In the case rank A = 0, it is shown that there is a one-to-one correspondence between affins Jacobi structures on A and local Lie algebras on A+. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited (strongly-affine or affine-homogeneous Jacobi structures) over a real vector space of finite dimension, we describe the leaves of its characteristic foliation as the orbits of an affine representation. These afline Jacobi structures can be viewed as an analog of the Kostant-Arnold-LiouviUe linear Poisson structure on the dual space of a real finite-dimensional Lie algebra.
Trehan, Sumeet; Durlofsky, Louis J.
2016-12-01
A new reduced-order model based on trajectory piecewise quadratic (TPWQ) approximations and proper orthogonal decomposition (POD) is introduced and applied for subsurface oil-water flow simulation. The method extends existing techniques based on trajectory piecewise linear (TPWL) approximations by incorporating second-derivative terms into the reduced-order treatment. Both the linear and quadratic reduced-order methods, referred to as POD-TPWL and POD-TPWQ, entail the representation of new solutions as expansions around previously simulated high-fidelity (full-order) training solutions, along with POD-based projection into a low-dimensional space. POD-TPWQ entails significantly more offline preprocessing than POD-TPWL as it requires generating and projecting several third-order (Hessian-type) terms. The POD-TPWQ method is implemented for two-dimensional systems. Extensive numerical results demonstrate that it provides consistently better accuracy than POD-TPWL, with speedups of about two orders of magnitude relative to high-fidelity simulations for the problems considered. We demonstrate that POD-TPWQ can be used as an error estimator for POD-TPWL, which motivates the development of a trust-region-based optimization framework. This procedure uses POD-TPWL for fast function evaluations and a POD-TPWQ error estimator to determine when retraining, which entails a high-fidelity simulation, is required. Optimization results for an oil-water problem demonstrate the substantial speedups that can be achieved relative to optimizations based on high-fidelity simulation.
Kernel Affine Projection Algorithms
Directory of Open Access Journals (Sweden)
José C. Príncipe
2008-05-01
Full Text Available The combination of the famed kernel trick and affine projection algorithms (APAs yields powerful nonlinear extensions, named collectively here, KAPA. This paper is a follow-up study of the recently introduced kernel least-mean-square algorithm (KLMS. KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a unifying model for several neural network techniques, including kernel least-mean-square algorithms, kernel adaline, sliding-window kernel recursive-least squares (KRLS, and regularization networks. Therefore, many insights can be gained into the basic relations among them and the tradeoff between computation complexity and performance. Several simulations illustrate its wide applicability.
Kernel Affine Projection Algorithms
Liu, Weifeng; Príncipe, José C.
2008-12-01
The combination of the famed kernel trick and affine projection algorithms (APAs) yields powerful nonlinear extensions, named collectively here, KAPA. This paper is a follow-up study of the recently introduced kernel least-mean-square algorithm (KLMS). KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a unifying model for several neural network techniques, including kernel least-mean-square algorithms, kernel adaline, sliding-window kernel recursive-least squares (KRLS), and regularization networks. Therefore, many insights can be gained into the basic relations among them and the tradeoff between computation complexity and performance. Several simulations illustrate its wide applicability.
On Affine Fusion and the Phase Model
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Mark A. Walton
2012-11-01
Full Text Available A brief review is given of the integrable realization of affine fusion discovered recently by Korff and Stroppel. They showed that the affine fusion of the su(n Wess-Zumino-Novikov-Witten (WZNW conformal field theories appears in a simple integrable system known as the phase model. The Yang-Baxter equation leads to the construction of commuting operators as Schur polynomials, with noncommuting hopping operators as arguments. The algebraic Bethe ansatz diagonalizes them, revealing a connection to the modular S matrix and fusion of the su(n WZNW model. The noncommutative Schur polynomials play roles similar to those of the primary field operators in the corresponding WZNW model. In particular, their 3-point functions are the su(n fusion multiplicities. We show here how the new phase model realization of affine fusion makes obvious the existence of threshold levels, and how it accommodates higher-genus fusion.
Complex Dynamical Behavior in Hybrid Systems
2012-09-29
2010. J15. T. Hu, T. Thibodeau , A.R. Teel, ``A Unified Lyapunov Approach to Analysis of Oscillations and Stability for Systems With Piecewise...Hu, T. Thibodeau , A.R. Teel, ``Analysis of oscillation and stability for systems with piecewise linear components via saturation functions
Ribeiro, Mariana Borsoi; Vijayalakshmi, Mookambesvaran; Todorova-Balvay, Daniele; Bueno, Sonia Maria Alves
2008-01-01
The purification of IgG from human plasma was studied by comparing two affinity membranes complexed with Ni(II), prepared by coupling iminodiacetic acid (IDA) and Tris(2-aminoethyl)amine (TREN) to poly(ethylenevinyl alcohol), PEVA, hollow fiber membranes. The Ni(II)-TREN-PEVA hollow fiber membrane had lower capacity for human IgG than the complex Ni(II)-IDA-PEVA, but with similar selectivity. The IgG in peak fractions eluted from the Ni(II)-IDA-PEVA with a stepwise concentration gradient of Tris-HCl pH 7.0 (100-700 mM) reached a purity of 98% (based on IgG, IgM, IgA, albumin, and transferrin nephelometric analysis). Adsorption IgG data at different temperatures (4-37 degrees C) were analyzed using Langmuir model resulting in a calculated maximum capacity at 25 degrees C of 204.6 mg of IgG/g of dry membrane. Decrease in Kd with increasing temperature (1.7x10(-5) to 5.3x10(-6) M) indicated an increase in affinity with increased temperature. The positive value of enthalpy change (26.2 kJ/mol) indicated that the adsorption of IgG in affinity membrane is endothermic. Therefore, lower temperature induces adsorption as verified experimentally.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps
Simpson, D J W
2010-01-01
Mode-locking regions (resonance tongues) formed by border-collision bifurcations of piecewise-smooth, continuous maps commonly exhibit a distinctive sausage-like geometry with pinch points called "shrinking points". In this paper we extend our unfolding of the piecewise-linear case [{\\em Nonlinearity}, 22(5):1123-1144, 2009] to show how shrinking points are destroyed by nonlinearity. We obtain a codimension-three unfolding of this shrinking point bifurcation for $N$-dimensional maps. We show that the destruction of the shrinking points generically occurs by the creation of a curve of saddle-node bifurcations that smooth one boundary of the sausage, leaving a kink in the other boundary.
Directory of Open Access Journals (Sweden)
H. Vazquez-Leal
2014-01-01
Full Text Available We present a homotopy continuation method (HCM for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.
On piecewise interpolation techniques for estimating solar radiation missing values in Kedah
Energy Technology Data Exchange (ETDEWEB)
Saaban, Azizan; Zainudin, Lutfi [School of Science Quantitative, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu [Faculty of Applied Science, Universiti Teknologi MARA, 02600 Arau, Perlis (Malaysia)
2014-12-04
This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Error (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.
Su, Yan; Jun, Xie Cheng
2006-08-01
An algorithm of combining LZC and arithmetic coding algorithm for image compression is presented and both theory deduction and simulation result prove the correctness and feasibility of the algorithm. According to the characteristic of context-based adaptive binary arithmetic coding and entropy, LZC was modified to cooperate the optimized piecewise arithmetic coding, this algorithm improved the compression ratio without any additional time consumption compared to traditional method.
Numerical Stability of Differential Equations with Piecewise Constant Arguments of Mixed Type
Institute of Scientific and Technical Information of China (English)
Qi WANG
2013-01-01
This paper deals with the stability analysis of the Euler-Maclaurin method for differential equations with piecewise constant arguments of mixed type.The expression of analytical solution is derived and the stability regions of the analytical solution are given.The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed.The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical examples are given.
Piecewise-polynomial and cascade models of predistorter for linearization of power amplifier
2012-01-01
To combat non-linear signal distortions in a power amplifier we suggest using predistorter with cascade structure in which first and second nodes have piecewise-polynomial and polynomial models. On example of linearizing the Winner–Hammerstein amplifier model we demonstrate that cascade structure of predistorter improves precision of amplifier’s linearization. To simplify predistorter’s synthesis the degree of polynomial model used in first node should be moderate, while precision should be i...
Institute of Scientific and Technical Information of China (English)
2008-01-01
In general normed spaces,we consider a multiobjective piecewise linear optimization problem with the ordering cone being convex and having a nonempty interior.We establish that the weak Pareto optimal solution set of such a problem is the union of finitely many polyhedra and that this set is also arcwise connected under the cone convexity assumption of the objective function.Moreover,we provide necessary and suffcient conditions about the existence of weak(sharp) Pareto solutions.
Zimmermann, Karl-Heinz; Achtziger, Wolfgang
2001-09-01
The size of a systolic array synthesized from a uniform recurrence equation, whose computations are mapped by a linear function to the processors, matches the problem size. In practice, however, there exist several limiting factors on the array size. There are two dual schemes available to derive arrays of smaller size from large-size systolic arrays based on the partitioning of the large-size arrays into subarrays. In LSGP, the subarrays are clustered one-to-one into the processors of a small-size array, while in LPGS, the subarrays are serially assigned to a reduced-size array. In this paper, we propose a common methodology for both LSGP and LPGS based on polyhedral partitionings of large-size k-dimensional systolic arrays which are synthesized from n-dimensional uniform recurrences by linear mappings for allocation and timing. In particular, we address the optimization problem of finding optimal piecewise linear timing functions for small-size arrays. These are mappings composed of linear timing functions for the computations of the subarrays. We study a continuous approximation of this problem by passing from piecewise linear to piecewise quasi-linear timing functions. The resultant problem formulation is then a quadratic programming problem which can be solved by standard algorithms for nonlinear optimization problems.
Dolgin, Madlena; Einziger, Pinchas D
2010-05-01
Image reconstruction in electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a case study, which uses a novel electrical impedance tomography method for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, utilizing Legendre expansion in conjunction with improved Prony method. It is shown that the proposed algorithm is capable of successfully reconstructing piecewise continuous conductivity profiles with moderate slop. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, i.e., the depths grid is not equispaced. Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (the image series expansion) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm. The effectiveness and the significance of inhomogeneous discretization in electrical impedance tomography reconstruction procedure is further demonstrated and verified via numerical simulations.
A WENO-type slope-limiter for a family of piecewise polynomial methods
Engwirda, Darren
2016-01-01
A new, high-order slope-limiting procedure for the Piecewise Parabolic Method (PPM) and the Piecewise Quartic Method (PQM) is described. Following a Weighted Essentially Non-Oscillatory (WENO)-type paradigm, the proposed slope-limiter seeks to reconstruct smooth, non-oscillatory piecewise polynomial profiles as a non-linear combination of the natural and monotone-limited PPM and PQM interpolants. Compared to existing monotone slope-limiting techniques, this new strategy is designed to improve accuracy at smooth extrema, while controlling spurious oscillations in the neighbourhood of sharp features. Using the new slope-limited PPM and PQM interpolants, a high-order accurate Arbitrary-Lagrangian-Eulerian framework for advection-dominated flows is constructed, and its effectiveness is examined using a series of one- and two-dimensional benchmark cases. It is shown that the new WENO-type slope-limiting techniques offer a significant improvement in accuracy compared to existing strategies, allowing the PPM- and PQ...
Davies, David L.; Smith, Peter H.; Liutermoza, John F.
1980-06-01
Profile analysis and piecewise correlation techniques for measuring internal machine part clearances by digital processing of industrial radiographs are described in this paper. These methods were developed at the Image and Pattern Analysis Laboratory of Pratt & Whitney Aircraft Group. Profile analysis requires mathematical modeling of the expected optical density of a radiograph as a function of machine part position. Part separations are estimated on the basis of individual image scan lines. A final part separation estimate is produced by fitting a polynominal to the individual estimates and correcting for imaging and processing degradations which are simulated using a mathematical model. Piecewise correlation involves an application of image registration where radiographs are correlated in a piecewise fashion to allow inference of the relative motion of machine parts in a time varying series of images. Each image is divided into segments which are dominated by a small number of features. Segments from one image are cross-correlated with subsequent images to identify machine part motion in image space. Correlation peak magnitude is used in assessing the confidence that a particular motion has occurred between images. The rigid feature motion of machine parts requires image registration by discon-tinuous parts. This method differs from the continuous deformations one encounters in perspective projective transformations characteristic of remote sensing applications.
A HYBRID TECHNIQUE FOR PAPR REDUCTION OF OFDM USING DHT PRECODING WITH PIECEWISE LINEAR COMPANDING
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Thammana Ajay
2016-06-01
Full Text Available Orthogonal Frequency Division Multiplexing (OFDM is a fascinating approach for wireless communication applications which require huge amount of data rates. However, OFDM signal suffers from its large Peak-to-Average Power Ratio (PAPR, which results in significant distortion while passing through a nonlinear device, such as a transmitter high power amplifier (HPA. Due to this high PAPR, the complexity of HPA as well as DAC also increases. For the reduction of PAPR in OFDM many techniques are available. Among them companding is an attractive low complexity technique for the OFDM signal’s PAPR reduction. Recently, a piecewise linear companding technique is recommended aiming at minimizing companding distortion. In this paper, a collective piecewise linear companding approach with Discrete Hartley Transform (DHT method is expected to reduce peak-to-average of OFDM to a great extent. Simulation results shows that this new proposed method obtains significant PAPR reduction while maintaining improved performance in the Bit Error Rate (BER and Power Spectral Density (PSD compared to piecewise linear companding method.
New contractivity condition in a population model with piecewise constant arguments
Muroya, Yoshiaki
2008-10-01
In this paper, we improve contractivity conditions of solutions for the positive equilibrium of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+[infinity]), r(t)[not identical with]0, , bi[greater-or-equal, slanted]0, i=0,1,2,...,m, and . In particular, for the case a=0 and m[greater-or-equal, slanted]1, we really improve the known three type conditions of the contractivity for solutions of this model (see for example, [Y. Muroya, A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido Math. J. 32 (2003) 75-83]). For the other case a[not equal to]0 and m[greater-or-equal, slanted]1, under the condition , the obtained result partially improves the known results on the contractivity of solutions for the positive equilibrium of this model given by the author [Y. Muroya, Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. Math. Anal. Appl. 270 (2002) 602-635] and others.
Energy Technology Data Exchange (ETDEWEB)
Lin Li [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China); Lin Weiqi [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China); Jiang Jianhui [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China); Zhou Yanping [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China); Shen Guoli [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China); Yu Ruqin [State Key Laboratory of Chemo/Biosensing and Chemometrics, College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082 (China)]. E-mail: rqyu@hnu.cn
2005-11-03
In the present work, we employed piecewise hyper-sphere modeling by particle swarm optimization (PHMPSO) which splits the dataset into subsets with desired linearity in each model for QSAR studies of a series of 2-aryl(heteroaryl)-2,5-dihydropyrazolo[4,3-c]quinolin-3-(3H)-ones (PQs) for their affinity to benzodiazepine receptor (BzR). The results were compared to those obtained by MLR modeling in a single model with the whole data set as well as in submodels based on K-means clustering analysis. It has been clearly shown that electronic descriptors and spatial descriptors play the important roles in the compounds' affinity to BzR. In addition, the molecular density, the Y component of the principal moment of inertia, the magnitude and the Y component of the dipole moment of the molecules can detrimentally affect PQ analogue BzR affinity, while the X component of the dipole moment of the molecules can favorably affect compounds' affinity.
Directory of Open Access Journals (Sweden)
Miguel Angel Luque-Fernandez
2016-10-01
Full Text Available Abstract Background In population-based cancer research, piecewise exponential regression models are used to derive adjusted estimates of excess mortality due to cancer using the Poisson generalized linear modelling framework. However, the assumption that the conditional mean and variance of the rate parameter given the set of covariates x i are equal is strong and may fail to account for overdispersion given the variability of the rate parameter (the variance exceeds the mean. Using an empirical example, we aimed to describe simple methods to test and correct for overdispersion. Methods We used a regression-based score test for overdispersion under the relative survival framework and proposed different approaches to correct for overdispersion including a quasi-likelihood, robust standard errors estimation, negative binomial regression and flexible piecewise modelling. Results All piecewise exponential regression models showed the presence of significant inherent overdispersion (p-value <0.001. However, the flexible piecewise exponential model showed the smallest overdispersion parameter (3.2 versus 21.3 for non-flexible piecewise exponential models. Conclusion We showed that there were no major differences between methods. However, using a flexible piecewise regression modelling, with either a quasi-likelihood or robust standard errors, was the best approach as it deals with both, overdispersion due to model misspecification and true or inherent overdispersion.
Value passing for Communicating Piecewise Deterministic Markov Processes
Strubbe, Stefan; Schaft, Arjan van der; Julius, Agung
2006-01-01
In this paper we extend the CPDP model, which is used for compositional specification of PDP-type stochastic hybrid systems, to the value passing CPDP model. With value passing we can express communication of values of continuous variables between CPDP components. We show that the class of value pas
Wang, Lu; Xu, Lisheng; Zhao, Dazhe; Yao, Yang; Song, Dan
2015-04-01
Because arterial pulse waves contain vital information related to the condition of the cardiovascular system, considerable attention has been devoted to the study of pulse waves in recent years. Accurate acquisition is essential to investigate arterial pulse waves. However, at the stage of developing equipment for acquiring and analyzing arterial pulse waves, specific pulse signals may be unavailable for debugging and evaluating the system under development. To produce test signals that reflect specific physiological conditions, in this paper, an arterial pulse wave generator has been designed and implemented using a field programmable gate array (FPGA), which can produce the desired pulse waves according to the feature points set by users. To reconstruct a periodic pulse wave from the given feature points, a method known as piecewise Gaussian-cosine fitting is also proposed in this paper. Using a test database that contains four types of typical pulse waves with each type containing 25 pulse wave signals, the maximum residual error of each sampling point of the fitted pulse wave in comparison with the real pulse wave is within 8%. In addition, the function for adding baseline drift and three types of noises is integrated into the developed system because the baseline occasionally wanders, and noise needs to be added for testing the performance of the designed circuits and the analysis algorithms. The proposed arterial pulse wave generator can be considered as a special signal generator with a simple structure, low cost and compact size, which can also provide flexible solutions for many other related research purposes.
Realization of Fractal Affine Transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its cor responding mathematical equations which are essential in fractal image construction.
Bounded contractions for affine buildings
Bestvina, Mladen; Savin, Gordan
2017-01-01
We consider affine buildings with refined chamber structure. For each vertex in the refined chamber structure we construct a contraction, based at the vertex, that is used to prove exactness of Schneider-Stuhler resolutions of arbitrary depth.
Affinity chromatography of phosphorylated proteins.
Tchaga, Grigoriy S
2008-01-01
This chapter covers the use of immobilized metal ion affinity chromatography (IMAC) for enrichment of phosphorylated proteins. Some requirements for successful enrichment of these types of proteins are discussed. An experimental protocol and a set of application data are included to enable the scientist to obtain high-yield results in a very short time with pre-packed phospho-specific metal ion affinity resin (PMAC).
Oriented angles in affine space
Directory of Open Access Journals (Sweden)
Włodzimierz Waliszewski
2004-05-01
Full Text Available The concept of a smooth oriented angle in an arbitrary affine space is introduced. This concept is based on a kinematics concept of a run. Also, a concept of an oriented angle in such a space is considered. Next, it is shown that the adequacy of these concepts holds if and only if the affine space, in question, is of dimension 2 or 1.
An improved piecewise Logistic map and its performance analysis%一种改进的分段Logistic映射及其性能分析
Institute of Scientific and Technical Information of China (English)
卫超; 孙爱晶; 范九伦
2012-01-01
在分析Logistic映射基本特性的基础上,提出了一种改进的分段Logistic映射,对这两种映射的倍周期分叉、自相关性和互相关性分别进行了实验分析和比较。结果表明,改进的分段Logistic映射改善了Logistic映射的性能,在系统参数取值变化时保持了良好的遍历性,而且拥有更大的密钥空间和更好的安全性。研究结果为Lo-gistic映射在保密技术中的进一步应用开辟了更为广阔的前景。%On the basis of analysis of basic features of Logistic mapping,an improved piecewise Logistic map is proposed.The mapping of the period doubling bifurcation and the autocorrelation and cross correlation of the experimental are analyzed and compared.The results show that the improved piecewise Logistic map improved the performance of Logistic map,and maintained a good ergodicity in the system parameter values change.Moreover,it offers a larger key space and better security.Results are promising for further application of Logistic mapping in security technology.
Perfect Sampling of Markov Chains with Piecewise Homogeneous Events
Bušić, Ana; Pin, Furcy
2010-01-01
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events in the system have monotonicity property. However, in the general (non-monotone) case, this technique needs to consider the whole state space, which limits its application only to chains with a state space of small cardinality. We propose here a new approach for the general case that only needs to consider two trajectories. Instead of the original chain, we use two bounding processes (envelopes) and we show that, whenever they couple, one obtains a sample under the stationary distribution of the original chain. We show that this new approach is particularly effective when the state space can be partitioned into pieces where envelopes can be easily computed. We further show that most Markovian queueing networks have this property and we propose efficient algorithms for some...
Institute of Scientific and Technical Information of China (English)
LI Chun-xi; CHEN Chang-jia
2009-01-01
Conventionally, P2P video is regarded as CBR traffic. However, our measurements have shown that the rate reset cannot be neglected in a practical IPTV system because each rate reset often leads to performance degradation. Thus, addressing the problem of inferring playback rate and rate reset in a P2P video system is significant. In this article, an algorithm termed piecewise linear envelope approximation (PLEA) is proposed, in which a follow-up time is introduced to smooth rate fluctuations in a small time scale and to adapt rate jumps in a large time scale automatically. With the PLEA algorithm, discontinuity introduced by blind segmentations adopted by current methods is avoided. Furthermore, unlike existing algorithms in which both segmentation and combinations are performed in multiple runs, only a single computation path is involved in the PLEA algorithm. This makes PLEA algorithm amenable to implementation of low complexity by either software or hardware. Both theoretical analysis and experiment based on measured data show that the PLEA outperforms existing algorithms based on segmentation.
Affinity Monolith-Integrated Microchips for Protein Purification and Concentration.
Gao, Changlu; Sun, Xiuhua; Wang, Huaixin; Qiao, Wei; Hu, Bo
2016-01-01
Affinity chromatography is a valuable method to purify and concentrate minute amount of proteins. Monoliths with epoxy groups for affinity immobilization were prepared by direct in-situ photopolymerization of glycidyl methacrylate and ethylene glycol dimethacrylate in porogenic solvents consisting of 1-dodecanol and cyclohexanol. By integrating affinity monoliths onto a microfluidic system, targeted biomolecules can be captured and retained on affinity column, while other biomolecules having no specific interactions toward the immobilized ligands flow through the microchannel. Therefore, proteins which remain on the affinity column are purified and concentrated, and then eluted by appropriate solutions and finally, separated by microchip capillary electrophoresis. This integrated microfluidic device has been applied to the purification and separation of specific proteins (FITC-labeled human serum albumin and IgG) in a mixture.
Institute of Scientific and Technical Information of China (English)
Li Meng; Zhu Lingren; Long Haiying
2003-01-01
In this paper, we use the standard deviation method and the fixed mass method to study theself-affine fractal and multi-fractal features along two topographic profiles across differenttectonic-geomorphic elements in the Tianshan area of Xinjiang region, China. The results showthat in the studied scaling range, the two profiles display different scaling fractal features, andthe form and value range of multi-fractal spectra Dq also show different characteristics. Thestudy suggests that the landforms are not completely random, but are deterministicallyrandom. The fractal dimension values in different scaling ranges express the mode, intensityand spatial dimension of the endogenic and exogenic processes. Meanwhile, a boundary pointbetween the macroscopic and microscopic scales of geomorphic process is suggested to be about5 km. These results are of significance in quantitative study of geomorphic dynamics.
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Stability and Multiscroll Attractors of Control Systems via the Abscissa
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Edgar-Cristian Díaz-González
2017-01-01
Full Text Available We present an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix in this paper. First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials. The starting point is the Gauss–Lucas theorem, we provide lower bounds for Hurwitz polynomials, and by successively decreasing the order of the derivative of the Hurwitz polynomial one obtains a sequence of lower bounds. The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors based on a class of unstable dissipative systems (UDS of affine linear type.
A three-layer preon star model from exact piecewise-continuous solutions of Einstein's equations
Pazameta, Zoran
2012-01-01
A metric of Birkhoffian form is employed to model a hybrid astrophysical compact object consisting of a preon gas core, a mantle of electrically charged hot quark-gluon plasma, and an outer envelope of charged hadronic matter which is matched to an exterior Reissner-Nordstr\\"om vacuum. The piecewise-continuous metric and the pressure and density functions consist of polynomials that are everywhere well-behaved. Boundary conditions at each interface yield estimates for physical parameters applicable to each layer, and to the star as a whole.
Analytic, piecewise solution to the Lane-Emden equation for stars with complex density profiles
Miller, Jeff; Bogdanovic, Tamara
2017-01-01
The polytropic models of stars are used for a variety of applications in computational astrophysics. These are typically obtained by numerically solving the Lane-Emden equation for a star in hydrostatic equilibrium under assumption that the pressure and density within the star obey the polytropic equation of state. We present an efficient analytic, piecewise differentiable solution to the Lane-Emden equation which allows “stitching” of different polytropes to represent complex pressure and density profiles. This approach can be used to model stars with distinct properties in their cores and envelopes, such as the evolved red giant and horizontal branch stars.
Regularity of absolutely continuous invariant measures for piecewise expanding unimodal maps
Contreras, Fabián; Dolgopyat, Dmitry
2016-09-01
Let f:[0,1]\\to [0,1] be a piecewise expanding unimodal map of class C k+1, with k≥slant 1 , and μ =ρ \\text{d}x the (unique) SRB measure associated to it. We study the regularity of ρ. In particular, points N where ρ is not differentiable has zero Hausdorff dimension, but is uncountable if the critical orbit of f is dense. This improves on a work of Szewc (1984). We also obtain results about higher orders of differentiability of ρ in the sense of Whitney.
Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
Giese, Guido
2009-11-01
Numerical schemes for hyperbolic conservation laws in 2-D on a Cartesian grid usually have the advantage of being easy to implement and showing good computational performances, without allowing the simulation of “real-world” problems on arbitrarily shaped domains. In this paper a numerical treatment of boundary conditions for the elastic-plastic wave equation is developed, which allows the simulation of problems on an arbitrarily shaped physical domain surrounded by a piece-wise smooth boundary curve, but using a PDE solver on a rectangular Cartesian grid with the afore-mentioned advantages.
Explicit Piecewise Smooth Solutions of Landau-Lifshitz Equation with Discontinuous External Field
Institute of Scientific and Technical Information of China (English)
Gan-shan Yang; Yun-zhang Zhang; Li-min Liu
2009-01-01
In this paper,we shall construct some explicit piecewise smooth(global continuous)solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation,subject to the external magnetic fields being both discontinuous and unbounded.When the external magnetic field is continuous,some explicit exact smooth solutions and blow up solution are also constructed.We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.
Phase patterns in finite oscillator networks with insights from the piecewise linear approximation
Goldstein, Daniel
2015-03-01
Recent experiments on spatially extend arrays of droplets containing Belousov-Zhabotinsky reactants have shown a rich variety of spatio-temporal patterns. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. When coupled, these two attractors have different preferred phase synchronizations, leading to complex behavior. We study rings of coupled oscillators and observe a rich array of oscillating patterns. We combine Turing analysis and a piecewise linear approximation to better understand the observed patterns.
An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application
DEFF Research Database (Denmark)
Kurita, Takamitsu; Nielsen, Heino Bohn; Rahbæk, Anders
for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where...... asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980....
A low-power piecewise linear analog to digital converter for use in particle tracking
Energy Technology Data Exchange (ETDEWEB)
Valencic, V.; Deval, P. [MEAD Microelectronics S.A., St. Sulpice (Switzerland)]|[EPFL, Lausanne (Switzerland). Electronics Labs.; Anghinolfi, F. [CERN, Geneva (Switzerland); Bonino, R.; Marra, D. La; Kambara, Hisanori [Univ. of Geneva (Switzerland)
1995-08-01
This paper describes a low-power piecewise linear A/D converter. A 5MHz {at} 5V with 25mW power consumption prototype has been implemented in a 1.5{micro}m CMOS process. The die area excluding pads is 5mm{sup 2}. 11-bit absolute accuracy is obtained with a new DC offset plus charge injection compensation technique used in the comparators scheme. This ADC with large dynamic range and high resolution is developed for the readout of a tracker and/or preshower in the future LHC experiments.
2016-01-01
response variable taking on ordinal values 1 to C and a 1x vector of explanatory variables , , the proportional odds model is given by...I N S T I T U T E F O R D E F E N S E A N A L Y S E S Regularization for Continuously Observed Ordinal Response Variables with Piecewise...response variable , quality of video provided by the Shadow to friendly ground units, was measured on an ordinal scale continuously over time. Functional
An Approach to Formulation of FNLP with Complex Piecewise Linear Membership Functions
Institute of Scientific and Technical Information of China (English)
闻博; 李宏光
2014-01-01
Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming (FNLP) problem with piecewise linear membership functions (PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.
Local structure of self-affine sets
Bandt, Christoph
2011-01-01
The structure of a self-similar set with open set condition does not change under magnification. For self-affine sets the situation is completely different. We consider planar self-affine Cantor sets E of the type studied by Bedford, McMullen, Gatzouras and Lalley, for which the projection onto the horizontal axis is an interval. We show that within small square neighborhoods of almost each point x in E, with respect to many product measures on address space, E is well approximated by product sets of an interval and a Cantor set. Even though E is totally disconnected, the limit sets have the product structure with interval fibres, reminiscent to the view of attractors of chaotic differentiable dynamical systems.
Balázs, András
2003-06-01
In the present paper, some physical considerations of the biological symbol-matter problem is exposed. First of all, the physical concept of quantum dynamical internal measuremental robustness is discussed. In this context, the significance of introducing affine molecular Hilbert spaces, the original (primordeal) internal quantum measurement, and the global constraining nature of time-inversion symmetry restoring, as a special restoration force, is discussed at some length. It is pointed out, as a summary, that global robustness of the internal dynamics of quantum measurements is due to two basic factors: on one hand, the global constraining nature of the chosen specific (symmetry-) restoring force, and on the other, the individual robustness of the discrete local internal measuremental interactions. The second condition is supposed to follow from a system-internalised ("objective") Bohr-type Copenhagen interpretation of quantum mechanics, corresponding, in an external context, to the Generalized Complementarity Principle of Bohr and Elsasser. It is not claimed, however, that this latter problem has been, as yet, satisfactorily settled physically. In fact, if it were, it would amount to a specifically biological quantum theory of internal measurement, which had to be rooted in the original primordeal global internal measurement, amounting to the origin of the genetic code.
Smart, Jonathan P; Cliff, Matthew J; Kelly, David J
2009-11-01
The food-borne pathogen Campylobacter jejuni possesses no known tungstoenzymes, yet encodes two ABC transporters (Cj0300-0303 and Cj1538-1540) homologous to bacterial molybdate (ModABC) uptake systems and the tungstate transporter (TupABC) of Eubacterium acidaminophilum respectively. The actual substrates and physiological role of these transporters were investigated. Tryptophan fluorescence spectroscopy and isothermal titration calorimetry of the purified periplasmic binding proteins of each system revealed that while Cj0303 is unable to discriminate between molybdate and tungstate (K(D) values for both ligands of 4-8 nM), Cj1540 binds tungstate with a K(D) of 1.0 +/- 0.2 pM; 50 000-fold more tightly than molybdate. Induction-coupled plasma mass spectroscopy of single and double mutants showed that this large difference in affinity is reflected in a lower cellular tungsten content in a cj1540 (tupA) mutant compared with a cj0303c (modA) mutant. Surprisingly, formate dehydrogenase (FDH) activity was decreased approximately 50% in the tupA strain, and supplementation of the growth medium with tungstate significantly increased FDH activity in the wild type, while inhibiting known molybdoenzymes. Our data suggest that C. jejuni possesses a specific, ultra-high affinity tungstate transporter that supplies tungsten for incorporation into FDH. Furthermore, possession of two MoeA paralogues may explain the formation of both molybdopterin and tungstopterin in this bacterium.
Gravitation, Electromagnetism and Cosmological Constant in Purely Affine Gravity
Popławski, Nikodem J.
2009-03-01
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous ( ΛCDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell- Λ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell- ΛCDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.
Institute of Scientific and Technical Information of China (English)
童长飞; 章辉; 孙优贤
2007-01-01
By means of polynomial decomposition, a control scheme for polynomial nonlinear systems with affine timevarying uncertain parameters is presented. The idea of polynomial decomposition is to convert the coefficients of polynomial into a matrix with free variables, so that the nonnegativity of polynomials with even orders can be checked by linear matrix inequality (LMI) solvers or bilinear matrix inequality (BMI)solvers. Control synthesis for polynomial nonlinear system is based on Lyapunov stability theorem in this paper. Constructing Lyapunov function and finding feedback controller are automatically finished by computer programming with algorithms given in this paper. For multidimension systems with relatively high-order controller, the controller constructed with full monomial base will be in numerous terms. To overcome this problem,the reduced-form controller with minimum monomial terms is derived by the proposed algorithm. Then a suboptimal control aiming at minimum cost performance with gain constraints is advanced. The control scheme achieves effective performance as illustrated by numerical examples.
Piecewise Function Hysteretic Model for Cold-Formed Steel Shear Walls with Reinforced End Studs
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Jihong Ye
2017-01-01
Full Text Available Cold-formed steel (CFS shear walls with concrete-filled rectangular steel tube (CFRST columns as end studs can upgrade the performance of mid-rise CFS structures, such as the vertical bearing capacity, anti-overturning ability, shear strength, and fire resistance properties, thereby enhancing the safety of structures. A theoretical hysteretic model is established according to a previous experimental study. This model is described in a simple mathematical form and takes nonlinearity, pinching, strength, and stiffness deterioration into consideration. It was established in two steps: (1 a discrete coordinate method was proposed to determine the load-displacement skeleton curve of the wall, by which governing deformations and their corresponding loads of the hysteretic loops under different loading cases can be obtained; afterwards; (2 a piecewise function was adopted to capture the hysteretic loop relative to each governing deformation, the hysteretic model of the wall was further established, and additional criteria for the dominant parameters of the model were stated. Finally, the hysteretic model was validated by experimental results from other studies. The results show that elastic lateral stiffness Ke and shear capacity Fp are key factors determining the load-displacement skeleton curve of the wall; hysteretic characteristics of the wall with reinforced end studs can be fully reflected by piecewise function hysteretic model, moreover, the model has intuitional expressions with clear physical interpretations for each parameter, paving the way for predicting the nonlinear dynamic responses of mid-rise CFS structures.
A Neurodynamic Approach for Real-Time Scheduling via Maximizing Piecewise Linear Utility.
Guo, Zhishan; Baruah, Sanjoy K
2016-02-01
In this paper, we study a set of real-time scheduling problems whose objectives can be expressed as piecewise linear utility functions. This model has very wide applications in scheduling-related problems, such as mixed criticality, response time minimization, and tardiness analysis. Approximation schemes and matrix vectorization techniques are applied to transform scheduling problems into linear constraint optimization with a piecewise linear and concave objective; thus, a neural network-based optimization method can be adopted to solve such scheduling problems efficiently. This neural network model has a parallel structure, and can also be implemented on circuits, on which the converging time can be significantly limited to meet real-time requirements. Examples are provided to illustrate how to solve the optimization problem and to form a schedule. An approximation ratio bound of 0.5 is further provided. Experimental studies on a large number of randomly generated sets suggest that our algorithm is optimal when the set is nonoverloaded, and outperforms existing typical scheduling strategies when there is overload. Moreover, the number of steps for finding an approximate solution remains at the same level when the size of the problem (number of jobs within a set) increases.
The stiffness variation of a micro-ring driven by a traveling piecewise-electrode.
Li, Yingjie; Yu, Tao; Hu, Yuh-Chung
2014-09-16
In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.
Group lassoing change-points in piecewise-constant AR processes
Angelosante, Daniele; Giannakis, Georgios B.
2012-12-01
Regularizing the least-squares criterion with the total number of coefficient changes, it is possible to estimate time-varying (TV) autoregressive (AR) models with piecewise-constant coefficients. Such models emerge in various applications including speech segmentation, biomedical signal processing, and geophysics. To cope with the inherent lack of continuity and the high computational burden when dealing with high-dimensional data sets, this article introduces a convex regularization approach enabling efficient and continuous estimation of TV-AR models. To this end, the problem is cast as a sparse regression one with grouped variables, and is solved by resorting to the group least-absolute shrinkage and selection operator (Lasso). The fresh look advocated here permeates benefits from advances in variable selection and compressive sampling to signal segmentation. An efficient block-coordinate descent algorithm is developed to implement the novel segmentation method. Issues regarding regularization and uniqueness of the solution are also discussed. Finally, an alternative segmentation technique is introduced to improve the detection of change instants. Numerical tests using synthetic and real data corroborate the merits of the developed segmentation techniques in identifying piecewise-constant TV-AR models.
Shen, Ji Yao; Abu-Saba, Elias G.; Mcginley, William M.; Sharpe, Lonnie, Jr.; Taylor, Lawrence W., Jr.
1992-01-01
Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.
Energy Technology Data Exchange (ETDEWEB)
Ramos, J.I. [Universidad de Malaga, E.T.S. Ingenieros Industriales, Room I-320-D, Plaza El Ejido, s/n, 29013 Malaga (Spain)]. E-mail: jirs@lcc.uma.es
2006-06-15
An approximate method based on piecewise linearization is developed for the determination of periodic orbits of nonlinear oscillators. The method is based on Taylor series expansions, provides piecewise analytical solutions in three-point intervals which are continuous everywhere and explicit three-point difference equations which are P-stable and have an infinite interval of periodicity. It is shown that the method presented here reduces to the well-known Stoermer technique, is second-order accurate, and yields, upon applying Taylor series expansion and a Pade approximation, another P-stable technique whenever the Jacobian is different from zero. The method is generalized for single degree-of-freedom problems that contain the velocity, and (approximate) analytical solutions are presented. Finally, by introducing the inverse of a vector and the vector product and quotient, and using Taylor series expansions and a Pade approximation, the method has been generalized to multiple degree-of-freedom problems and results in explicit three-point finite difference equations which only involve vector multiplications.
Yang, Xitao; Yuan, Rong
2006-10-01
In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.
Affine Contractions on the Plane
Celik, D.; Ozdemir, Y.; Ureyen, M.
2007-01-01
Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…
Gravity theory through affine spheres
Minguzzi, E.
2017-08-01
In this work it is argued that in order to improve our understanding of gravity and spacetime our most successful theory, general relativity, must be destructured. That is, some geometrical assumptions must be dropped and recovered just under suitable limits. Along this line of thought we pursue the idea that the roundness of the light cone, and hence the isotropy of the speed of light, must be relaxed and that, in fact, the shape of light cones must be regarded as a dynamical variable. Mathematically, we apply some important results from affine differential geometry to this problem, the idea being that in the transition we should preserve the identification of the spacetime continuum with a manifold endowed with a cone structure and a spacetime volume form. To that end it is suggested that the cotangent indicatrix (dispersion relation) must be described by an equation of Monge-Ampère type determining a hyperbolic affine sphere, at least whenever the matter content is negligible. Non-relativistic spacetimes fall into this description as they are recovered whenever the center of the affine sphere is at infinity. In the more general context of Lorentz-Finsler theories it is shown that the lightlike unparametrized geodesic flow is completely determined by the distribution of light cones. Moreover, the transport of lightlike momenta is well defined though there could be no notion of affine parameter. Finally, we show how the perturbed indicatrix can be obtained from the perturbed light cone.
The sodium ion affinities of asparagine, glutamine, histidine and arginine
Wang, Ping; Ohanessian, Gilles; Wesdemiotis, Chrys
2008-01-01
The sodium ion affinities of the amino acids Asn, Gln, His and Arg have been determined by experimental and computational approaches (for Asn, His and Arg). Na+-bound heterodimers with amino acid and peptide ligands (Pep1, Pep2) were produced by electrospray ionization. From the dissociation kinetics of these Pep1-Na+-Pep2 ions to Pep1-Na+ and Pep2-Na+, determined by collisionally activated dissociation, a ladder of relative affinities was constructed and subsequently converted to absolute affinities by anchoring the relative values to known Na+ affinities. The Na+ affinities of Asn, His and Arg, were calculated at the MP2(full)/6-311+G(2d,2p)//MP2/6-31G(d) level of ab initio theory. The resulting experimental and computed Na+ affinities are in excellent agreement with one another. These results, combined with those of our previous studies, yield the sodium ion affinities of 18 out of the 20 [alpha]-amino acids naturally occurring in peptides and proteins of living systems.
Durstewitz, Daniel
2017-06-01
The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic) network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional) state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs) are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs) within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC) obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast) maximum-likelihood estimation framework for PLRNNs that may enable to recover relevant aspects
Directory of Open Access Journals (Sweden)
Daniel Durstewitz
2017-06-01
Full Text Available The computational and cognitive properties of neural systems are often thought to be implemented in terms of their (stochastic network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit recordings or neuroimaging data, is an important step toward understanding its computations. Ideally, one would not only seek a (lower-dimensional state space representation of the dynamics, but would wish to have access to its statistical properties and their generative equations for in-depth analysis. Recurrent neural networks (RNNs are a computationally powerful and dynamically universal formal framework which has been extensively studied from both the computational and the dynamical systems perspective. Here we develop a semi-analytical maximum-likelihood estimation scheme for piecewise-linear RNNs (PLRNNs within the statistical framework of state space models, which accounts for noise in both the underlying latent dynamics and the observation process. The Expectation-Maximization algorithm is used to infer the latent state distribution, through a global Laplace approximation, and the PLRNN parameters iteratively. After validating the procedure on toy examples, and using inference through particle filters for comparison, the approach is applied to multiple single-unit recordings from the rodent anterior cingulate cortex (ACC obtained during performance of a classical working memory task, delayed alternation. Models estimated from kernel-smoothed spike time data were able to capture the essential computational dynamics underlying task performance, including stimulus-selective delay activity. The estimated models were rarely multi-stable, however, but rather were tuned to exhibit slow dynamics in the vicinity of a bifurcation point. In summary, the present work advances a semi-analytical (thus reasonably fast maximum-likelihood estimation framework for PLRNNs that may enable to recover
Institute of Scientific and Technical Information of China (English)
翁永鹏; 高宪文; 吕明阳
2014-01-01
An improved model-free adaptive control(IMFAC) approach is proposed for the more general non-affine nonlinear discrete systems. The nonparametric dynamic linearization technique is used in the controller design. By applying the observer strategy, the real-time dynamic linearization for the disturbance systems is realized. Thus the application scope of MFAC approach is extended to the more general non-affine nonlinear discrete-time systems. Then, the robust convergence of the IMFAC algorithm is also addressed. A numerical example is selected to validate the feasibility and effectiveness of the proposed method.%针对一类更广泛的非仿射非线性离散系统，提出一种改进的无模型自适应控制算法。该算法基于非参数动态线性化方法，运用观测器的思想，实现带有扰动系统的实时动态线性化，进而将无模型自适应控制方法的应用推广到更广泛的非仿射非线性离散系统。同时，对推广后的改进无模型自适应控制方法进行理论上的证明，并通过仿真实例验证了所提出的改进无模型自适应控制方法的可行性和有效性。
Institute of Scientific and Technical Information of China (English)
蔡丹; 季晓勇; 史贺; 潘家民
2016-01-01
Logistic chaotic maps and Tent chaotic maps are widely applied in the field of the communication security . Tent chaotic maps have piecewise characteristics ;sowe can apply the piecewise features in Logistic chaotic mapsnaturally .The paperproposes a method that Logistic chaotic maps can be divided into three segments which are tangent each other(three‐segment and tangential piecewise Logistic chaotic maps ) .The method can avoid the process that Tent chaotic maps need to apply the stochastic perturbation ,and it also improves the randomness of Logistic chaotic maps ,which increases the complexity and anti‐attack capability of the chaotic system .Onbasis of the experiment ,the paper proves that three‐segment and tangential piecewise Logistic chaotic maps can enter into chaotic state earlier on the same interval ,and their trajectory are increasingly unstable when μis between 3 .57 and 4 .The Lyapunov exponent is positive and it increases gradually ,thus more complicated nonlinear equation improves the security of system .Under the same bifurcate criterion threshold ,the number of iterations is decreased dramatically when three‐segment and tangential piecewise Logistic chaotic maps enter into chaotic state .Therefore ,three‐segment and tangential piecewise Logistic chaotic sequences have better randomness and unpredictability .The experiment shows that three‐segment and tangential piecewise Logistic chaotic maps are initial‐value sensitivity ,so they will be widely applied in the field of information security .%Logistic混沌映射和Tent映射是两种广泛应用于通信安全领域的混沌映射，Tent映射具有分段特性，由此联想到将Logistic混沌映射推广为分段映射．提出一种三分段相切的Logistic混沌序列的方法，不仅规避了 Tent映射需施加随机扰动的过程，并改善了Logistic混沌映射的随机性能，增加了系统的复杂度和抗攻击能力．实验证明在相同的区间上，三
Kong, Xiangxi; Sun, Wei; Wang, Bo; Wen, Bangchun
2015-06-01
The dynamic behaviors and stability of the linear guide considering contact actions are studied by multi-term incremental harmonic balance method (IHBM). Based on fully considering the parameters of the linear guide, a static model is developed and the contact stiffness is calculated according to Hertz contact theory. A generalized time-varying and piecewise-nonlinear dynamic model of the linear guide is formulated to perform an accurate investigation on its dynamic behaviors and stability. The numerical simulation is used to confirm the feasibility of the approach. The effects of excitation force and mean load on the system are analyzed in low-order nonlinearity. Multi-term IHBM and numerical simulation are employed to the effect of high-order nonlinearity and show the transition to chaos. Additionally, the effects of preload, initial contact angle, the number and diameter of balls are discussed.
Simpson, D. J. W.
2017-01-01
The mode-locking regions of a dynamical system are subsets of parameter space within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a distinctive chain structure with points of zero width called shrinking points. In this paper a local analysis about an arbitrary shrinking point is performed. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional centre manifolds in order to build a comprehensive theoretical framework for the local dynamics. The main results are universal quantitative descriptions for the shape of nearby mode-locking regions, the location of nearby shrinking points, and the key properties of these shrinking points. The results are applied to the three-dimensional border-collision normal form, a model of an oscillator subject to dry friction, and a model of a DC/DC power converter.
DEFF Research Database (Denmark)
Wolf, Paul A.; Jørgensen, Jakob Sauer; Schmidt, Taly G.
2013-01-01
A sparsity-exploiting algorithm intended for few-view Single Photon Emission Computed Tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true...
Electron affinity of chlorine dioxide
Energy Technology Data Exchange (ETDEWEB)
Babcock, L.M.; Pentecost, T.; Koppenol, W.H. (Louisiana State Univ., Baton Rouge (USA))
1989-12-14
The flowing afterglow technique was used to determine the electron affinity of chlorine dioxide. A value of 2.37 {plus minus} 0.10 eV was found by bracketing between the electron affinities of HS* and SF{sub 4} as a lower limit and that of NO{sub 2} as an upper limit. This value is in excellent agreement with 2.32 eV predicted from a simple thermodynamic cycle involving the reduction potential of the ClO{sub 2}/ClO{sub 2}{sup {minus}} couple and a Gibbs hydration energy identical with that of SO{sub 2}{sup {sm bullet}{minus}}.
The electron affinity of tungsten
Energy Technology Data Exchange (ETDEWEB)
Lindahl, A.O.; Andersson, P.; Klason, P.; Hanstorp, D. [Department of Physics, University of Gothenburg (Sweden); Diehl, C. [Institut fur Physik, Johannes Gutenberg-Universitat, Mainz (Germany); Present Address: Max-Planck-Institut fur Kernphysik, Heidelberg (Germany); Forstner, O. [Faculty of Physics, University of Vienna, Wien (Austria)
2010-11-15
The electron affinity of tungsten has been measured using laser photodetachment threshold spectroscopy in a collinear geometry. The electron affinity was determined to 6583.6(6) cm{sup -1} by observing the onset of the process when W{sup -} ions in the 5d{sup 5}6s{sup 2} {sup 6}S{sub 5/2} ground state are photo-detached producing neutral W atoms in the 5d{sup 4}6s{sup 2} {sup 5}D{sub 0} ground state. The measured value is in agreement with previous measurements and improves the accuracy by almost two orders of magnitude. Further, a photodetachment signal below the ground state photodetachment threshold was found, which indicates the existence of a bound excited state in W{sup -}. (authors)
Generalized Methods and Solvers for Noise Removal from Piecewise Constant Signals
Little, Max A
2010-01-01
Removing noise from piecewise constant (PWC) signals, is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need separating into stratigraphic zones, and in biophysics, jumps between molecular dwell states need extracting from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited however. This paper shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following, and coordinate descent. We intr...
Mandrekar, Pratik
2011-01-01
We study the properties of least time trajectories for particles moving on a two dimensional surface which consists of piecewise homogeneous regions. The particles are assumed to move with different constant speeds on different regions and on the boundary between regions. The speed of the particle is assumed to be highest when it moves along the edges formed by the boundary of two regions. We get an analogous behavior to Snell's Law of light refraction, but in a more generalized form. The model could be used for studying properties of animal and insect trails which tend to form predominantly along edges. The model predicts three types of behavior for the trajectories near a corner forming edge: fully edge following, partial edge following and complete avoidance of the edge, which are indeed observed in natural ant trails.
Synchronization regions of two pulse-coupled electronic piecewise linear oscillators
Rubido, N.; Cabeza, C.; Kahan, S.; Ramírez Ávila, G. M.; Marti, Arturo C.
2011-03-01
Stable synchronous states of different order were analytically, numerically and experimentally characterized in pulse-coupled light-controlled oscillators (LCOs). The Master-Slave (MS) configuration was studied in conditions where different time-scale parameters were tuned under varying coupling strength. Arnold tongues calculated analytically - based on the piecewise two-time-scale model for LCOs - and obtained numerically were consistent with experimental results. The analysis of the stability pattern and tongue shape for (1 : n) synchronization was based on the construction of return maps representing the Slave LCO evolution induced by the action of the Master LCO. The analysis of these maps showed that both tongue shape and stability pattern remained invariant. Considering the wide variation range of LCO parameters, the obtained results could have further applications on ethological models.
Energy Technology Data Exchange (ETDEWEB)
Budantsev, M. V., E-mail: budants@isp.nsc.ru; Lavrov, R. A.; Pogosov, A. G.; Zhdanov, E. Yu.; Pokhabov, D. A. [Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics, Siberian Branch (Russian Federation)
2011-02-15
Extraordinary piecewise parabolic behavior of the magnetoresistance has been experimentally detected in the two-dimensional electron gas with a dense triangular lattice of antidots, where commensurability magnetoresistance oscillations are suppressed. The magnetic field range of 0-0.6 T can be divided into three wide regions, in each of which the magnetoresistance is described by parabolic dependences with high accuracy (comparable to the experimental accuracy) and the transition regions between adjacent regions are much narrower than the regions themselves. In the region corresponding to the weakest magnetic fields, the parabolic behavior becomes almost linear. The observed behavior is reproducible as the electron gas density changes, which results in a change in the resistance by more than an order of magnitude. Possible physical mechanisms responsible for the observed behavior, including so-called 'memory effects,' are discussed.
An Adaptive Piecewise Curve-Fitting Package Using a Look-Ahead Strategy.
1981-01-01
LOOK-AHEAD STRATEGY# ,PI -lNGC- ;EI AqF AUTHO~fqj T-8 CC’NTPA:T DFZ -CNALN NJIMiiEP BlD C.Platt G. D. /aylor ’_,_.____--_-__ T-EPiRORMINGO CRAWANIH 44VN...8. SMTH= 6. TOL= . 100 . KNOTS ARE INDICATED BY 0. .700E-01 .600E-01 .500E-01 .400E-01 .300E-01 .2OCE-01 * IOCE-01 0 . . I I I I I I l I I I I I I I I...SMTH= 1, TOL= . 100 . KNOTS ARE INDICATED BY 0. * IOOE-01 X a. .. I0E+01 .200E+01 .300E-C PIECEWISE POLYNOMIAL APPROX. USING (DISCRETE) L2 APPROX
Directory of Open Access Journals (Sweden)
Dufan Wu
2013-01-01
Full Text Available Dual energy CT has the ability to give more information about the test object by reconstructing the attenuation factors under different energies. These images under different energies share identical structures but different attenuation factors. By referring to the fully sampled low-energy image, we show that it is possible to greatly reduce the sampling rate of the high-energy image in order to lower dose. To compensate the attenuation factor difference between the two modalities, we use piecewise polynomial fitting to fit the low-energy image to the high-energy image. During the reconstruction, the result is constrained by its distance to the fitted image, and the structural information thus can be preserved. An ASD-POCS-based optimization schedule is proposed to solve the problem, and numerical simulations are taken to verify the algorithm.
Development of New Loan Payment Models with Piecewise Geometric Gradient Series
Directory of Open Access Journals (Sweden)
Erdal Aydemir
2014-12-01
Full Text Available Engineering economics plays an important role in decision making. Also, the cash flows, time value of money and interest rates are the most important research fields in mathematical finance. Generalized formulae obtained from a variety of models with the time value of money and cash flows are inadequate to solve some problems. In this study, a new generalized formulae is considered for the first time and derived from a loan payment model which is a certain number of payment amount determined by customer at the beginning of payment period and the other repayments with piecewise linear gradient series. As a result, some numerical examples with solutions are given for the developed models.
Averaging for a Fully-Coupled Piecewise Deterministic Markov Process in Infinite Dimension
Genadot, Alexandre
2011-01-01
In this paper, we consider the generalized Hodgkin-Huxley model introduced by Austin in \\cite{Austin}. This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully-coupled Piecewise Deterministic Markov Process (PDMP) in infinite dimension. We introduce two time scales in this model in considering that some ion channels open and close at faster jump rates than others. We perform a slow-fast analysis of this model and prove that asymptotically this two time scales model reduces to the so called averaged model which is still a PDMP in infinite dimension for which we provide effective evolution equations and jump rates.
Locomotion of C. elegans: a piecewise-harmonic curvature representation of nematode behavior.
Directory of Open Access Journals (Sweden)
Venkat Padmanabhan
Full Text Available Caenorhabditis elegans, a free-living soil nematode, displays a rich variety of body shapes and trajectories during its undulatory locomotion in complex environments. Here we show that the individual body postures and entire trails of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase.
Nie, Xiaobing; Zheng, Wei Xing
2015-11-01
In this paper, we discuss the coexistence and dynamical behaviors of multiple equilibrium points for recurrent neural networks with a class of discontinuous nonmonotonic piecewise linear activation functions. It is proved that under some conditions, such n -neuron neural networks can have at least 5(n) equilibrium points, 3(n) of which are locally stable and the others are unstable, based on the contraction mapping theorem and the theory of strict diagonal dominance matrix. The investigation shows that the neural networks with the discontinuous activation functions introduced in this paper can have both more total equilibrium points and more locally stable equilibrium points than the ones with continuous Mexican-hat-type activation function or discontinuous two-level activation functions. An illustrative example with computer simulations is presented to verify the theoretical analysis.
3D Aware Correction and Completion of Depth Maps in Piecewise Planar Scenes
Thabet, Ali Kassem
2015-04-16
RGB-D sensors are popular in the computer vision community, especially for problems of scene understanding, semantic scene labeling, and segmentation. However, most of these methods depend on reliable input depth measurements, while discarding unreliable ones. This paper studies how reliable depth values can be used to correct the unreliable ones, and how to complete (or extend) the available depth data beyond the raw measurements of the sensor (i.e. infer depth at pixels with unknown depth values), given a prior model on the 3D scene. We consider piecewise planar environments in this paper, since many indoor scenes with man-made objects can be modeled as such. We propose a framework that uses the RGB-D sensor’s noise profile to adaptively and robustly fit plane segments (e.g. floor and ceiling) and iteratively complete the depth map, when possible. Depth completion is formulated as a discrete labeling problem (MRF) with hard constraints and solved efficiently using graph cuts. To regularize this problem, we exploit 3D and appearance cues that encourage pixels to take on depth values that will be compatible in 3D to the piecewise planar assumption. Extensive experiments, on a new large-scale and challenging dataset, show that our approach results in more accurate depth maps (with 20 % more depth values) than those recorded by the RGB-D sensor. Additional experiments on the NYUv2 dataset show that our method generates more 3D aware depth. These generated depth maps can also be used to improve the performance of a state-of-the-art RGB-D SLAM method.
The Stiffness Variation of a Micro-Ring Driven by a Traveling Piecewise-Electrode
Directory of Open Access Journals (Sweden)
Yingjie Li
2014-09-01
Full Text Available In the practice of electrostatically actuated micro devices; the electrostatic force is implemented by sequentially actuated piecewise-electrodes which result in a traveling distributed electrostatic force. However; such force was modeled as a traveling concentrated electrostatic force in literatures. This article; for the first time; presents an analytical study on the stiffness variation of microstructures driven by a traveling piecewise electrode. The analytical model is based on the theory of shallow shell and uniform electrical field. The traveling electrode not only applies electrostatic force on the circular-ring but also alters its dynamical characteristics via the negative electrostatic stiffness. It is known that; when a structure is subjected to a traveling constant force; its natural mode will be resonated as the traveling speed approaches certain critical speeds; and each natural mode refers to exactly one critical speed. However; for the case of a traveling electrostatic force; the number of critical speeds is more than that of the natural modes. This is due to the fact that the traveling electrostatic force makes the resonant frequencies of the forward and backward traveling waves of the circular-ring different. Furthermore; the resonance and stability can be independently controlled by the length of the traveling electrode; though the driving voltage and traveling speed of the electrostatic force alter the dynamics and stabilities of microstructures. This paper extends the fundamental insights into the electromechanical behavior of microstructures driven by electrostatic forces as well as the future development of MEMS/NEMS devices with electrostatic actuation and sensing.
Institute of Scientific and Technical Information of China (English)
许晔; 郭谋发; 杨耿杰; 高伟; 缪希仁
2015-01-01
对谐振接地系统单相接地故障特征的分析表明，单相接地初始阶段故障线路与健全线路间的零序电流波形相似度低于各健全线路间的零序电流波形相似度，且故障初始时刻故障线路与健全线路的零序电流极性相反，高阻接地时该结论仍成立。仿射不变矩恰能反映各零序电流波形的整体形状特征和极性关系，且不受波形平移、旋转和缩放等仿射变换的影响，抗干扰能力强。对从各故障暂态零序电流波形图中提取的仿射不变矩特征量进行谱系聚类分析，并计算聚类有效性指标，选取聚类有效性最高的聚类树实现故障选线。各种故障工况的大量仿真表明，该选线方法适应性好，可靠性高。%The analysis of the characteristic of neutral point resonant earthed system with single⁃phase⁃to⁃ground fault is made. The result shows that the similarities of zero sequence current waveforms between the fault line and each healthy line are below those between healthy lines, and zero sequence current of the fault line is in opposite polarity as those of healthy lines in initial stage of single⁃phase⁃to⁃ground fault. This situation remains during high resistance grounded fault. Affine moment invariants can just reflect the overall shape and polarity of each zero se⁃quence current without influence from affine transformation (such as rotation, translation and scale), and has a strong anti⁃jamming capability. The fault line is detected according to the pedigree clustering analysis of affine mo⁃ment invariants which is extracted from transient zero⁃sequence current waveforms of each line. Substantial simula⁃tions are conducted among various kinds of fault conditions. The results in various fault conditions show that the method is flexible and reliable.
Directory of Open Access Journals (Sweden)
Olav Slupphaug
2001-01-01
Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.
Affine connections on involutive G-structures
Merkulov, Sergey A.
1995-01-01
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of non-metric torsion-free affine connections was and remains rather unclear. One of the results discussed in this review asserts that any torsion-free holomorphic affine connecti...
The Quasi—affine Maps and Fractals
Institute of Scientific and Technical Information of China (English)
LunhaiLONG; GangCHEN
1997-01-01
In this paper,we discuss the discretization of the affine maps in R2,that is ,we consider a class of maps in Z2,which are induced by affine maps and called the quasi-affine maps.We investigate the properties and the dynamical behaviour of such maps,and give a sort of construction of complicated fractals by using quasi-affine maps.
Manifolds with integrable affine shape operator
Directory of Open Access Journals (Sweden)
Daniel A. Joaquín
2005-05-01
Full Text Available This work establishes the conditions for the existence of vector fields with the property that theirs covariant derivative, with respect to the affine normal connection, be the affine shape operatorS in hypersurfaces. Some results are obtained from this property and, in particular, for some kind of affine decomposable hypersurfaces we explicitely get the actual vector fields.
High affinity ligands for 'diazepam-insensitive' benzodiazepine receptors.
Wong, G; Skolnick, P
1992-01-14
Structurally diverse compounds have been shown to possess high affinities for benzodiazepine receptors in their 'diazepam-sensitive' (DS) conformations. In contrast, only the imidazobenzodiazepinone Ro 15-4513 has been shown to exhibit a high affinity for the 'diazepam-insensitive' (DI) conformation of benzodiazepine receptors. We examined a series of 1,4-diazepines containing one or more annelated ring systems for their affinities at DI and DS benzodiazepine receptors, several 1,4-diazepinone carboxylates including Ro 19-4603, Ro 16-6028 and Ro 15-3505 were found to possess high affinities (Ki approximately 2.6-20 nM) for DI. Nonetheless, among the ligands examined, Ro 15-4513 was the only substance with a DI/DS potency ratio approximately 1; other substances had ratios ranging from 13 to greater than 1000. Ligands with high to moderate affinities at DI were previously classified as partial agonists, antagonists, or partial inverse agonists at DS benzodiazepine receptors, but behaved as 'GABA neutral' (antagonist) substances at DI. The identification of several additional high affinity ligands at DI benzodiazepine receptors may be helpful in elucidating the pharmacological and physiological importance of these sites.
Topological conjugacy classes of affine maps
2008-01-01
A map $f: \\ff^n \\to \\ff^n$ over a field $\\ff$ is called affine if it is of the form $f(x)=Ax+b$, where the matrix $A \\in \\ff^{n\\times n}$ is called the linear part of affine map and $b \\in \\ff^n$. The affine maps over $\\ff=\\rr$ or $\\cc$ are investigated. We prove that affine maps having fixed points are topologically conjugate if and only if their linear parts are topologically conjugate. If affine maps have no fixed points and $n=1$ or 2, then they are topologically conjugate if and only if ...
Using Affinity Diagrams to Evaluate Interactive Prototypes
DEFF Research Database (Denmark)
Lucero, Andrés
2015-01-01
Affinity diagramming is a technique used to externalize, make sense of, and organize large amounts of unstructured, far-ranging, and seemingly dissimilar qualitative data. HCI and interaction design practitioners have adopted and used affinity diagrams for different purposes. This paper discusses...... our particular use of affinity diagramming in prototype evaluations. We reflect on a decade’s experience using affinity diagramming across a number of projects, both in industry and academia. Our affinity diagramming process in interaction design has been tailored and consists of four stages: creating...
Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
Frenkel, Edward
2016-01-01
We prove a system of relations in the Grothendieck ring of the category O of representations of the Borel subalgebra of an untwisted quantum affine algebra U_q(g^) introduced in [HJ]. This system was discovered in [MRV1, MRV2], where it was shown that solutions of this system can be attached to certain affine opers for the Langlands dual affine Kac-Moody algebra of g^, introduced in [FF5]. Together with the results of [BLZ3, BHK], which enable one to associate quantum g^-KdV Hamiltonians to representations from the category O, this provides strong evidence for the conjecture of [FF5] linking the spectra of quantum g^-KdV Hamiltonians and affine opers for the Langlands dual affine algebra. As a bonus, we obtain a direct and uniform proof of the Bethe Ansatz equations for a large class of quantum integrable models associated to arbitrary untwisted quantum affine algebras, under a mild genericity condition.
Supervised Machine Learning Methods Applied to Predict Ligand- Binding Affinity.
Heck, Gabriela S; Pintro, Val O; Pereira, Richard R; de Ávila, Mauricio B; Levin, Nayara M B; de Azevedo, Walter F
2017-01-01
Calculation of ligand-binding affinity is an open problem in computational medicinal chemistry. The ability to computationally predict affinities has a beneficial impact in the early stages of drug development, since it allows a mathematical model to assess protein-ligand interactions. Due to the availability of structural and binding information, machine learning methods have been applied to generate scoring functions with good predictive power. Our goal here is to review recent developments in the application of machine learning methods to predict ligand-binding affinity. We focus our review on the application of computational methods to predict binding affinity for protein targets. In addition, we also describe the major available databases for experimental binding constants and protein structures. Furthermore, we explain the most successful methods to evaluate the predictive power of scoring functions. Association of structural information with ligand-binding affinity makes it possible to generate scoring functions targeted to a specific biological system. Through regression analysis, this data can be used as a base to generate mathematical models to predict ligandbinding affinities, such as inhibition constant, dissociation constant and binding energy. Experimental biophysical techniques were able to determine the structures of over 120,000 macromolecules. Considering also the evolution of binding affinity information, we may say that we have a promising scenario for development of scoring functions, making use of machine learning techniques. Recent developments in this area indicate that building scoring functions targeted to the biological systems of interest shows superior predictive performance, when compared with other approaches. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.