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.
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
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
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.
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.
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.
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...
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....
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.
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.
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....
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...
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.
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.
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.
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...
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...
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.
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.
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.
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".
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.
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...
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...
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.
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
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.
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.
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.
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.
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.
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…
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.
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...
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.
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-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.
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...
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.
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.
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...
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)
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.
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.
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.
Interactive object modelling based on piecewise planar surface patches.
Prankl, Johann; Zillich, Michael; Vincze, Markus
2013-06-01
Detecting elements such as planes in 3D is essential to describe objects for applications such as robotics and augmented reality. While plane estimation is well studied, table-top scenes exhibit a large number of planes and methods often lock onto a dominant plane or do not estimate 3D object structure but only homographies of individual planes. In this paper we introduce MDL to the problem of incrementally detecting multiple planar patches in a scene using tracked interest points in image sequences. Planar patches are reconstructed and stored in a keyframe-based graph structure. In case different motions occur, separate object hypotheses are modelled from currently visible patches and patches seen in previous frames. We evaluate our approach on a standard data set published by the Visual Geometry Group at the University of Oxford [24] and on our own data set containing table-top scenes. Results indicate that our approach significantly improves over the state-of-the-art algorithms.
Interactive object modelling based on piecewise planar surface patches☆
Prankl, Johann; Zillich, Michael; Vincze, Markus
2013-01-01
Detecting elements such as planes in 3D is essential to describe objects for applications such as robotics and augmented reality. While plane estimation is well studied, table-top scenes exhibit a large number of planes and methods often lock onto a dominant plane or do not estimate 3D object structure but only homographies of individual planes. In this paper we introduce MDL to the problem of incrementally detecting multiple planar patches in a scene using tracked interest points in image sequences. Planar patches are reconstructed and stored in a keyframe-based graph structure. In case different motions occur, separate object hypotheses are modelled from currently visible patches and patches seen in previous frames. We evaluate our approach on a standard data set published by the Visual Geometry Group at the University of Oxford [24] and on our own data set containing table-top scenes. Results indicate that our approach significantly improves over the state-of-the-art algorithms. PMID:24511219
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.
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....
Piecewise Function Hysteretic Model for Cold-Formed Steel Shear Walls with Reinforced End Studs
Directory of Open Access Journals (Sweden)
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.
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.
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.
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
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.
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.
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.
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...
Fan affinity laws from a collision model
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour of air is incorporated. Our calculations prove the affinity laws and provide numerical estimates of the air delivery, thrust and drag on a rotating fan.
On Affine Fusion and the Phase Model
Directory of Open Access Journals (Sweden)
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.
Linear vs. piecewise Weibull model for genetic evaluation of sires for longevity in Simmental cattle
Directory of Open Access Journals (Sweden)
Nikola Raguž
2014-09-01
Full Text Available This study was focused on genetic evaluation of longevity in Croatian Simmental cattle using linear and survival models. The main objective was to create a genetic model that is most appropriate to describe the longevity data. Survival analysis, using piecewise Weibull proportional hazards model, used all information on the length of productive life including censored as well as uncensored observations. Linear models considered culled animals only. The relative milk production within herd had a highest impact on cows’ longevity. In comparison of estimated genetic parameters among methods, survival analysis yielded higher heritability value (0.075 than linear sire (0.037 and linear animal model (0.056. When linear models were used, genetic trend of Simmental bulls for longevity was slightly increasing over the years, unlike a decreasing trend in case of survival analysis methodology. Average reliability of bulls’ breeding values was higher in case of survival analysis. The rank correlations between survival analysis and linear models bulls’ breeding values for longevity were ranged between 0.44 and 0.46 implying huge differences in ranking of sires.
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.
Directory of Open Access Journals (Sweden)
Shujin Qin
2016-01-01
Full Text Available Workforce scheduling is an important and common task for projects with high labour intensities. It becomes particularly complex when employees have multiple skills and the employees’ productivity changes along with their learning of knowledge according to the tasks they are assigned to. Till now, in this context, only little work has considered the minimum quality limit of tasks and the quality learning effect. In this research, the workforce scheduling model is developed for assigning tasks to multiskilled workforce by considering learning of knowledge and requirements of project quality. By using piecewise linearization to learning curve, the mixed 0-1 nonlinear programming model (MNLP is transformed into a mixed 0-1 linear programming model (MLP. After that, the MLP model is further improved by taking account of the upper bound of employees’ experiences accumulation, and the stable performance of mature employees. Computational experiments are provided using randomly generated instances based on the investigation of a software company. The results demonstrate that the proposed MLPs can precisely approach the original MNLP model but can be calculated in much less time.
Einstein's gravity from an affine model
Castillo-Felisola, Oscar
2015-01-01
We show that the effective field equations for a recently formulated affine model of gravity, in the sector of a metric (torsion-free) connection, accept general Einstein manifolds --- with or without cosmological constant --- as solutions. Moreover, these effective field equations coincide with the ones obtained from a gravitational Yang--Mills theory known as Stephenson--Kilmister--Yang theory. Additionally, we find an equivalence between a minimally coupled massless scalar field in General Relativity with a "minimally" coupled scalar field in this affine model.
Piecewise log-normal approximation of size distributions for aerosol modelling
Directory of Open Access Journals (Sweden)
K. von Salzen
2006-01-01
Full Text Available An efficient and accurate method for the representation of particle size distributions in atmospheric models is proposed. The method can be applied, but is not necessarily restricted, to aerosol mass and number size distributions. A piecewise log-normal approximation of the number size distribution within sections of the particle size spectrum is used. Two of the free parameters of the log-normal approximation are obtained from the integrated number and mass concentration in each section. The remaining free parameter is prescribed. The method is efficient in a sense that only relatively few calculations are required for applications of the method in atmospheric models. Applications of the method in simulations of particle growth by condensation and simulations with a single column model for nucleation, condensation, gravitational settling, wet deposition, and mixing are described. The results are compared to results from simulations employing single- and double-moment bin methods that are frequently used in aerosol modelling. According to these comparisons, the accuracy of the method is noticeably higher than the accuracy of the other methods.
Farag, Mohammed; Fleckenstein, Matthias; Habibi, Saeid
2017-02-01
Model-order reduction and minimization of the CPU run-time while maintaining the model accuracy are critical requirements for real-time implementation of lithium-ion electrochemical battery models. In this paper, an isothermal, continuous, piecewise-linear, electrode-average model is developed by using an optimal knot placement technique. The proposed model reduces the univariate nonlinear function of the electrode's open circuit potential dependence on the state of charge to continuous piecewise regions. The parameterization experiments were chosen to provide a trade-off between extensive experimental characterization techniques and purely identifying all parameters using optimization techniques. The model is then parameterized in each continuous, piecewise-linear, region. Applying the proposed technique cuts down the CPU run-time by around 20%, compared to the reduced-order, electrode-average model. Finally, the model validation against real-time driving profiles (FTP-72, WLTP) demonstrates the ability of the model to predict the cell voltage accurately with less than 2% error.
Directory of Open Access Journals (Sweden)
Yanan Liu
2016-10-01
Full Text Available There are many uncertainties and risks in residential electricity consumption associated with economic development. Knowledge of the relationship between residential electricity consumption and its key determinant—income—is important to the sustainable development of the electric power industry. Using panel data from 30 provinces for the 1995–2012 period, this study investigates how residential electricity consumption changes as incomes increase in China. Previous studies typically used linear or quadratic double-logarithmic models imposing ex ante restrictions on the indistinct relationship between residential electricity consumption and income. Contrary to those models, we employed a reduced piecewise linear model that is self-adaptive and highly flexible and circumvents the problem of “prior restrictions”. Robust tests of different segment specifications and regression methods are performed to ensure the validity of the research. The results provide strong evidence that the income elasticity was approximately one, and it remained stable throughout the estimation period. The income threshold at which residential electricity consumption automatically remains stable or slows has not been reached. To ensure the sustainable development of the electric power industry, introducing higher energy efficiency standards for electrical appliances and improving income levels are vital. Government should also emphasize electricity conservation in the industrial sector rather than in residential sector.
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.
Fan Affinity Laws from a Collision Model
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…
Fan Affinity Laws from a Collision Model
Bhattacharjee, Shayak
2012-01-01
The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…
Hernández-Lloreda, María Victoria; Colmenares, Fernando; Martínez-Arias, Rosario
2004-09-01
In behavioral science, developmental discontinuities are thought to arise when the association between an outcome measure and the underlying process changes over time. Sudden changes in behavior across time are often taken to indicate that a reorganization in the outcome-process relationship may have occurred. The authors proposed in this article the use of piecewise hierarchical linear growth modeling as a statistical methodology to search for discontinuities in behavioral development and illustrated its possibilities by applying 2-piece hierarchical linear models to the study of developmental trajectories of baboon (Papio hamadryas) mothers' behavior during their infants' 1st year of life. The authors provided empirical evidence that piecewise growth modeling can be used to determine whether abrupt changes in development trajectories are tied to changes in the underlying process. ((c) 2004 APA, all rights reserved).
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.
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.
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.
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.
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.
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...
Mamey, Mary Rose; Barbosa-Leiker, Celestina; McPherson, Sterling; Burns, G. Leonard; Parks, Craig; Roll, John
2015-01-01
Researchers often want to examine two comorbid conditions simultaneously. One strategy to do so is through the use of parallel latent growth curve modeling (LGCM). This statistical technique allows for the simultaneous evaluation of two disorders to determine the explanations and predictors of change over time. Additionally, a piecewise model can help identify whether there are more than two growth processes within each disorder (e.g., during a clinical trial). A parallel piecewise LGCM was applied to self-reported attention deficit/hyperactivity disorder (ADHD) and self-reported substance use symptoms in 303 adolescents enrolled in cognitive behavioral therapy treatment for a substance use disorder (SUD) and receiving either oral-methylphenidate or placebo for ADHD across 16 weeks. Assessing these two disorders concurrently allowed us to determine whether elevated levels of one disorder predicted elevated levels or increased risk of the other disorder. First, a piecewise growth model measured ADHD and SU separately. Next, a parallel piecewise LGCM was used to estimate the regressions across disorders to determine whether higher scores at baseline of the disorders (i.e., ADHD or SUD) predicted rates of change in the related disorder. Finally, treatment was added to the model to predict change. While the analyses revealed no significant relationships across disorders, this study explains and applies a parallel piecewise growth model to examine the developmental processes of comorbid conditions over the course of a clinical trial. Strengths of piecewise and parallel LGCMs for other addictions researchers interested in examining dual processes over time are discussed. PMID:26389639
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.
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.
Piecewise-Constant-Model-Based Interior Tomography Applied to Dentin Tubules
Directory of Open Access Journals (Sweden)
Peng He
2013-01-01
Full Text Available Dentin is a hierarchically structured biomineralized composite material, and dentin’s tubules are difficult to study in situ. Nano-CT provides the requisite resolution, but the field of view typically contains only a few tubules. Using a plate-like specimen allows reconstruction of a volume containing specific tubules from a number of truncated projections typically collected over an angular range of about 140°, which is practically accessible. Classical computed tomography (CT theory cannot exactly reconstruct an object only from truncated projections, needless to say a limited angular range. Recently, interior tomography was developed to reconstruct a region-of-interest (ROI from truncated data in a theoretically exact fashion via the total variation (TV minimization under the condition that the ROI is piecewise constant. In this paper, we employ a TV minimization interior tomography algorithm to reconstruct interior microstructures in dentin from truncated projections over a limited angular range. Compared to the filtered backprojection (FBP reconstruction, our reconstruction method reduces noise and suppresses artifacts. Volume rendering confirms the merits of our method in terms of preserving the interior microstructure of the dentin specimen.
Abacus models for parabolic quotients of affine Weyl groups
Hanusa, Christopher R H
2011-01-01
We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine Weyl group of type C due to Eriksson to generalize a construction of James for the symmetric group. We also describe several combinatorial models for these parabolic quotients that generalize classical results in affine type A related to core partitions.
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.
Edwards, C. L.; Edwards, M. L.
2009-05-01
MEMS micro-mirror technology offers the opportunity to replace larger optical actuators with smaller, faster ones for lidar, network switching, and other beam steering applications. Recent developments in modeling and simulation of MEMS two-axis (tip-tilt) mirrors have resulted in closed-form solutions that are expressed in terms of physical, electrical and environmental parameters related to the MEMS device. The closed-form analytical expressions enable dynamic time-domain simulations without excessive computational overhead and are referred to as the Micro-mirror Pointing Model (MPM). Additionally, these first-principle models have been experimentally validated with in-situ static, dynamic, and stochastic measurements illustrating their reliability. These models have assumed that the mirror has a rectangular shape. Because the corners can limit the dynamic operation of a rectangular mirror, it is desirable to shape the mirror, e.g., mitering the corners. Presented in this paper is the formulation of a generalized electrostatic micromirror (GEM) model with an arbitrary convex piecewise linear shape that is readily implemented in MATLAB and SIMULINK for steady-state and dynamic simulations. Additionally, such a model permits an arbitrary shaped mirror to be approximated as a series of linearly tapered segments. Previously, "effective area" arguments were used to model a non-rectangular shaped mirror with an equivalent rectangular one. The GEM model shows the limitations of this approach and provides a pre-fabrication tool for designing mirror shapes.
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.
Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J
2017-06-06
Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non
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.
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.
Affine group formulation of the Standard Model coupled to gravity
Energy Technology Data Exchange (ETDEWEB)
Chou, Ching-Yi, E-mail: l2897107@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Taiwan (China); Ita, Eyo, E-mail: ita@usna.edu [Department of Physics, US Naval Academy, Annapolis, MD (United States); Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Taiwan (China)
2014-04-15
In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of the Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. -- Highlights: •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program. •WDW formulated for interaction of matter and all forces, including gravity, as affine algebra. •WDW features Hermitian generators in spite of fermionic content: Standard Model addressed. •Constructed a family of physical states for the full, coupled theory via affine coherent states. •Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.
Affine structures and a tableau model for E_6 crystals
Jones, Brant
2009-01-01
We provide the unique affine crystal structure for type E_6^{(1)} Kirillov-Reshetikhin crystals corresponding to the multiples of fundamental weights s Lambda_1, s Lambda_2, and s Lambda_6 for all s \\geq 1 (in Bourbaki's labeling of the Dynkin nodes, where 2 is the adjoint node). Our methods introduce a generalized tableaux model for classical highest weight crystals of type E and use the order three automorphism of the affine E_6^{(1)} Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E_7^{(1)} Kirillov-Reshetikhin crystals corresponding to the adjoint node.
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 Efficient Piecewise Linear Model for Predicting Activity of Caspase-3 Inhibitors
Directory of Open Access Journals (Sweden)
Alireza Foroumadi
2012-09-01
Full Text Available Background and purpose of the study Multimodal distribution of descriptors makes it more difficult to fit a single global model to model the entire data set in quantitative structure activity relationship (QSAR studies.Methods:The linear (Multiple linear regression; MLR, non-linear (Artificial neural network; ANN, and an approach based on "Extended Classifier System in Function approximation" (XCSF were applied herein to model the biological activity of 658 caspase-3 inhibitors. Results:Various kinds of molecular descriptors were calculated to represent the molecular structures of the compounds. The original data set was partitioned into the training and test sets by the K-means classification method. Prediction error on the test data set indicated that the XCSF as a local model estimates caspase-3 inhibition activity, better than the global models such as MLR and ANN. The atom-centered fragment type CR2X2, electronegativity, polarizability, and atomic radius and also the lipophilicity of the molecule, were the main independent factors contributing to the caspase-3 inhibition activity. Conclusions:The results of this study may be exploited for further design of novel caspase-3 inhibitors.
T-Duality in Affine NA Toda Models
Gomes, J F; Zimerman, A H
2004-01-01
The construction of Non Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non conformal two dimensional integrable models naturally leads to the construction of a pair of actions which share the same spectra and are related by canonical transformations.
Métris, Aline; George, Susie M; Ropers, Delphine
2017-01-02
Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available
Affine Poisson Groups and WZW Model
Directory of Open Access Journals (Sweden)
Ctirad Klimcík
2008-01-01
Full Text Available We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.
Lei, Jinzhi; Yvinec, Romain; Zhuge, Changjing
2012-01-01
This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription. We prove that an adiabatic reduction can be performed in a stochastic slow/fast system with a jump Markov process. In the gene expression model, the production of mRNA (the fast variable) is assumed to follow a compound Poisson process (the phenomena called bursting in molecular biology) and the production of protein (the slow variable) is linear as a function of mRNA. When the dynamics of mRNA is assumed to be faster than the protein dynamics (due to a mRNA degradation rate larger than for the protein) we prove that, with the appropriate scaling, the bursting phenomena can be transmitted to the slow variable. We show that the reduced equation is either a stochastic differential equation with a jump Markov process or a deterministic ordinary differential equation depending on the scaling that is appropriate. These results are significant because adiabatic reduction techniques seem to have not been de...
Prediction of peptide bonding affinity: kernel methods for nonlinear modeling
Bergeron, Charles; Sundling, C Matthew; Krein, Michael; Katt, Bill; Sukumar, Nagamani; Breneman, Curt M; Bennett, Kristin P
2011-01-01
This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear partial least squares (PLS) algorithm, outperforms PLS, and that the incorporation of transferable atom equivalent features improves predictive capability.
Affine group formulation of the Standard Model coupled to gravity
Chou, Ching-Yi; Soo, Chopin
2013-01-01
Using the affine group formalism, we perform a nonperturbative quantization leading to the construction of elements of a physical Hilbert space for full, Lorentzian quantum gravity coupled to the Standard Model in four spacetime dimensions. This paper constitutes a first step toward understanding the phenomenology of quantum gravitational effects stemming from a consistent treatment of minimal couplings to matter.
Kohli, Nidhi; Sullivan, Amanda L; Sadeh, Shanna; Zopluoglu, Cengiz
2015-04-01
Effective instructional planning and intervening rely heavily on accurate understanding of students' growth, but relatively few researchers have examined mathematics achievement trajectories, particularly for students with special needs. We applied linear, quadratic, and piecewise linear mixed-effects models to identify the best-fitting model for mathematics development over elementary and middle school and to ascertain differences in growth trajectories of children with learning disabilities relative to their typically developing peers. The analytic sample of 2150 students was drawn from the Early Childhood Longitudinal Study - Kindergarten Cohort, a nationally representative sample of United States children who entered kindergarten in 1998. We first modeled students' mathematics growth via multiple mixed-effects models to determine the best fitting model of 9-year growth and then compared the trajectories of students with and without learning disabilities. Results indicate that the piecewise linear mixed-effects model captured best the functional form of students' mathematics trajectories. In addition, there were substantial achievement gaps between students with learning disabilities and students with no disabilities, and their trajectories differed such that students without disabilities progressed at a higher rate than their peers who had learning disabilities. The results underscore the need for further research to understand how to appropriately model students' mathematics trajectories and the need for attention to mathematics achievement gaps in policy. Copyright © 2015 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.
Affinity and Hostility in Divided Communities: a Mathematical Model
Thron, Christopher
2015-01-01
We propose, develop, and analyze a mathematical model of intergroup attitudes in a community that is divided between two distinct social groups (which may be distinguished by religion, ethnicity, or some other socially distinguishing factor). The model is based on very simple premises that are both intuitive and justified by sociological research. We investigate the behavior of the model in various special cases, for various model configurations. We discuss the stability of the model, and the continuous or discontinuous dependence of model behavior on various parameters. Finally, we discuss possible implications for strategies to improve intergroup affinity, and to defuse tension and prevent deterioration of intergroup relationships.
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/.
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.
Restricted Quantum Affine Symmetry of Perturbed Minimal Models
Felder, G
1992-01-01
We study the structure of superselection sectors of an arbitrary perturbation of a conformal field theory. We describe how a restriction of the q-deformed $\\hat{sl(2)}$ affine Lie algebra symmetry of the sine-Gordon theory can be used to derive the S-matrices of the $\\Phi^{(1,3)}$ perturbations of the minimal unitary series. This analysis provides an identification of fields which create the massive kink spectrum. We investigate the ultraviolet limit of the restricted sine-Gordon model, and explain the relation between the restriction and the Fock space cohomology of minimal models. We also comment on the structure of degenerate vacuum states. Deformed Serre relations are proven for arbitrary affine Toda theories, and it is shown in certain cases how relations of the Serre type become fractional spin supersymmetry relations upon restriction.
Directory of Open Access Journals (Sweden)
Jens Jirschitzka
Full Text Available In four studies we tested a new methodological approach to the investigation of evaluation bias. The usage of piecewise growth curve modeling allowed for investigation into the impact of people's attitudes on their persuasiveness ratings of pro- and con-arguments, measured over the whole range of the arguments' polarity from an extreme con to an extreme pro position. Moreover, this method provided the opportunity to test specific hypotheses about the course of the evaluation bias within certain polarity ranges. We conducted two field studies with users of an existing online information portal (Studies 1a and 2a as participants, and two Internet laboratory studies with mostly student participants (Studies 1b and 2b. In each of these studies we presented pro- and con-arguments, either for the topic of MOOCs (massive open online courses, Studies 1a and 1b or for the topic of M-learning (mobile learning, Studies 2a and 2b. Our results indicate that using piecewise growth curve models is more appropriate than simpler approaches. An important finding of our studies was an asymmetry of the evaluation bias toward pro- or con-arguments: the evaluation bias appeared over the whole polarity range of pro-arguments and increased with more and more extreme polarity. This clear-cut result pattern appeared only on the pro-argument side. For the con-arguments, in contrast, the evaluation bias did not feature such a systematic picture.
Jirschitzka, Jens; Kimmerle, Joachim; Cress, Ulrike
2016-01-01
In four studies we tested a new methodological approach to the investigation of evaluation bias. The usage of piecewise growth curve modeling allowed for investigation into the impact of people's attitudes on their persuasiveness ratings of pro- and con-arguments, measured over the whole range of the arguments' polarity from an extreme con to an extreme pro position. Moreover, this method provided the opportunity to test specific hypotheses about the course of the evaluation bias within certain polarity ranges. We conducted two field studies with users of an existing online information portal (Studies 1a and 2a) as participants, and two Internet laboratory studies with mostly student participants (Studies 1b and 2b). In each of these studies we presented pro- and con-arguments, either for the topic of MOOCs (massive open online courses, Studies 1a and 1b) or for the topic of M-learning (mobile learning, Studies 2a and 2b). Our results indicate that using piecewise growth curve models is more appropriate than simpler approaches. An important finding of our studies was an asymmetry of the evaluation bias toward pro- or con-arguments: the evaluation bias appeared over the whole polarity range of pro-arguments and increased with more and more extreme polarity. This clear-cut result pattern appeared only on the pro-argument side. For the con-arguments, in contrast, the evaluation bias did not feature such a systematic picture.
Spatial model of affinity maturation in germinal centers
Kesmir, C.; Boer, R.J. de
2003-01-01
Affinity maturation of humoral responses to T-cell-dependent antigens occurs in germinal centers (GC). In GCs antigen-specific B cells undergo rounds of somatic mutations that alter their affinity. High-affinity mutants take over GCs very soon after they appear; the replacement rate is as high as 4
Pricing swaptions and coupon bond options in affine term structure models
Schrager, D.F.; Pelsser, A.A.J.
2005-01-01
We propose an approach to …nd an approximate price of a swaption in Affine Term Structure Models. Our approach is based on the derivation of approximate dynamics in which the volatility of the Forward Swap Rate is itself an affine function of the factors. Hence we remain in the Affine framework and
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.
Interest Rates with Long Memory: A Generalized Affine Term-Structure Model
DEFF Research Database (Denmark)
Osterrieder, Daniela
We propose a model for the term structure of interest rates that is a generalization of the discrete-time, Gaussian, affine yield-curve model. Compared to standard affine models, our model allows for general linear dynamics in the vector of state variables. In an application to real yields of U...
Electron affinities of uracil: microsolvation effects and polarizable continuum model.
Melicherčík, Miroslav; Pašteka, Lukáš F; Neogrády, Pavel; Urban, Miroslav
2012-03-08
We present adiabatic electron affinities (AEAs) and the vertical detachment energies (VDEs) of the uracil molecule interacting with one to five water molecules. Credibility of MP2 and DFT/B3LYP calculations is supported by comparison with available benchmark CCSD(T) data. AEAs and VDEs obtained by MP2 and DFT/B3LYP methods copy trends of benchmark CCSD(T) results for the free uracil and uracil-water complexes in the gas phase being by 0.20 - 0.28 eV higher than CCSD(T) values depending on the particular structure of the complex. AEAs and VDEs from MP2 are underestimated by 0.09-0.15 eV. For the free uracil and uracil-(H(2)O)(n) (n = 1,2,3,5) complexes, we also consider the polarizable continuum model (PCM) and discuss the importance of the microsolvation when combined with PCM. AEAs and VDEs of uracil and uracil-water complexes enhance rapidly with increasing relative dielectric constant (ε) of the solvent. Highest AEAs and VDEs of the U(H(2)O)(5) complexes from B3LYP with ε = 78.4 are 2.03 and 2.81 eV, respectively, utilizing the correction from CCSD(T). Specific structural features of the microsolvated uracil-(H(2)O)(n) complexes and their anions are preserved also upon considering PCM in calculations of AEAs and VDEs.
Directory of Open Access Journals (Sweden)
Scott W. Keith
2014-09-01
Full Text Available This paper details the design, evaluation, and implementation of a framework for detecting and modeling nonlinearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and nonparametric bootstrapping. Unlike other nonlinear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI; kg/m2 and the complex multi-stage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic nonlinear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and nonlinearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarz’s Bayesian Information Criterion (BIC and Akaike’s Information Criterion (AIC, in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions.
Affinity maturation of antibodies assisted by in silico modeling
Barderas, R.; Desmet, J.; Timmerman, P.; Meloen, R.; Casal, J.I.
2008-01-01
Rational engineering methods can be applied with reasonable success to optimize physicochemical characteristics of proteins, in particular, antibodies. Here, we describe a combined CDR3 walking randomization and rational design-based approach to enhance the affinity of the human anti-gastrin TA4
Demazure modules and vertex models the affine sl(2) case
Foda, O E; Okado, M; Foda, Omar; Misra, Kailash C; Okado, Masato
1996-01-01
We characterize, in the case of affine sl(2), the crystal base of the Demazure module E_w(\\La) in terms of extended Young diagrams or paths for any dominant integral weight \\La and Weyl group element w. Its character is evaluated via two expressions, 'bosonic' and 'fermionic'.
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.
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...
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".
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.
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.
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.
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.
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.
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...
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.
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.
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.
An affine two-factor heteroskedastic macro-finance term structure model
Spreij, P.; Veerman, E.; Vlaar, P.
2011-01-01
We propose an affine macro-finance term structure model for interest rates that allows for both constant volatilities (homoskedastic model) and state-dependent volatilities (heteroskedastic model). In a homoskedastic model, interest rates are symmetric, which means that either very low interest rate
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...
Extension of the selection of protein chromatography and the rate model to affinity chromatography.
Sandoval, G; Shene, C; Andrews, B A; Asenjo, J A
2010-01-01
The rational selection of optimal protein purification sequences, as well as mathematical models that simulate and allow optimization of chromatographic protein purification processes have been developed for purification procedures such as ion-exchange, hydrophobic interaction and gel filtration chromatography. This paper investigates the extension of such analysis to affinity chromatography both in the selection of chromatographic processes and in the use of the rate model for mathematical modelling and simulation. Two affinity systems were used: Blue Sepharose and Protein A. The extension of the theory developed previously for ion-exchange and HIC chromatography to affinity separations is analyzed in this paper. For the selection of operations two algorithms are used. In the first, the value of η, which corresponds to the efficiency (resolution) of the actual chromatography and, Σ, which determines the amount of a particular contaminant eliminated after each separation step, which determines the purity, have to be determined. It was found that the value of both these parameters is not generic for affinity separations but will depend on the type of affinity system used and will have to be determined on a case by case basis. With Blue Sepharose a salt gradient was used and with Protein A, a pH gradient. Parameters were determined with individual proteins and simulations of the protein mixtures were done. This approach allows investigation of chromatographic protein purification in a holistic manner that includes ion-exchange, HIC, gel filtration and affinity separations for the first time.
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.
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.
The affine constrained GNSS attitude model and its multivariate integer least-squares solution
Teunissen, P.J.G.
2012-01-01
A new global navigation satellite system (GNSS) carrier-phase attitude model and its solution are introduced in this contribution. This affine-constrained GNSS attitude model has the advantage that it avoids the computational complexity of the orthonormality-constrained GNSS attitude model, while it
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...
Dai, Hanjun
2017-07-26
Motivation: An accurate characterization of transcription factor (TF)-DNA affinity landscape is crucial to a quantitative understanding of the molecular mechanisms underpinning endogenous gene regulation. While recent advances in biotechnology have brought the opportunity for building binding affinity prediction methods, the accurate characterization of TF-DNA binding affinity landscape still remains a challenging problem. Results: Here we propose a novel sequence embedding approach for modeling the transcription factor binding affinity landscape. Our method represents DNA binding sequences as a hidden Markov model (HMM) which captures both position specific information and long-range dependency in the sequence. A cornerstone of our method is a novel message passing-like embedding algorithm, called Sequence2Vec, which maps these HMMs into a common nonlinear feature space and uses these embedded features to build a predictive model. Our method is a novel combination of the strength of probabilistic graphical models, feature space embedding and deep learning. We conducted comprehensive experiments on over 90 large-scale TF-DNA data sets which were measured by different high-throughput experimental technologies. Sequence2Vec outperforms alternative machine learning methods as well as the state-of-the-art binding affinity prediction methods.
Institute of Scientific and Technical Information of China (English)
MohammadRezaAboudzadehRovais; JiawenZhu; BinWu
2004-01-01
A non-equilibrium chromatographic rate model was employed to simulate the affinity chromatography of urokinase. The chromatography process was developed to a yield of high purity product of urokinase from crude materials. The affinity gel used in the process was prepared by an epichlorohydrin-activation method using epichlorohydrin activated Sepharose 4B as a matrix and p-aminobenzamidine as a ligand. The chromatographic process were numerically simulated and analyzed with the aid of VERSE-LC computer simulator. Considering the basic principles, rate model with the back mixing in column inlet was utilized in simulating and studying the effect of the column inlet pattern on other parameters. Comparison of the simulation results with the experimental data showed that the rate model can be used to describe the affinity chromatography of urokinase in a fixed bed column with satisfactory accuracy.
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
Directory of Open Access Journals (Sweden)
Marcus C. Christiansen
2013-10-01
Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....
Boyte, Stephen P.; Wylie, Bruce K.; Major, Donald J.; Brown, Jesslyn F.
2015-01-01
Cheatgrass exhibits spatial and temporal phenological variability across the Great Basin as described by ecological models formed using remote sensing and other spatial data-sets. We developed a rule-based, piecewise regression-tree model trained on 99 points that used three data-sets – latitude, elevation, and start of season time based on remote sensing input data – to estimate cheatgrass beginning of spring growth (BOSG) in the northern Great Basin. The model was then applied to map the location and timing of cheatgrass spring growth for the entire area. The model was strong (R2 = 0.85) and predicted an average cheatgrass BOSG across the study area of 29 March–4 April. Of early cheatgrass BOSG areas, 65% occurred at elevations below 1452 m. The highest proportion of cheatgrass BOSG occurred between mid-April and late May. Predicted cheatgrass BOSG in this study matched well with previous Great Basin cheatgrass green-up studies.
Institute of Scientific and Technical Information of China (English)
林静; 唐国强; 覃良文
2016-01-01
在金融时间序列中，一组金融序列可被视为由不同时间段的分段函数拟合连接而成。利用3σ准则确定分段函数的临界点，并根据 AIC准则及调整后R2对分段点进行验证，从而分段点把数据分割成两部分。对两序列分别用合适的函数进行拟合，并用 ARMA-GARCH模型对残差序列进行修正。由上证综合指数数据的实证分析结果表明：3σ准则能很好地检索出临界点，同时建立的分段函数模型预测效果要优于 ARMA与 EGARCH模型，以及 ARMA-GARCH模型的引入对模型的精确度有所提高。所介绍的方法简单易懂、便于操作、精度高，为金融投资者和学者提供参考价值。%In the financial time series,a group of financial sequence can be used as a function,in which piecewise fitting connection is made in different time periods.The Pauta criterion was exploited to determine the critical point of piecewise func-tions,according to AIC guidelines and coefficient of determination after adj ustment to test breaking point,thus the staging point split the data into two parts.Two sequences were fitted with the appropriate function,and ARMA-GARCH model was used to amend the residual sequence.The empirical results of Shanghai composite index show that the 3σguidelines can retrieve critical point commendably.At the same time,the forecasting efficiency of piecewise function model is better than ARMA mod-el and EGARCH model.Also,the precision of the model is improved by the introduction of ARMA-GARCH model.Moreo-ver,the method is simple,easy to understand and operate,and accurate,which provides reference value for financial investors and scholars.
模糊分段光滑图像分割模型及其快速算法%Fuzzy piecewise smooth image segmentation model and a fast algorithm
Institute of Scientific and Technical Information of China (English)
赵在新; 成礼智
2011-01-01
灰度分布不均图像是图像分割中一个难点,为此提出一种模糊分段光滑(FPS)图像分割模型.借鉴分段光滑Mumford-Shah(MS)模型与模糊聚类思想,新模型通过两个定义在图像域的光滑函数描述区域特征,并利用模糊隶属度函数代替MS模型中的特征函数.同时,边界检测算子的引入能够有效保护图像中的边界信息.数值求解采用分裂Bregman方法与Gauss-Seidel迭代相结合的快速算法.对合成图像以及真实图像分割实验表明,本文算法能够有效分割灰度分布不均图像,同时具有较高的计算效率.%A fuzzy piecewise smooth (FPS) model is proposed aiming at the intensity- inhomogeneous image segmentation. Motivated by piecewise smooth Munford-Shah (MS) model and fuzzy clustering,two smooth functions were used to represent the region characteristics respectively and a fuzzy membership function was adopted to replace the hard membership function of MS model. An edge detection operator was also incorporated into the minimization ernergy function. The new energy is convex for the membership function,and the final segmentation does not depend on the initial contour. For numerical computation, a fast algorithm based on split Bregman method and Gauss-Seidel iteration was employed. Experimental results for synthetic and real images show desirable performance of the proposed method.
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.
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...
Noncommmutative solitons and kinks in the affine Toda model coupled to matter
Blas, H
2008-01-01
Some properties of the non-commutative (NC) versions of the generalized sine-Gordon model (NCGSG) and its dual massive Thirring theory are studied. Our method relies on the NC extension of integrable models and the master lagrangian approach to deal with dual theories. The master lagrangian turns out to be the NC version of the so-called affine Toda model coupled to matter related to the group GL(n), in which the Toda field $g \\subset GL(n), (n=2, 3)$. Moreover, as a reduction of GL(3) NCGSG one gets a NC version of the remarkable double sine-Gordon model.
Wang, Xiaolei
2014-12-12
Background: A quantitative understanding of interactions between transcription factors (TFs) and their DNA binding sites is key to the rational design of gene regulatory networks. Recent advances in high-throughput technologies have enabled high-resolution measurements of protein-DNA binding affinity. Importantly, such experiments revealed the complex nature of TF-DNA interactions, whereby the effects of nucleotide changes on the binding affinity were observed to be context dependent. A systematic method to give high-quality estimates of such complex affinity landscapes is, thus, essential to the control of gene expression and the advance of synthetic biology. Results: Here, we propose a two-round prediction method that is based on support vector regression (SVR) with weighted degree (WD) kernels. In the first round, a WD kernel with shifts and mismatches is used with SVR to detect the importance of subsequences with different lengths at different positions. The subsequences identified as important in the first round are then fed into a second WD kernel to fit the experimentally measured affinities. To our knowledge, this is the first attempt to increase the accuracy of the affinity prediction by applying two rounds of string kernels and by identifying a small number of crucial k-mers. The proposed method was tested by predicting the binding affinity landscape of Gcn4p in Saccharomyces cerevisiae using datasets from HiTS-FLIP. Our method explicitly identified important subsequences and showed significant performance improvements when compared with other state-of-the-art methods. Based on the identified important subsequences, we discovered two surprisingly stable 10-mers and one sensitive 10-mer which were not reported before. Further test on four other TFs in S. cerevisiae demonstrated the generality of our method. Conclusion: We proposed in this paper a two-round method to quantitatively model the DNA binding affinity landscape. Since the ability to modify
A mathematical model for the germinal center morphology and affinity maturation
Meyer-Hermann, M
2002-01-01
During germinal center reactions the appearance of two specific zones is observed: the dark and the light zone. Up to now, the origin and function of these zones are poorly understood. In the framework of a stochastic and discrete model several possible pathways of zone development during germinal center reactions are investigated. The importance of the zones in the germinal center for affinity maturation, i.e. the process of antibody optimization is discussed.
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity.
Asti, Lorenzo; Uguzzoni, Guido; Marcatili, Paolo; Pagnani, Andrea
2016-04-01
The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6), outperforming other sequence- and structure-based models.
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity.
Directory of Open Access Journals (Sweden)
Lorenzo Asti
2016-04-01
Full Text Available The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6, outperforming other sequence- and structure-based models.
Gupta, Shikha; Basant, Nikita; Rai, Premanjali; Singh, Kunwar P
2015-11-01
Binding affinity of chemical to carbon is an important characteristic as it finds vast industrial applications. Experimental determination of the adsorption capacity of diverse chemicals onto carbon is both time and resource intensive, and development of computational approaches has widely been advocated. In this study, artificial intelligence (AI)-based ten different qualitative and quantitative structure-property relationship (QSPR) models (MLPN, RBFN, PNN/GRNN, CCN, SVM, GEP, GMDH, SDT, DTF, DTB) were established for the prediction of the adsorption capacity of structurally diverse chemicals to activated carbon following the OECD guidelines. Structural diversity of the chemicals and nonlinear dependence in the data were evaluated using the Tanimoto similarity index and Brock-Dechert-Scheinkman statistics. The generalization and prediction abilities of the constructed models were established through rigorous internal and external validation procedures performed employing a wide series of statistical checks. In complete dataset, the qualitative models rendered classification accuracies between 97.04 and 99.93%, while the quantitative models yielded correlation (R(2)) values of 0.877-0.977 between the measured and the predicted endpoint values. The quantitative prediction accuracies for the higher molecular weight (MW) compounds (class 4) were relatively better than those for the low MW compounds. Both in the qualitative and quantitative models, the Polarizability was the most influential descriptor. Structural alerts responsible for the extreme adsorption behavior of the compounds were identified. Higher number of carbon and presence of higher halogens in a molecule rendered higher binding affinity. Proposed QSPR models performed well and outperformed the previous reports. A relatively better performance of the ensemble learning models (DTF, DTB) may be attributed to the strengths of the bagging and boosting algorithms which enhance the predictive accuracies. The
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.
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 deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models
Energy Technology Data Exchange (ETDEWEB)
Kawaguchi, Io; Yoshida, Kentaroh [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-06-01
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.
DEFF Research Database (Denmark)
Baadsgaard, Mikkel; Nielsen, Jan Nygaard; Madsen, Henrik
2000-01-01
An econometric analysis of continuous-timemodels of the term structure of interest rates is presented. A panel of coupon bond prices with different maturities is used to estimate the embedded parameters of a continuous-discrete state space model of unobserved state variables: the spot interest rate......, the central tendency and stochastic volatility. Emphasis is placed on the particular class of exponential-affine term structure models that permits solving the bond pricing PDE in terms of a system of ODEs. It is assumed that coupon bond prices are contaminated by additive white noise, where the stochastic...
Microarrays as Model Biosensor Platforms to Investigate the Structure and Affinity of Aptamers
Directory of Open Access Journals (Sweden)
Jennifer A. Martin
2016-01-01
Full Text Available Immobilization of nucleic acid aptamer recognition elements selected free in solution onto the surface of biosensor platforms has proven challenging. This study investigated the binding of multiple aptamer/target pairs immobilized on a commercially available microarray as a model system mimicking biosensor applications. The results indicate a minimum distance (linker length from the surface and thymine nucleobase linker provides reproducible binding across varying conditions. An indirect labeling method, where the target was labeled with a biotin followed by a brief Cy3-streptavidin incubation, provided a higher signal-to-noise ratio and over two orders of magnitude improvement in limit of detection, compared to direct Cy3-protein labeling. We also showed that the affinities of the aptamer/target interaction can change between direct and indirect labeling and conditions to optimize for the highest fluorescence intensity will increase the sensitivity of the assay but will not change the overall affinity. Additionally, some sequences which did not initially bind demonstrated binding when conditions were optimized. These results, in combination with studies demonstrating enhanced binding in nonselection buffers, provided insights into the structure and affinity of aptamers critical for biosensor applications and allowed for generalizations in starting conditions for researchers wishing to investigate aptamers on a microarray surface.
Pence, Thomas J; Monroe, Ryan J; Wright, Neil T
2008-08-01
Some recent analyses modeled the response of collagenous tissues, such as epicardium, using a hypothetical network consisting of interconnected springlike fibers. The fibers in the network were organized such that internal nodes served as the connection point between three such collagen springs. The results for assumed affine and nonaffine deformations are contrasted after a homogeneous deformation at the boundary. Affine deformation provides a stiffer mechanical response than nonaffine deformation. In contrast to nonaffine deformation, affine deformation determines the displacement of internal nodes without imposing detailed force balance, thereby complicating the simplest intuitive notion of stress, one based on free body cuts, at the single node scale. The standard notion of stress may then be recovered via average field theory computations based on large micromesh realizations. An alternative and by all indications complementary viewpoint for the determination of stress in these collagen fiber networks is discussed here, one in which stress is defined using elastic energy storage, a notion which is intuitive at the single node scale. It replaces the average field theory computations by an averaging technique over randomly oriented isolated simple elements. The analytical operations do not require large micromesh realizations, but the tedious nature of the mathematical manipulation is clearly aided by symbolic algebra calculation. For the example case of linear elastic deformation, this results in material stiffnesses that relate the infinitesimal strain and stress. The result that the affine case is stiffer than the nonaffine case is recovered, as would be expected. The energy framework also lends itself to the natural inclusion of changes in mechanical response due to the chemical, electrical, or thermal environment.
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity
DEFF Research Database (Denmark)
Asti, Lorenzo; Uguzzoni, Guido; Marcatili, Paolo
2016-01-01
The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high...... of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6), outperforming other sequence- and structure-based models....
Affine Invariant, Model-Based Object Recognition Using Robust Metrics and Bayesian Statistics
Zografos, Vasileios; 10.1007/11559573_51
2010-01-01
We revisit the problem of model-based object recognition for intensity images and attempt to address some of the shortcomings of existing Bayesian methods, such as unsuitable priors and the treatment of residuals with a non-robust error norm. We do so by using a refor- mulation of the Huber metric and carefully chosen prior distributions. Our proposed method is invariant to 2-dimensional affine transforma- tions and, because it is relatively easy to train and use, it is suited for general object matching problems.
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
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.
Davydov, E A
2013-01-01
Nowadays it is widely accepted that the evolution of the universe was driven by some scalar degrees of freedom both on its early stage and at present. The corresponding cosmological models often involve some scalar fields introduced ad hoc. In this paper we cultivate a different approach, which is based on a derivation of new scalar degrees of freedom from fundamental modifications of Einstein's gravity. In elaboration of our previous work, we here investigate properties of the dilaton-scalar gravity obtained by dimensional reductions of a recently proposed affine generalized gravity theory. We show that these models possess the same symmetries as related models of GR with ordinary scalar fields. As a result, for a rather general class of dilaton-scalar gravity models we construct additional first integrals and formulate an integral equation well suited for solving by iterations.
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.
Reshetova, Polina; van Schaik, Barbera D. C.; Klarenbeek, Paul L.; Doorenspleet, Marieke E.; Esveldt, Rebecca E. E.; Tak, Paul-Peter; Guikema, Jeroen E. J.; de Vries, Niek; van Kampen, Antoine H. C.
2017-01-01
Immunoglobulin repertoire sequencing has successfully been applied to identify expanded antigen-activated B-cell clones that play a role in the pathogenesis of immune disorders. One challenge is the selection of the Ag-specific B cells from the measured repertoire for downstream analyses. A general feature of an immune response is the expansion of specific clones resulting in a set of subclones with common ancestry varying in abundance and in the number of acquired somatic mutations. The expanded subclones are expected to have BCR affinities for the Ag higher than the affinities of the naive B cells in the background population. For these reasons, several groups successfully proceeded or suggested selecting highly abundant subclones from the repertoire to obtain the Ag-specific B cells. Given the nature of affinity maturation one would expect that abundant subclones are of high affinity but since repertoire sequencing only provides information about abundancies, this can only be verified with additional experiments, which are very labor intensive. Moreover, this would also require knowledge of the Ag, which is often not available for clinical samples. Consequently, in general we do not know if the selected highly abundant subclone(s) are also the high(est) affinity subclones. Such knowledge would likely improve the selection of relevant subclones for further characterization and Ag screening. Therefore, to gain insight in the relation between subclone abundancy and affinity, we developed a computational model that simulates affinity maturation in a single GC while tracking individual subclones in terms of abundancy and affinity. We show that the model correctly captures the overall GC dynamics, and that the amount of expansion is qualitatively comparable to expansion observed from B cells isolated from human lymph nodes. Analysis of the fraction of high- and low-affinity subclones among the unexpanded and expanded subclones reveals a limited correlation between
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.
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.
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.
Structural insights into a high affinity nanobody:antigen complex by homology modelling
DEFF Research Database (Denmark)
Skottrup, Peter Durand
2017-01-01
B binding were identified and used as input to the docking. Furthermore, residues likely involved in the RgpB epitope was identified based upon RgpB:RgpA alignment and analysis of residue surface accessibility. CDR residues and putitative RgpB epitope residues were used as input to an information-driven...... flexible docking approach using the HADDOCK server. Analysis of the VHH7:RgpB model demonstrated that the epitope was found in the immunoglobulin-like domain and residue pairs located at the molecular paratope:epitope interface important for complex stability was identified. Collectively, the VHH7 homology...... model and VHH7:RgpB docking supplies knowledge of the residues involved in the high affinity interaction. This information could prove valuable in the design of an antibody-drug conjugate for specific RgpB targeting....
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.
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.
Improving Network Performance with Affinity based Mobility Model in Opportunistic Network
Batabyal, Suvadip; 10.5121/ijwmn.2012.4213
2012-01-01
Opportunistic network is a type of Delay Tolerant Network which is characterized by intermittent connectivity amongst the nodes and communication largely depends upon the mobility of the participating nodes. The network being highly dynamic, traditional MANET protocols cannot be applied and the nodes must adhere to store-carry-forward mechanism. Nodes do not have the information about the network topology, number of participating nodes and the location of the destination node. Hence, message transfer reliability largely depends upon the mobility pattern of the nodes. In this paper we have tried to find the impact of RWP (Random Waypoint) mobility on packet delivery ratio. We estimate mobility factors like number of node encounters, contact duration(link time) and inter-contact time which in turn depends upon parameters like playfield area (total network area), number of nodes, node velocity, bit-rate and RF range of the nodes. We also propose a restricted form of RWP mobility model, called the affinity based ...
Scale-up of affinity membrane modules: comparison between lumped and physical models.
Dimartino, Simone; Boi, Cristiana; Sarti, Giulio C
2015-03-01
Membrane chromatography represents one of the emerging technologies for downstream processing in the biotechnology industry. This process is currently used in polishing steps for antibody manufacturing, while its application is still under development for the capture step. To promote its employment in large-scale processes, it is crucial to develop a simple, yet reliable, simulation tool able to describe the process performance in a predictive way at all scales. In this work, the physical model for the description of protein purification with affinity membrane chromatography has been used to predict the performance of scaled-up systems and compared with the lumped model, frequently used for its deceptive simplicity. Two commonly used binding kinetics have been implemented in the models, namely the Langmuir and the bi-Langmuir equations. The two models describe equally well experimental data obtained in a lab-scale apparatus, while, on the contrary, important differences are observed in scaled-up systems even at the early stages of breakthrough, which are particularly relevant in industrial-scale operations. It is seen that for both kinetics, the physical model is more appropriate and safer to use for scale-up purposes. Copyright © 2015 John Wiley & Sons, Ltd.
van der Ploeg, A.P.C.; Boswijk, H.P.; de Jong, F.
2003-01-01
We propose a class of stochastic volatility (SV) option pricing models that is more flexible than the more conventional models in different ways. We assume the conditional variance of the stock returns to be driven by an affine function of an arbitrary number of latent factors, which follow mean-rev
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Energy Technology Data Exchange (ETDEWEB)
Anber, Mohamed M.; Poppitz, Erich; /Toronto U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Zhang, Yu-Chen; Zhang, Shao-Wu; Liu, Lian; Liu, Hui; Zhang, Lin; Cui, Xiaodong; Huang, Yufei; Meng, Jia
2015-01-01
With the development of new sequencing technology, the entire N6-methyl-adenosine (m(6)A) RNA methylome can now be unbiased profiled with methylated RNA immune-precipitation sequencing technique (MeRIP-Seq), making it possible to detect differential methylation states of RNA between two conditions, for example, between normal and cancerous tissue. However, as an affinity-based method, MeRIP-Seq has yet provided base-pair resolution; that is, a single methylation site determined from MeRIP-Seq data can in practice contain multiple RNA methylation residuals, some of which can be regulated by different enzymes and thus differentially methylated between two conditions. Since existing peak-based methods could not effectively differentiate multiple methylation residuals located within a single methylation site, we propose a hidden Markov model (HMM) based approach to address this issue. Specifically, the detected RNA methylation site is further divided into multiple adjacent small bins and then scanned with higher resolution using a hidden Markov model to model the dependency between spatially adjacent bins for improved accuracy. We tested the proposed algorithm on both simulated data and real data. Result suggests that the proposed algorithm clearly outperforms existing peak-based approach on simulated systems and detects differential methylation regions with higher statistical significance on real dataset.
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.
多阶段混合增长模型的影响因素：距离与形态%Factors of Piecewise Growth Mixture Model:Distance and Pattern
Institute of Scientific and Technical Information of China (English)
刘源; 骆方; 刘红云
2014-01-01
The piecewise growth mixture model (PGMM) has been a very popular analytical approach in recent studies of longitudinal data. PGMM builds on the piecewise growth model (PGM) and the growth mixture model (GMM). It is used to locate the turning point of growth trajectory as well as to identify the latent class of the population. It is particularly useful in detecting the non-continuous growing trend in a heterogeneous population. A simplified version of the model, the latent class growth analysis (LCGA), has also been often used with a restriction on the variance of PGMM. Understandably, factors affecting PGM and GMM will affect the estimates and performance of PGMM. These factors may include the change of the slope, the distance of latent classes, and the sample size. PGMM being developed from the two growth-related models (PGM, GMM) also attempts to analyze the growth pattern in latent growth trajectory as a special and newly emerged issue. Even for models with the same distance, their different slopes can be combined to form different patterns. This issue has not been fully explored in previous literature. Yet in empirical studies, factors such as the distance of the latent classes, the growth pattern, the existing criteria of model fit indices, and the precision of parameter estimates are well worth examining issues. In the present simulation study, a two-class-two-period model was adopted. The three simulation conditions being considered were:the sample size, the distance of latent class, and the pattern of the growth trajectory. The sample size was set to be 100, 200 and 500. The distance of the latent classes was defined as the squared Mahalanobis distance (SMD), with 1.5, 3 and 5 being used to represent the small, medium and large distance of latent classes respectively. Four different types of growth pattern were selected to represent one parallel and three non-parallel patterns. Finally, the LCGA was selected as the reference model to see whether PGMM
Institute of Scientific and Technical Information of China (English)
宋锦萍; 李率杰
2007-01-01
For quick segmentation and denoising, the classical Mumford-Shah (MS) model needs to enhance the penalization term,i.e. to increase the penalization parameter, which leads to gradual disappearance of objects. In this paper, we propose an improved Mumford-Shah (IMS) model to avoid the phenomenon, and adopt the piecewise constant level set method (PCLSM) and the gradient descent method to solve the minimization problem. Numerical experiments are given to show the efficiency and advantages of the new model and the algorithms.
[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.
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
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.
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.
Paulke, Alexander; Proschak, Ewgenij; Sommer, Kai; Achenbach, Janosch; Wunder, Cora; Toennes, Stefan W
2016-03-14
The number of new synthetic psychoactive compounds increase steadily. Among the group of these psychoactive compounds, the synthetic cannabinoids (SCBs) are most popular and serve as a substitute of herbal cannabis. More than 600 of these substances already exist. For some SCBs the in vitro cannabinoid receptor 1 (CB1) affinity is known, but for the majority it is unknown. A quantitative structure-activity relationship (QSAR) model was developed, which allows the determination of the SCBs affinity to CB1 (expressed as binding constant (Ki)) without reference substances. The chemically advance template search descriptor was used for vector representation of the compound structures. The similarity between two molecules was calculated using the Feature-Pair Distribution Similarity. The Ki values were calculated using the Inverse Distance Weighting method. The prediction model was validated using a cross validation procedure. The predicted Ki values of some new SCBs were in a range between 20 (considerably higher affinity to CB1 than THC) to 468 (considerably lower affinity to CB1 than THC). The present QSAR model can serve as a simple, fast and cheap tool to get a first hint of the biological activity of new synthetic cannabinoids or of other new psychoactive compounds.
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...
Glane, Sebastian; Reich, Felix A.; Müller, Wolfgang H.
2017-06-01
This study is dedicated to continuum-scale material modeling of isotropic permanent magnets. An affine-linear extension to the commonly used ideal hard model for permanent magnets is proposed, motivated, and detailed. In order to demonstrate the differences between these models, bar and horseshoe magnets are considered. The structure of the boundary value problem for the magnetic field and related solution techniques are discussed. For the ideal model, closed-form analytical solutions were obtained for both geometries. Magnetic fields of the boundary value problems for both models and differently shaped magnets were computed numerically by using the boundary element method. The results show that the character of the magnetic field is strongly influenced by the model that is used. Furthermore, it can be observed that the shape of an affine-linear magnet influences the near-field significantly. Qualitative comparisons with experiments suggest that both the ideal and the affine-linear models are relevant in practice, depending on the magnetic material employed. Mathematically speaking, the ideal magnetic model is a special case of the affine-linear one. Therefore, in applications where knowledge of the near-field is important, the affine-linear model can yield more accurate results—depending on the magnetic material.
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...
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.
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.
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
Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
Identifying Affinity Classes of Inorganic Materials Binding Sequences via a Graph-Based Model.
Du, Nan; Knecht, Marc R; Swihart, Mark T; Tang, Zhenghua; Walsh, Tiffany R; Zhang, Aidong
2015-01-01
Rapid advances in bionanotechnology have recently generated growing interest in identifying peptides that bind to inorganic materials and classifying them based on their inorganic material affinities. However, there are some distinct characteristics of inorganic materials binding sequence data that limit the performance of many widely-used classification methods when applied to this problem. In this paper, we propose a novel framework to predict the affinity classes of peptide sequences with respect to an associated inorganic material. We first generate a large set of simulated peptide sequences based on an amino acid transition matrix tailored for the specific inorganic material. Then the probability of test sequences belonging to a specific affinity class is calculated by minimizing an objective function. In addition, the objective function is minimized through iterative propagation of probability estimates among sequences and sequence clusters. Results of computational experiments on two real inorganic material binding sequence data sets show that the proposed framework is highly effective for identifying the affinity classes of inorganic material binding sequences. Moreover, the experiments on the structural classification of proteins (SCOP) data set shows that the proposed framework is general and can be applied to traditional protein sequences.
Liu, Huihui; Yang, Xianhai; Yin, Cen; Wei, Mengbi; He, Xiao
2017-02-01
Disturbing the transport process is a crucial pathway for endocrine disrupting chemicals (EDCs) exerting disrupting endocrine function. However, this mechanism has not received enough attention compared with that of hormones receptors and synthetase. Recently, we have explored the interaction between EDCs and sex hormone-binding globulin of human (hSHBG). In this study, interactions between EDCs and sex hormone-binding globulin of eight fish species (fSHBG) were investigated by employing classification methods and quantitative structure-activity relationships (QSAR). In the modeling, the relative binding affinity (RBA) of a chemical with 17β-estradiol binding to fSHBG was selected as the endpoint. Classification models were developed for two fish species, while QSAR models were established for the other six fish species. Statistical results indicated that the models had satisfactory goodness of fit, robustness and predictive ability, and that application domain covered a large number of endogenous and exogenous steroidal and non-steroidal chemicals. Additionally, by comparing the log RBA values, it was found that the same chemical may have different affinities for fSHBG from different fish species, thus species diversity should be taken into account. However, the affinity of fSHBG showed a high correlation for fishes within the same Order (i.e., Salmoniformes, Cypriniformes, Perciformes and Siluriformes), thus the fSHBG binding data for one fish species could be used to extrapolate other fish species in the same Order.
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.
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.
Classical models of affinely-rigid bodies with "thickness" in degenerate dimension
Kovalchuk, Vasyl
2009-01-01
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional affinely-rigid body moving in the $n$-dimensional physical space, $m
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.
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
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...
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.
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.
Directory of Open Access Journals (Sweden)
Mittelmann Hans D
2010-01-01
Full Text Available Abstract Background The binding of peptide fragments of extracellular peptides to class II MHC is a crucial event in the adaptive immune response. Each MHC allotype generally binds a distinct subset of peptides and the enormous number of possible peptide epitopes prevents their complete experimental characterization. Computational methods can utilize the limited experimental data to predict the binding affinities of peptides to class II MHC. Results We have developed the Regularized Thermodynamic Average, or RTA, method for predicting the affinities of peptides binding to class II MHC. RTA accounts for all possible peptide binding conformations using a thermodynamic average and includes a parameter constraint for regularization to improve accuracy on novel data. RTA was shown to achieve higher accuracy, as measured by AUC, than SMM-align on the same data for all 17 MHC allotypes examined. RTA also gave the highest accuracy on all but three allotypes when compared with results from 9 different prediction methods applied to the same data. In addition, the method correctly predicted the peptide binding register of 17 out of 18 peptide-MHC complexes. Finally, we found that suboptimal peptide binding registers, which are often ignored in other prediction methods, made significant contributions of at least 50% of the total binding energy for approximately 20% of the peptides. Conclusions The RTA method accurately predicts peptide binding affinities to class II MHC and accounts for multiple peptide binding registers while reducing overfitting through regularization. The method has potential applications in vaccine design and in understanding autoimmune disorders. A web server implementing the RTA prediction method is available at http://bordnerlab.org/RTA/.
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Directory of Open Access Journals (Sweden)
Vladimir S. Gerdjikov
2006-02-01
Full Text Available The construction of a family of real Hamiltonian forms (RHF for the special class of affine 1+1-dimensional Toda field theories (ATFT is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.
A New 3-D Piecewise-Linear System for Chaos Generation
Directory of Open Access Journals (Sweden)
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.
Mozafari, Mona; Balasupramaniam, Shantheya; Preu, Lutz; El Deeb, Sami; Reiter, Christian G; Wätzig, Hermann
2017-03-03
A fast and precise affinity capillary electrophoresis (ACE) method has been developed and applied for the investigation of the binding interactions between P-selectin and heparinoids as potential P-selectin inhibitors in the presence and absence of calcium ions. Furthermore, model proteins and vitronectin were used to appraise the binding behavior of P-selectin. The normalized mobility ratios (∆R/Rf ), which provided information about the binding strength and the overall charge of the protein-ligand complex, were used to evaluate the binding affinities. It was found that P-selectin interacts more strongly with heparinoids in the presence of calcium ions. P-selectin was affected by heparinoids at the concentration of 3 mg/L. In addition, the results of the ACE experiments showed that among other investigated proteins, albumins and vitronectin exhibited strong interactions with heparinoids. Especially with P-selectin and vitronectin, the interaction may additionally induce conformational changes. Subsequently, computational models were applied to interpret the ACE experiments. Docking experiments explained that the binding of heparinoids on P-selectin is promoted by calcium ions. These docking models proved to be particularly well suited to investigate the interaction of charged compounds, and are therefore complementary to ACE experiments. This article is protected by copyright. All rights reserved.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Politi, Regina [Laboratory for Molecular Modeling, Division of Chemical Biology and Medicinal Chemistry, University of North Carolina, Chapel Hill, NC 27599 (United States); Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599 (United States); Rusyn, Ivan, E-mail: iir@unc.edu [Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599 (United States); Tropsha, Alexander, E-mail: alex_tropsha@unc.edu [Laboratory for Molecular Modeling, Division of Chemical Biology and Medicinal Chemistry, University of North Carolina, Chapel Hill, NC 27599 (United States)
2014-10-01
The thyroid hormone receptor (THR) is an important member of the nuclear receptor family that can be activated by endocrine disrupting chemicals (EDC). Quantitative Structure–Activity Relationship (QSAR) models have been developed to facilitate the prioritization of THR-mediated EDC for the experimental validation. The largest database of binding affinities available at the time of the study for ligand binding domain (LBD) of THRβ was assembled to generate both continuous and classification QSAR models with an external accuracy of R{sup 2} = 0.55 and CCR = 0.76, respectively. In addition, for the first time a QSAR model was developed to predict binding affinities of antagonists inhibiting the interaction of coactivators with the AF-2 domain of THRβ (R{sup 2} = 0.70). Furthermore, molecular docking studies were performed for a set of THRβ ligands (57 agonists and 15 antagonists of LBD, 210 antagonists of the AF-2 domain, supplemented by putative decoys/non-binders) using several THRβ structures retrieved from the Protein Data Bank. We found that two agonist-bound THRβ conformations could effectively discriminate their corresponding ligands from presumed non-binders. Moreover, one of the agonist conformations could discriminate agonists from antagonists. Finally, we have conducted virtual screening of a chemical library compiled by the EPA as part of the Tox21 program to identify potential THRβ-mediated EDCs using both QSAR models and docking. We concluded that the library is unlikely to have any EDC that would bind to the THRβ. Models developed in this study can be employed either to identify environmental chemicals interacting with the THR or, conversely, to eliminate the THR-mediated mechanism of action for chemicals of concern. - Highlights: • This is the largest curated dataset for ligand binding domain (LBD) of the THRβ. • We report the first QSAR model for antagonists of AF-2 domain of THRβ. • A combination of QSAR and docking enables
Shared Frailty Model for Left-Truncated Multivariate Survival Data
DEFF Research Database (Denmark)
Jensen, Henrik; Brookmeyer, Ron; Aaby, Peter;
multivariate survival data, left truncation, multiplicative hazard model, shared gamma frailty, conditional model, piecewise exponential model, childhood survival......multivariate survival data, left truncation, multiplicative hazard model, shared gamma frailty, conditional model, piecewise exponential model, childhood survival...
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.
DEFF Research Database (Denmark)
Lepist, E I; Kusk, T; Larsen, D H
2000-01-01
-Glu(OBzl)-Ala and Asp(OBzl)-Sar in aqueous solution and in relevant biological media and to compare these results with those of our previous study of D-Asp(OBzl)-Ala. Furthermore, the resulting aqueous stability and in vitro metabolism data are related to our previous affinity data to evaluate if Glu-Sar, D......-Glu-Ala, and Asp-Sar have potential as pro-moieties in these kinds of prodrugs. The degradation rates follow first-order kinetics, show maximun stability at pH 4-5 with maximum half-lives for Asp(OBzl)-Sar, Glu(OBzl)-Sar, and D-Glu(OBzl)-Ala of 115 h, 30 days and 152 days, respectively. The stability was dependent...... on buffer concentration, temperature, pH, and ionic strength. In biological media such as 80% human plasma, human gastric juice and intestinal fluid, and 10% rat jejunal homogenate at 37 degrees C, the half-lives were greater than 1 h except for the hydrolysis of Glu(OBzl)-Sar in 10% rat jejunal homogenate...
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.
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.
Modeling hepatitis C virus therapies combining drugs and lectin affinity plasmapheresis.
Tullis, Richard H; Duffin, R Paul; Ichim, Thomas E; Joyce, James A; Levin, Nathan W
2010-01-01
Hepatitis C virus (HCV) infection can be cured by standard pegylated interferon (IFN) + ribavirin drug therapy in 30-50% of treatment-naïve genotype 1 HCV patients. Cure rate is defined as a sustained viral response measured 6 months after the end of treatment. Recently, Fujiwara et al. [Hepatol Res 2007;37:701-710], using a double-filtration plasmapheresis (DFPP) technique, showed that simple physical reduction in circulating HCV using a 1-week pretreatment increased the cure rate for treatment-naïve type 1 HCV patients from 50 (controls) to 78% (treated). For previous nonresponders, the cure rate increased from 30 to 71%. This effect occurs even though the DFPP per treatment HCV viral load reduction averaged 26%. In clinical studies discussed here, a lectin affinity plasmapheresis (LAP) device caused an estimated 41% decrease in viral load as previously reported. A more detailed analysis using normalized data to correct for any variations in initial viral load gave an average 29% per treatment viral load reduction in 5 HCV-positive dialysis patients. The latter data indicate that continuous application of LAP could bring HCV viral load to undetectable levels in 4.1 days. Compared to DFPP, the LAP approach has the advantage that no plasma losses are incurred. In addition hemopurification can be carried out for extended periods of time analogous to continuous renal replacement therapy for the treatment of acute kidney failure, making the process much more effective. Calculations based on these data predict that continuous hemopurification would substantially increase the rate of viral load reduction (approx. 14-fold) and therefore increase the cure rate for HCV standard-of-care drug therapies without adding additional drugs and their associated side effects.
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
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.
Continuous-time Identification of Exponential-Affine Term Structure Models
Arianto Wibowo, A.W.
2006-01-01
This thesis addresses the problem of parameter estimation of the exponentialaffine class of models, which is a class of multi-factor models for the short rate. We propose a continuous-time maximum likelihood estimation method to estimate the parameters of a short rate model, given set of
Luo, Dan; Chen, Lei; Yu, Baoping
2017-06-17
The mechanisms underlying chronic and persistent pain associated with chronic pancreatitis (CP) are not completely understood. The cholinergic system is one of the major neural pathways of the pancreas. Meanwhile, this system plays an important role in chronic pain. We hypothesized that the high affinity choline transporter CHT1, which is a main determinant of cholinergic signaling capacity, is involved in regulating pain associated with CP. CP was induced by intraductal injection of 2% trinitrobenzene sulfonic acid (TNBS) in Sprague-Dawley rats. Pathological examination was used to evaluate the inflammation of pancreas and hyperalgesia was assessed by measuring the number of withdrawal events evoked by application of the von Frey filaments. CHT1 expression in pancreas-specific dorsal root ganglia (DRGs) was assessed through immunohistochemistry and western blotting. We also intraperitoneally injected the rats with hemicholinium-3 (HC-3, a specific inhibitor of CHT1). Then we observed its effects on the visceral hyperalgesia induced by CP, and on the acetylcholine (ACh) levels in the DRGs through using an acetylcholine/acetylcholinesterase assay kit. Signs of CP were observed 21 days after TNBS injection. Rats subjected to TNBS infusions had increased sensitivity to mechanical stimulation of the abdomen. CHT1-immunoreactive cells were increased in the DRGs from rats with CP compared to naive or sham rats. Western blots indicated that CHT1 expression was significantly up-regulated in TNBS-treated rats when compared to naive or sham-operated rats at all time points following surgery. In the TNBS group, CHT1 expression was higher on day 28 than on day 7 or day 14, but there was no statistical difference in CHT1 expression on day 28 vs. day 21. Treatment with HC-3 (60 μg/kg, 80 μg/kg, or 100 μg/kg) markedly enhanced the mechanical hyperalgesia and reduced ACh levels in a dose-dependent manner in rats with CP. We report for the first time that CHT1 may be involved
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.
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.
Directory of Open Access Journals (Sweden)
Chubing Zhang
2013-01-01
Full Text Available We study the optimal investment strategies of DC pension, with the stochastic interest rate (including the CIR model and the Vasicek model and stochastic salary. In our model, the plan member is allowed to invest in a risk-free asset, a zero-coupon bond, and a single risky asset. By applying the Hamilton-Jacobi-Bellman equation, Legendre transform, and dual theory, we find the explicit solutions for the CRRA and CARA utility functions, respectively.
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.
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
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.
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...
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...
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.
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.
Directory of Open Access Journals (Sweden)
Thomas Stockner
Full Text Available The high-resolution crystal structure of the leucine transporter (LeuT is frequently used as a template for homology models of the dopamine transporter (DAT. Although similar in structure, DAT differs considerably from LeuT in a number of ways: (i when compared to LeuT, DAT has very long intracellular amino and carboxyl termini; (ii LeuT and DAT share a rather low overall sequence identity (22% and (iii the extracellular loop 2 (EL2 of DAT is substantially longer than that of LeuT. Extracellular zinc binds to DAT and restricts the transporter's movement through the conformational cycle, thereby resulting in a decrease in substrate uptake. Residue H293 in EL2 praticipates in zinc binding and must be modelled correctly to allow for a full understanding of its effects. We exploited the high-affinity zinc binding site endogenously present in DAT to create a model of the complete transmemberane domain of DAT. The zinc binding site provided a DAT-specific molecular ruler for calibration of the model. Our DAT model places EL2 at the transporter lipid interface in the vicinity of the zinc binding site. Based on the model, D206 was predicted to represent a fourth co-ordinating residue, in addition to the three previously described zinc binding residues H193, H375 and E396. This prediction was confirmed by mutagenesis: substitution of D206 by lysine and cysteine affected the inhibitory potency of zinc and the maximum inhibition exerted by zinc, respectively. Conversely, the structural changes observed in the model allowed for rationalizing the zinc-dependent regulation of DAT: upon binding, zinc stabilizes the outward-facing state, because its first coordination shell can only be completed in this conformation. Thus, the model provides a validated solution to the long extracellular loop and may be useful to address other aspects of the transport cycle.
Stockner, Thomas; Montgomery, Therese R; Kudlacek, Oliver; Weissensteiner, Rene; Ecker, Gerhard F; Freissmuth, Michael; Sitte, Harald H
2013-01-01
The high-resolution crystal structure of the leucine transporter (LeuT) is frequently used as a template for homology models of the dopamine transporter (DAT). Although similar in structure, DAT differs considerably from LeuT in a number of ways: (i) when compared to LeuT, DAT has very long intracellular amino and carboxyl termini; (ii) LeuT and DAT share a rather low overall sequence identity (22%) and (iii) the extracellular loop 2 (EL2) of DAT is substantially longer than that of LeuT. Extracellular zinc binds to DAT and restricts the transporter's movement through the conformational cycle, thereby resulting in a decrease in substrate uptake. Residue H293 in EL2 praticipates in zinc binding and must be modelled correctly to allow for a full understanding of its effects. We exploited the high-affinity zinc binding site endogenously present in DAT to create a model of the complete transmemberane domain of DAT. The zinc binding site provided a DAT-specific molecular ruler for calibration of the model. Our DAT model places EL2 at the transporter lipid interface in the vicinity of the zinc binding site. Based on the model, D206 was predicted to represent a fourth co-ordinating residue, in addition to the three previously described zinc binding residues H193, H375 and E396. This prediction was confirmed by mutagenesis: substitution of D206 by lysine and cysteine affected the inhibitory potency of zinc and the maximum inhibition exerted by zinc, respectively. Conversely, the structural changes observed in the model allowed for rationalizing the zinc-dependent regulation of DAT: upon binding, zinc stabilizes the outward-facing state, because its first coordination shell can only be completed in this conformation. Thus, the model provides a validated solution to the long extracellular loop and may be useful to address other aspects of the transport cycle.
DEFF Research Database (Denmark)
Steffansen, B; Lepist, E I; Taub, M E
1999-01-01
The model prodrug D-Asp(OBzl)-Ala has previously been shown to have affinity and to be transported by the oligopeptide transporter PepT1 expressed in Caco-2 cells. The main objective of the present study was to investigate the aqueous stability of D-Asp(OBzl)-Ala and its in vitro metabolism...... in different gastrointestinal media arising from rats and humans, as well as in human plasma. The second major aim of the study was to evaluate our previous study in Caco-2 cell culture, by determining the effective intestinal permeability (Peff) of D-Asp(OBzl)-Ala in situ using the single-pass rat perfusion...... model. The aqueous stability studies show water, general buffer, as well as specific acid and base catalysis of D-Asp(OBzl)-Ala. The degradation of the model prodrug was independent of ionic strength. The half-lives in rat jejunal fluid and homogenate were >3 h. In human gastric and intestinal fluids...
Affine q-deformed symmetry and the classical Yang-Baxter σ-model
Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.
2017-03-01
The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.
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.
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.
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.
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.
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
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.
Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy
Directory of Open Access Journals (Sweden)
David M. Schmidtt
2010-05-01
Full Text Available We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of (N,N supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construction is based on an extended Riemann-Hilbert problem for affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic-like fermionic local current identities is introduced and it is shown that the simplest one, corresponding to the lowest isospectral times t_{±1} provides the supercharges generating rigid supersymmetry transformations in 2D superspace. The number of supercharges is equal to the dimension of the fermionic kernel of a given semisimple element E in ^g which defines both, the physical degrees of freedom and the symmetries of the model. The general construction is applied to the N=(1,1 and N=(2,2 sinh-Gordon models which are worked out in detail.
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.
Tang, Xiaolin; Bendjennat, Mourad; Saffarian, Saveez
2014-01-01
Vesicular stomatitis virus (VSV) is the prototype for negative sense non segmented (NNS) RNA viruses which include potent human and animal pathogens such as Rabies, Ebola and measles. The polymerases of NNS RNA viruses only initiate transcription at or near the 3′ end of their genome template. We measured the dissociation constant of VSV polymerases from their whole genome template to be 20 pM. Given this low dissociation constant, initiation and sustainability of transcription becomes nontrivial. To explore possible mechanisms, we simulated the first hour of transcription using Monte Carlo methods and show that a one-time initial dissociation of all polymerases during entry is not sufficient to sustain transcription. We further show that efficient transcription requires a sliding mechanism for non-transcribing polymerases and can be realized with different polymerase-polymerase interactions and distinct template topologies. In conclusion, we highlight a model in which collisions between transcribing and sliding non-transcribing polymerases result in release of the non-transcribing polymerases allowing for redistribution of polymerases between separate templates during transcription and suggest specific experiments to further test these mechanisms. PMID:25501005
Energy Technology Data Exchange (ETDEWEB)
Jacobson, Orit [Department of Medical Biophysics and Nuclear Medicine, Hebrew University of Jerusalem, Hadassah Hospital, Jerusalem 91120 (Israel); Laky, Desideriu [Department of Medical Biophysics and Nuclear Medicine, Hebrew University of Jerusalem, Hadassah Hospital, Jerusalem 91120 (Israel); Carlson, Kathryn E. [Department of Chemistry, University of Illinois, Urbana, IL 61801 (United States); Elgavish, Sharona [Bioinformatics Unit, Hebrew University of Jerusalem, Jerusalem 91120 (Israel); Gozin, Michael [School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978 (Israel); Even-Sapir, Einat [Department of Nuclear Medicine, Tel Aviv Sourasky Medical Center, Sackler School of Medicine, Tel Aviv University, Tel Aviv 64239 (Israel); Leibovitc, Ilan [Department of Urology, Meir Medical Center, Sackler School of Medicine, Tel Aviv University, Kfar Sava 44281 (Israel); Gutman, Mordechai [Department of Surgery A, Sapir Medical Center, Sackler School of Medicine, Tel Aviv University, Kfar Sava 44281 (Israel); Chisin, Roland [Department of Medical Biophysics and Nuclear Medicine, Hebrew University of Jerusalem, Hadassah Hospital, Jerusalem 91120 (Israel); Katzenellenbogen, John A. [Department of Chemistry, University of Illinois, Urbana, IL 61801 (United States); Mishani, Eyal [Department of Medical Biophysics and Nuclear Medicine, Hebrew University of Jerusalem, Hadassah Hospital, Jerusalem 91120 (Israel)]. E-mail: mishani@md.huji.ac.il
2006-08-15
Most prostate cancers are androgen dependent upon initial diagnosis. On the other hand, some very aggressive forms of prostate cancer were shown to have lost the expression of the androgen receptor (AR). Although the AR is routinely targeted in endocrine treatment, the clinical outcome remains suboptimal. Therefore, it is crucial to demonstrate the presence and activity of the AR in each case of prostate cancer, before and after treatment. While noninvasive positron emission tomography (PET) has the potential to determine AR expression of tumor cells in vivo, fully optimized PET imaging agents are not yet available. Based on molecular modeling, three novel derivatives of hydroxyflutamide (Compounds 1-3) were designed and synthesized. They contain an electron-rich group (dimethylamine) located on the methyl moiety, which may confer a better stability to the molecule in vivo. Compounds 1-3 have AR binding that is similar or higher than that of the currently used commercial drugs. An automated carbon-11 radiolabeling route was developed, and the compounds were successfully labeled with a 10-15% decay-corrected radiochemical yield, 99% radiochemical purity and a specific activity of 4Ci/{mu}mol end of bombardment (n=15). These labeled biomarkers may facilitate the future quantitative molecular imaging of AR-positive prostate cancer using PET and may also allow for image-guided treatment of prostate cancer.
DEFF Research Database (Denmark)
Nielsen, C U; Andersen, R; Brodin, Birger
2001-01-01
The human intestinal di/tri-peptide carrier, hPepT1, has been suggested as a drug delivery target via increasing the intestinal transport of low permeability compounds by designing peptidomimetic prodrugs. Model ester prodrugs using the stabilized dipeptides D-Glu-Ala and D-Asp-Ala as pro......-moieties for benzyl alcohol have been shown to maintain affinity for hPepT1. The primary aim of the present study was to investigate if modifications of the benzyl alcohol model drug influence the corresponding D-Glu-Ala and D-Asp-Ala model prodrugs' affinity for hPepT1 in Caco-2 cells. A second aim...... was to investigate the transepithelial transport and hydrolysis parameters for D-Asp(BnO)-Ala and D-Glu(BnO)-Ala across Caco-2 cell monolayers. In the present study, all investigated D-Asp-Ala and D-Glu-Ala model prodrugs retained various degrees of affinity for hPepT1 in Caco-2 cells. These affinities are used...
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...
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.
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...
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.
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.
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.
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.
Lind, Mats; Lee, Young Lim; Mazanowski, Janusz; Kountouriotis, Georgios K; Bingham, Geoffrey P
2014-02-01
G. P. Bingham and M. Lind (2008, Large continuous perspective transformations are necessary and sufficient for accurate perception of metric shape, Perception & Psychophysics, Vol. 70, pp. 524-540) showed that observers could perceive metric shape, given perspective changes ≥ 45° relative to a principal axis of elliptical cylinders. In this article, we tested (a) arbitrary perspective changes of 45°, (b) whether perception gradually improves with more perspective change, (c) speed of rotation, (d) whether this works with other shapes (asymmetric polyhedrons), (e) different slants, and (f) perspective changes >45°. Experiment 1 compared 45° perspective change away from, versus centered on, a principal axis. Observers adjusted an ellipse to match the cross-section of an elliptical cylinder viewed in a stereo-motion display. Experiment 2 tested whether performance would improve gradually with increases in perspective change, or suddenly with a 45° change. We also tested speed of rotation. Experiment 3 tested (a) asymmetric polyhedrons, (b) perspective change beyond 45°, and (c) the effect of slant. The results showed (a) a particular perspective was not required, (b) judgments only improved with ≥ 45° change, (c) speed was not relevant, (d) it worked with asymmetric polyhedrons, (e) slant was not relevant, and (f) judgments remained accurate beyond 45° of change. A model shows how affine operations, together with a symmetry yielded by 45° perspective change, bootstrap perception of metric shape.
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.
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.
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...
Considerations Related to Interpolation of Experimental Data Using Piecewise Functions
Directory of Open Access Journals (Sweden)
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.
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.
Image Alignment by Piecewise Planar Region Matching
Lou, Z.; Gevers, T.
2014-01-01
Robust image registration is a challenging problem, especially when dealing with severe changes in illumination and viewpoint. Previous methods assume a global geometric model (e.g., homography) and, hence, are only able to align images under predefined constraints (e.g., planar scenes and parallax-
Xia, Youshen; Feng, Gang; Wang, Jun
2004-09-01
This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications.
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.
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.
Takeda, Hiroshi; Mori, Hiroshi; Hiroi, Takahiro; Saito, Jun
1994-01-01
We studied five new Antartic achondrites, MacAlpine Hills (MAC) 88177, Yamato (Y)74357, Y75274, Y791491 and Elephant Moraine (EET)84302 by mineralogical techniques to gain a better understanding of the mineral assemblages of a group of meteorites with an affinity to Lodran (stony-iron meteorite) and their formation processes. This group is being called lodranites. These meteorites contain major coarse-grained orthopyroxene (Opx) and olivine as in Lodran and variable amounts of FeNi metal and troilite etc. MAC88177 has more augite and less FeNi than Lodran; Y74357 has more olivine and contains minor augite; Y791491 contains in addition plagioclase. EET84302 has an Acapulco-like chondritic mineral assembladge and is enriched in FeNi metal and plagioclase, but one part is enriched in Opx and chromite. The EET84302 and MAC88177 Opx crystals have dusty cores as in Acapulco. EET84302 and Y75274 are more Mg-rich than other members of the lodranite group, and Y74357 is intermediate. Since these meteorites all have coarse-grained textures, similar major mineral assemblages, variable amounts of augite, plagioclase, FeNi metal, chromite and olivine, we suggest that they are related and are linked to a parent body with modified chondritic compositions. The variability of the abundances of these minerals are in line with a proposed model of the surface mineral assemblages of the S asteroids. The mineral assemblages can best be explained by differing degrees of loss or movements of lower temperature partial melts and recrystallization, and reduction. A portion of EET84302 rich in metal and plagioclase may represent a type of component removed from the lodranite group meteorites. Y791058 and Caddo County, which were studied for comparison, are plagioclase-rich silicate inclusions in IAB iron meteorites and may have been derived by similar process but in a different body.
Directory of Open Access Journals (Sweden)
Lucy S Jun
Full Text Available Class B G protein-coupled receptors (GPCRs are important regulators of endocrine physiology, and peptide-based therapeutics targeting some of these receptors have proven effective at treating disorders such as hypercalcemia, osteoporosis, and type 2 diabetes mellitus (T2DM. As next generation efforts attempt to develop novel non-peptide, orally available molecules for these GPCRs, new animal models expressing human receptor orthologs may be required because small molecule ligands make fewer receptor contacts, and thus, the impact of amino acid differences across species may be substantially greater. The objective of this report was to generate and characterize a new mouse model of the human glucagon-like peptide-1 receptor (hGLP-1R, a class B GPCR for which established peptide therapeutics exist for the treatment of T2DM. hGLP-1R knock-in mice express the receptor from the murine Glp-1r locus. Glucose tolerance tests and gastric emptying studies show hGLP-1R mice and their wild-type littermates display similar physiological responses for glucose metabolism, insulin secretion, and gastric transit, and treatment with the GLP-1R agonist, exendin-4, elicits similar responses in both groups. Further, ex vivo assays show insulin secretion from humanized islets is glucose-dependent and enhanced by GLP-1R agonists. To enable additional utility, the targeting construct of the knock-in line was engineered to contain both flanking LoxP sites and a C-terminal FLAG epitope. Anti-FLAG affinity purification shows strong expression of hGLP-1R in islets, lung, and stomach. We crossed the hGLP-1R line with Rosa26Cre mice and generated global Glp-1r-/- animals. Immunohistochemistry of pancreas from humanized and knock-out mice identified a human GLP-1R-specific antibody that detects the GLP-1R in human pancreas as well as in the pancreas of hGLP-1r knock-in mice. This new hGLP-1R model will allow tissue-specific deletion of the GLP-1R, purification of potential
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
On affine non-negative matrix factorization
DEFF Research Database (Denmark)
Laurberg, Hans; Hansen, Lars Kai
2007-01-01
We generalize the non-negative matrix factorization (NMF) generative model to incorporate an explicit offset. Multiplicative estimation algorithms are provided for the resulting sparse affine NMF model. We show that the affine model has improved uniqueness properties and leads to more accurate...
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.
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
宋斌
2012-01-01
In order to simplify the interior ballistic model of Cased Telescoped Ammunition (CTA) .divided the interior ballistic process into tow stages. Combined with the classical interior ballistic theory and the modern interior ballistic theory, a mathematical model composed of igniter squid zero dimension model and one dimension two-phase flow interior ballistic model of Cased Telescoped Ammunition simulated by using the two-phase flow method and computational fluid dynamics is established, and is confirmed with MATLAB software. Showed the distribution in space after the shell of ballistic parameters, a new model creation method of analyzing interior ballistic performance of cased telescoped ammunition is provided. Important theoretical guidance for revising and optimizing the CTA gun charge structure are provide.%为了简化埋头弹的内弹道模型,将埋头弹内弹道过程分为两个阶段.结合经典内弹道和高等内弹道理论,并应用两相流体力学模型和计算流体动力学技术,分别建立了埋头弹传火管零维模型和身管内一维两相流模型；并利用MATLAB软件进行了数值模拟.获得了内弹道参数在弹后空间的分布情况,为分析埋头弹内弹道性能提供了一种新的建模方法.为埋头弹装药结构的修正和优化提供了理论指导.
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.
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.
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.
Grudinin, Sergei; Kadukova, Maria; Eisenbarth, Andreas; Marillet, Simon; Cazals, Frédéric
2016-09-01
The 2015 D3R Grand Challenge provided an opportunity to test our new model for the binding free energy of small molecules, as well as to assess our protocol to predict binding poses for protein-ligand complexes. Our pose predictions were ranked 3-9 for the HSP90 dataset, depending on the assessment metric. For the MAP4K dataset the ranks are very dispersed and equal to 2-35, depending on the assessment metric, which does not provide any insight into the accuracy of the method. The main success of our pose prediction protocol was the re-scoring stage using the recently developed Convex-PL potential. We make a thorough analysis of our docking predictions made with AutoDock Vina and discuss the effect of the choice of rigid receptor templates, the number of flexible residues in the binding pocket, the binding pocket size, and the benefits of re-scoring. However, the main challenge was to predict experimentally determined binding affinities for two blind test sets. Our affinity prediction model consisted of two terms, a pairwise-additive enthalpy, and a non pairwise-additive entropy. We trained the free parameters of the model with a regularized regression using affinity and structural data from the PDBBind database. Our model performed very well on the training set, however, failed on the two test sets. We explain the drawback and pitfalls of our model, in particular in terms of relative coverage of the test set by the training set and missed dynamical properties from crystal structures, and discuss different routes to improve it.
Petros, Amy K; Reddi, Amit R; Kennedy, Michelle L; Hyslop, Alison G; Gibney, Brian R
2006-12-11
Metal-ligand interactions are critical components of metalloprotein assembly, folding, stability, electrochemistry, and catalytic function. Research over the past 3 decades on the interaction of metals with peptide and protein ligands has progressed from the characterization of amino acid-metal and polypeptide-metal complexes to the design of folded protein scaffolds containing multiple metal cofactors. De novo metalloprotein design has emerged as a valuable tool both for the modular synthesis of these complex metalloproteins and for revealing the fundamental tenets of metalloprotein structure-function relationships. Our research has focused on using the coordination chemistry of de novo designed metalloproteins to probe the interactions of metal cofactors with protein ligands relevant to biological phenomena. Herein, we present a detailed thermodynamic analysis of Fe(II), Co(II), Zn(II), and[4Fe-4S]2(+/+) binding to IGA, a 16 amino acid peptide ligand containing four cysteine residues, H2N-KLCEGG-CIGCGAC-GGW-CONH2. These studies were conducted to delineate the inherent metal-ion preferences of this unfolded tetrathiolate peptide ligand as well as to evaluate the role of the solution pH on metal-peptide complex speciation. The [4Fe-4S]2(+/+)-IGA complex is both an excellent peptide-based synthetic analogue for natural ferredoxins and is flexible enough to accommodate mononuclear metal-ion binding. Incorporation of a single ferrous ion provides the FeII-IGA complex, a spectroscopic model of a reduced rubredoxin active site that possesses limited stability in aqueous buffers. As expected based on the Irving-Williams series and hard-soft acid-base theory, the Co(II) and Zn(II) complexes of IGA are significantly more stable than the Fe(II) complex. Direct proton competition experiments, coupled with determinations of the conditional dissociation constants over a range of pH values, fully define the thermodynamic stabilities and speciation of each MII-IGA complex. The
Maftei, Madalina; Tian, Xiaodan; Manea, Marilena; Exner, Thomas E; Schwanzar, Daniel; von Arnim, Christine A F; Przybylski, Michael
2012-06-01
Humanin (HN) is a linear 24-aa peptide recently detected in human Alzheimer's disease (AD) brain. HN specifically inhibits neuronal cell death in vitro induced by ß-amyloid (Aß) peptides and by amyloid precursor protein and its gene mutations in familial AD, thereby representing a potential therapeutic lead structure for AD; however, its molecular mechanism of action is not well understood. We report here the identification of the binding epitopes between HN and Aß(1-40) and characterization of the interaction structure through a molecular modeling study. Wild-type HN and HN-sequence mutations were synthesized by SPPS and the HPLC-purified peptides characterized by MALDI-MS. The interaction epitopes between HN and Aß(1-40) were identified by affinity-MS using proteolytic epitope excision and extraction, followed by elution and mass spectrometric characterization of the affinity-bound peptides. The affinity-MS analyses revealed HN(5-15) as the epitope sequence of HN, whereas Aß(17-28) was identified as the Aß interaction epitope. The epitopes and binding sites were ascertained by ELISA of the complex of HN peptides with immobilized Aß(1-40) and by ELISA with Aß(1-40) and Aß-partial sequences as ligands to immobilized HN. The specificity and affinity of the HN-Aß interaction were characterized by direct ESI-MS of the HN-Aß(1-40) complex and by bioaffinity analysis using a surface acoustic wave biosensor, providing a K(D) of the complex of 610 nm. A molecular dynamics simulation of the HN-Aß(1-40) complex was consistent with the binding specificity and shielding effects of the HN and Aß interaction epitopes. These results indicate a specific strong association of HN and Aß(1-40) polypeptide and provide a molecular basis for understanding the neuroprotective function of HN.
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.
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.
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.
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.
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.
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.
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.
Evidence of multi-affinity in the Japanese stock market
Katsuragi, Hiroaki
2000-04-01
Fluctuations of the Japanese stock market (Tokyo Stock Price Index: TOPIX) are analyzed using a multi-affine analysis method. In the research to date, only some simulated self-affine models have shown multi-affinity. In most experiments using observations of self-affine fractal profiles, multi-affinity has not been found. However, we find evidence of multi-affinity in fluctuations of the Japanese stock market (TOPIX). The qth-order Hurst exponent Hq varies with changes in q. This multi-affinity indicates that there are plural mechanisms that affect the same time scale as stock market price fluctuation dynamics.
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.
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.
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
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.
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.
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.
Schlicker, E.; Kathmann, M; Reidemeister, S.; Stark, H.; Schunack, W
1994-01-01
1. We determined the affinities of ten novel H3 receptor antagonists in an H3 receptor binding assay and their potencies in two functional H3 receptor models. The novel compounds differ from histamine in that the aminoethyl side chain is replaced by a propyl or butyl chain linked to a polar group (amide, thioamide, ester, guanidine, guanidine ester or urea) which, in turn, is connected to a hexocyclic ring or to an alicyclic ring-containing alkyl residue [corrected]. 2. The specific binding o...
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.
Wasserman, Evgeny; Rustad, James R.; Felmy, Andrew R.
1999-03-01
Calculation of the energy of a charged defect on a surface in supercell geometry is discussed. An important example of such a calculation is evaluation of surface proton affinities and acidities, as adding or removing a proton creates a charged unit cell. Systems with periodic boundary conditions in three spatial directions and a vacuum gap between slabs are demonstrated to be inadequate for unit cells having non-zero ionic charge and uniform neutralizing background. In such a system the calculated energy diverges linearly with the thickness of the vacuum gap. A system periodic in two directions and finite in the direction perpendicular to the surface (2-D PBC) with the neutralizing background distributed as the surface charge density is free from this problem. Furthermore, the correction for the interaction of the charged defect with its own translational images is needed to speed up the convergence to the infinite dilution limit. The expression for the asymptotic correction for the energy of interaction of a charged defect with its translational images in 2-D PBC geometry has been developed in this study. The asymptotic correction is evaluated as the interaction energy of a 2-D translationally periodic array of point charges located above and below the plate of non-uniform dielectric. This is a generalization of the method of M. Leslie and M.J. Gillan [J. Phys. C, 18 (1985) 973] for the calculation of the energy of a charged defect in bulk crystals. The usefulness of this correction was demonstrated on two test cases involving the calculation of proton affinity and acidity at the (012) surface of hematite. The proposed method is likely to be important in ab initio calculations of the energy effect of the surface protonation reactions, where computational limitations dictate a small size for the unit cell.
Affine processes on positive semidefinite matrices
Cuchiero, Christa; Mayerhofer, Eberhard; Teichmann, Josef
2009-01-01
This paper provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. These matrix-valued affine processes have arisen from a large and growing range of useful applications in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.
Local identification of piecewise deterministic models of genetic networks
Cinquemani, Eugenio; Milias-Argeitis, Andreas; Summers, Sean; Lygeros, John
2009-01-01
We address the identification of genetic networks under stationary conditions. A stochastic hybrid description of the genetic interactions is considered and an approximation of it in stationary conditions is derived. Contrary to traditional structure identification methods based on fitting determini
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.
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.
Cui, Ying; Chen, Qinggang; Li, Yaxiao; Tang, Ling
2017-02-01
Flavonoids exhibit a high affinity for the purified cytosolic NBD (C-terminal nucleotide-binding domain) of P-glycoprotein (P-gp). To explore the affinity of flavonoids for P-gp, quantitative structure-activity relationship (QSAR) models were developed using support vector machines (SVMs). A novel method coupling a modified particle swarm optimization algorithm with random mutation strategy and a genetic algorithm coupled with SVM was proposed to simultaneously optimize the kernel parameters of SVM and determine the subset of optimized features for the first time. Using DRAGON descriptors to represent compounds for QSAR, three subsets (training, prediction and external validation set) derived from the dataset were employed to investigate QSAR. With excluding of the outlier, the correlation coefficient (R(2)) of the whole training set (training and prediction) was 0.924, and the R(2) of the external validation set was 0.941. The root-mean-square error (RMSE) of the whole training set was 0.0588; the RMSE of the cross-validation of the external validation set was 0.0443. The mean Q(2) value of leave-many-out cross-validation was 0.824. With more informations from results of randomization analysis and applicability domain, the proposed model is of good predictive ability, stability.
Directory of Open Access Journals (Sweden)
Tamara Bruna-Larenas
2012-01-01
Full Text Available We report the results of a search for model-based relationships between mu, delta, and kappa opioid receptor binding affinity and molecular structure for a group of molecules having in common a morphine structural core. The wave functions and local reactivity indices were obtained at the ZINDO/1 and B3LYP/6-31 levels of theory for comparison. New developments in the expression for the drug-receptor interaction energy expression allowed several local atomic reactivity indices to be included, such as local electronic chemical potential, local hardness, and local electrophilicity. These indices, together with a new proposal for the ordering of the independent variables, were incorporated in the statistical study. We found and discussed several statistically significant relationships for mu, delta, and kappa opioid receptor binding affinity at both levels of theory. Some of the new local reactivity indices incorporated in the theory appear in several equations for the first time in the history of model-based equations. Interaction pharmacophores were generated for mu, delta, and kappa receptors. We discuss possible differences regulating binding and selectivity in opioid receptor subtypes. This study, contrarily to the statistically backed ones, is able to provide a microscopic insight of the mechanisms involved in the binding process.
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.
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.
Breaking the continuity of a piecewise linear map
Directory of Open Access Journals (Sweden)
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
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.
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.
Chang, Wen-Jer; Meng, Yu-Teh; Tsai, Kuo-Hui
2012-12-01
In this article, Takagi-Sugeno (T-S) fuzzy control theory is proposed as a key tool to design an effective active queue management (AQM) router for the transmission control protocol (TCP) networks. The probability control of packet marking in the TCP networks is characterised by an input constrained control problem in this article. By modelling the TCP network into a time-delay affine T-S fuzzy model, an input constrained fuzzy control methodology is developed in this article to serve the AQM router design. The proposed fuzzy control approach, which is developed based on the parallel distributed compensation technique, can provide smaller probability of dropping packets than previous AQM design schemes. Lastly, a numerical simulation is provided to illustrate the usefulness and effectiveness of the proposed design approach.
Zayed, Mohamed F; Ihmaid, Saleh K; Ahmed, Hany E A; El-Adl, Khaled; Asiri, Ahmed M; Omar, Abdelsattar M
2017-01-24
Some novel fluorinated quinazolines (5a-j) were designed and synthesized to be evaluated for their anticonvulsant activity and their neurotoxicity. Structures of all newly synthesized compounds were confirmed by their infrared (IR), mass spectrometry (MS) spectra, ¹H nuclear magnetic resonance (NMR), (13)C-NMR, and elemental analysis (CHN). The anticonvulsant activity was evaluated by a subcutaneous pentylenetetrazole (scPTZ) test and maximal electroshock (MES)-induced seizure test, while neurotoxicity was evaluated by a rotorod test. The molecular docking was performed for all newly-synthesized compounds to assess their binding affinities to the GABA-A receptor in order to rationalize their anticonvulsant activities in a qualitative way. The data obtained from the molecular modeling was correlated with that obtained from the biological screening. These data showed considerable anticonvulsant activity for all newly-synthesized compounds. Compounds 5b, 5c, and 5d showed the highest binding affinities toward the GABA-A receptor, along with the highest anticonvulsant activities in experimental mice. These compounds also showed low neurotoxicity and low toxicity in the median lethal dose test compared to the reference drugs. A GABA enzymatic assay was performed for these highly active compounds to confirm the obtained results and explain the possible mechanism for anticonvulsant action. The most active compounds might be used as leads for future modification and optimization.
Kathmann, M; Schlicker, E; Detzner, M; Timmerman, H
1993-11-01
We determined the affinities of nordimaprit, homodimaprit, clobenpropit and imetit for H3 binding sites (labelled by 3H-N alpha-methylhistamine) in rat brain cortex homogenates and their potencies at presynaptic H3A receptors on noradrenergic nerve endings in mouse brain cortex slices. 3H-N alpha-Methylhistamine bound saturably to rat brain cortex homogenates with a Kd of 0.70 nmol/l and a Bmax of 98 fmol/mg protein. Binding of 3H-N alpha-methylhistamine was displaced monophasically by dimaprit (pKi 6.55), nordimaprit (5.94), homodimaprit (6.44), clobenpropit (9.16), imetit (9.83), R-(-)-alpha-methylhistamine (8.87) and histamine (8.20), and biphasically by burimamide (pKi high 7.73, pKi low 5.97). In superfused mouse brain cortex slices preincubated with 3H-noradrenaline, the electrically (0.3 Hz) evoked tritium overflow was inhibited by imetit (pIC35 8.93), R-(-)-alpha-methylhistamine (7.87) and histamine (7.03). The effect of histamine was attenuated by nordimaprit, homodimaprit, clobenpropit and N-ethoxycarbonyl-2- ethoxy-1,2-dihydroquinoline (EEDQ); EEDQ (but not nordimaprit, homodimaprit and clobenpropit) attenuated the effect of histamine also in slices pre-exposed to the drug 60-30 min prior to superfusion. The concentration-response curve of histamine was shifted to the right by homodimaprit and clobenpropit; Schild plots yielded straight lines with a slope of unity for both drugs (pA2 5.94 and 9.55, respectively). Nordimaprit depressed the maximum effect of histamine (pD'2 5.55) and also slightly increased the concentration of histamine producing the half-maximum effect.(ABSTRACT TRUNCATED AT 250 WORDS)
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.
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...
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.
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).
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.
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.
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.
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.
Werner, Rolf; Valev, Dimitar; Danov, Dimitar; Guineva, Veneta
2015-12-01
The study of climate trends taking into consideration possible structural changes is important for understanding climate development characterized by a stochastic trend or by a determined one. In the paper global and hemisphere temperature anomalies are modeled by piecewise linear regression and break points in the temperature evolution are found. It was demonstrated that the used method allowed finding of breaks characterized by long time trends (low frequency processes) as well as abrupt changes (fast frequency processes). The obtained break points for slow temperature change are close to the ones found by other authors however additional conditions (as segment length, gradient and others) are not used here. The results for higher break point numbers are like the ones of step slope models. It was demonstrated that the successive phases of warming and cooling and most of the break points subdividing these periods in the Northern Hemisphere are introduced by the Atlantic multidecadal oscillation. Because the strong quasi periodicity of the Atlantic multidecadal oscillation the authors recommend the removal of its influence on the temperature from the temperature series before studies of trends or structural changes. The Northern Hemisphere temperature data after the removal of the Atlantic multidecadal oscillation influence show structures like the Southern Hemisphere temperatures. Model selection by the Schwarz-Bayesian Information Criterion developed by Liu, Wu and Zidek (LWZ criterion) shows that models with only one break point are to be preferred.
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).
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
Sun, Haitao
2016-05-16
We propose a new methodology for the first-principles description of the electronic properties relevant for charge transport in organic molecular crystals. This methodology, which is based on the combination of a non-empirical, optimally tuned range-separated hybrid functional with the polarizable continuum model, is applied to a series of eight representative molecular semiconductor crystals. We show that it provides ionization energies, electron affinities, and transport gaps in very good agreement with experimental values as well as with the results of many-body perturbation theory within the GW approximation at a fraction of the computational costs. Hence, this approach represents an easily applicable and computationally efficient tool to estimate the gas-to-crystal-phase shifts of the frontier-orbital quasiparticle energies in organic electronic materials.
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...
Institute of Scientific and Technical Information of China (English)
Ehsan Salehi; Leila Bakhtiari; Mahdi Askari
2016-01-01
Transport of copper ions through nanocomposite chitosan/polyvinyl alcohol thin adsorptive membranes has been mathematical y investigated in the current study. Unsteady-state diffusive transport model was coupled with the Freundlich isotherm to predict the concentration of the ions in dialysis permeation operation. Pristine model was not successful in predicting the experimental data based upon its low coefficients of determination (0.1﹤R2﹤0.65). Well-behaved polynomial and exponential functions were used to describe time-dependency of the inlet-concentration in the first extension of the model with a little improvement in the model adjustment (0.4﹤R2﹤0.69). Similar time-dependent functions were employed for tracking the ion diffusivity and then applied in combination with the optimized functions of inlet-concentration in the second extension of the model. A sensible enhancement was obtained in the adjustment of the second extended models as a result of this combination (0.73﹤R2﹤0.93). APRE, AAPRE, RSME, RMSE, STD and R-square statistical analyses were per-formed to verify the agreement of the models with the experimental results. Concentration distribution versus time and location (inside the membrane) was obtained as 3D plots with the help of the optimized models. Modeling results emphasized on the transiency of diffusivity and feed-side concentration in dialysis permeation through chitosan membranes.
Yu, Han
2013-09-01
The Talbot-Ogden hydrology model provides a fast mass conservative method to compute infiltration in unsaturated soils. As a replacement for a model based on Richards equation, it separates the groundwater movement into infiltration and redistribution for every time step. The typical feature making this method fast is the discretization of the moisture content domain rather than the spatial one. The Talbot-Ogden model rapidly determines how well ground water and aquifers are recharged only. Hence, it differs from models based on advanced reservoir modeling that are uniformly far more expensive computationally since they determine where the water moves in space instead, a completely different and more complex problem.According to the pore-size distribution curve for many soils, this paper extends the one dimensional moisture content domain into a two dimensional one by keeping the vertical spatial axis. The proposed extension can describe any pore-size or porosity distribution as an important soil feature. Based on this extension, infiltration and redistribution are restudied. The unconditional conservation of mass in the Talbot-Ogden model is inherited in this extended model. A numerical example is given for the extended model.
Paricharak, Shardul; Cortés-Ciriano, Isidro; IJzerman, Adriaan P; Malliavin, Thérèse E; Bender, Andreas
2015-01-01
The rampant increase of public bioactivity databases has fostered the development of computational chemogenomics methodologies to evaluate potential ligand-target interactions (polypharmacology) both in a qualitative and quantitative way. Bayesian target prediction algorithms predict the probability of an interaction between a compound and a panel of targets, thus assessing compound polypharmacology qualitatively, whereas structure-activity relationship techniques are able to provide quantitative bioactivity predictions. We propose an integrated drug discovery pipeline combining in silico target prediction and proteochemometric modelling (PCM) for the respective prediction of compound polypharmacology and potency/affinity. The proposed pipeline was evaluated on the retrospective discovery of Plasmodium falciparum DHFR inhibitors. The qualitative in silico target prediction model comprised 553,084 ligand-target associations (a total of 262,174 compounds), covering 3,481 protein targets and used protein domain annotations to extrapolate predictions across species. The prediction of bioactivities for plasmodial DHFR led to a recall value of 79% and a precision of 100%, where the latter high value arises from the structural similarity of plasmodial DHFR inhibitors and T. gondii DHFR inhibitors in the training set. Quantitative PCM models were then trained on a dataset comprising 20 eukaryotic, protozoan and bacterial DHFR sequences, and 1,505 distinct compounds (in total 3,099 data points). The most predictive PCM model exhibited R (2) 0 test and RMSEtest values of 0.79 and 0.59 pIC50 units respectively, which was shown to outperform models based exclusively on compound (R (2) 0 test/RMSEtest = 0.63/0.78) and target information (R (2) 0 test/RMSEtest = 0.09/1.22), as well as inductive transfer knowledge between targets, with respective R (2) 0 test and RMSEtest values of 0.76 and 0.63 pIC50 units. Finally, both methods were integrated to predict the protein
Corner Transfer Matrices and Quantum Affine Algebras
Foda, O E; Foda, Omar; Miwa, Tetsuji
1992-01-01
Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the anti-ferroelectric regime. It acts on the infinite tensor product W = V . V . V ....., where is the 2-dimensional irreducible representation of the quantum affine sl(2). We observe that H is the derivation of quantum affine sl(2), and conjecture that the eigenvectors of H form the level-1 vacuum representation of quantum affine sl(2). We report on checks in support of our conjecture.
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.
Williams, Michael; Schwartz, Steven
2015-03-01
The previous version of our cardiac thin filament (CTF) model consisted of the troponin complex (cTn), two coiled-coil dimers of tropomyosin (Tm), and 29 actin units. We now present the newest revision of the model to include explicit solvation. The model was developed to continue our study of genetic mutations in the CTF proteins which are linked to familial hypertrophic cardiomyopathies. Binding of calcium to the cTnC subunit causes subtle conformational changes to propagate through the cTnC to the cTnI subunit which then detaches from actin. Conformational changes propagate through to the cTnT subunit, which allows Tm to move into the open position along actin, leading to muscle contraction. Calcium disassociation allows for the reverse to occur, which results in muscle relaxation. The inclusion of explicit TIP3 water solvation allows for the model to get better individual local solvent to protein interactions; which are important when observing the N-lobe calcium binding pocket of the cTnC. We are able to compare in silica and in vitro experimental results to better understand the physiological effects from mutants, such as the R92L/W and F110V/I of the cTnT, on the calcium binding affinity compared to the wild type.
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.
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.
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device.
DEFF Research Database (Denmark)
Christensen, Bent Jesper; van der Wel, Michel
of the risk premium is associated with the slope factor, and individual risk prices depend on own past values, factor realizations, and past values of other risk prices, and are significantly related to the output gap, consumption, and the equity risk price. The absence of arbitrage opportunities is strongly...... is tested, but in addition to the standard bilinear term in factor loadings and market prices of risk, the relevant mean restriction in the term structure case involves an additional nonlinear (quadratic) term in factor loadings. We estimate our general model using likelihood-based dynamic factor model...... techniques for a variety of volatility factors, and implement the relevant likelihood ratio tests. Our factor model estimates are similar across a general state space implementation and an alternative robust two-step principal components approach. The evidence favors time-varying market prices of risk. Most...
Directory of Open Access Journals (Sweden)
Nicholas Allen Kinney
Full Text Available Three dimensional nuclear architecture is important for genome function, but is still poorly understood. In particular, little is known about the role of the "boundary conditions"--points of attachment between chromosomes and the nuclear envelope. We describe a method for modeling the 3D organization of the interphase nucleus, and its application to analysis of chromosome-nuclear envelope (Chr-NE attachments of polytene (giant chromosomes in Drosophila melanogaster salivary glands. The model represents chromosomes as self-avoiding polymer chains confined within the nucleus; parameters of the model are taken directly from experiment, no fitting parameters are introduced. Methods are developed to objectively quantify chromosome territories and intertwining, which are discussed in the context of corresponding experimental observations. In particular, a mathematically rigorous definition of a territory based on convex hull is proposed. The self-avoiding polymer model is used to re-analyze previous experimental data; the analysis suggests 33 additional Chr-NE attachments in addition to the 15 already explored Chr-NE attachments. Most of these new Chr-NE attachments correspond to intercalary heterochromatin--gene poor, dark staining, late replicating regions of the genome; however, three correspond to euchromatin--gene rich, light staining, early replicating regions of the genome. The analysis also suggests 5 regions of anti-contact, characterized by aversion for the NE, only two of these correspond to euchromatin. This composition of chromatin suggests that heterochromatin may not be necessary or sufficient for the formation of a Chr-NE attachment. To the extent that the proposed model represents reality, the confinement of the polytene chromosomes in a spherical nucleus alone does not favor the positioning of specific chromosome regions at the NE as seen in experiment; consequently, the 15 experimentally known Chr-NE attachment positions do not
Jimbo, Michio
2013-03-01
Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.
Nunes-Alves, Ariane; Arantes, Guilherme Menegon
2014-08-25
Accurate calculations of free energies involved in small-molecule binding to a receptor are challenging. Interactions between ligand, receptor, and solvent molecules have to be described precisely, and a large number of conformational microstates has to be sampled, particularly for ligand binding to a flexible protein. Linear interaction energy models are computationally efficient methods that have found considerable success in the prediction of binding free energies. Here, we parametrize a linear interaction model for implicit solvation with coefficients adapted by ligand and binding site relative polarities in order to predict ligand binding free energies. Results obtained for a diverse series of ligands suggest that the model has good predictive power and transferability. We also apply implicit ligand theory and propose approximations to average contributions of multiple ligand-receptor poses built from a protein conformational ensemble and find that exponential averages require proper energy discrimination between plausible binding poses and false-positives (i.e., decoys). The linear interaction model and the averaging procedures presented can be applied independently of each other and of the method used to obtain the receptor structural representation.
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.
Anighoro, Andrew; Graziani, Davide; Bettinelli, Ilaria; Cilia, Antonio; De Toma, Carlo; Longhi, Matteo; Mangiarotti, Fabio; Menegon, Sergio; Pirona, Lorenza; Poggesi, Elena; Riva, Carlo; Rastelli, Giulio
2015-07-01
Metabotropic glutamate receptor 5 (mGlu5) is a biological target implicated in major neurological and psychiatric disorders. In the present study, we have investigated structural determinants of the interaction of negative allosteric modulators (NAMs) with the seven-transmembrane (7TM) domain of mGlu5. A homology model of the 7TM receptor domain built on the crystal structure of the mGlu1 template was obtained, and the binding modes of known NAMs, namely MPEP and fenobam, were investigated by docking and molecular dynamics simulations. The results were validated by comparison with mutagenesis data available in the literature for these two ligands, and subsequently corroborated by the recently described mGlu5 crystal structure. Moreover, a new series of NAMs was synthesized and tested, providing compounds with nanomolar affinity. Several structural modifications were sequentially introduced with the aim of identifying structural features important for receptor binding. The synthesized NAMs were docked in the validated homology model and binding modes were used to interpret and discuss structure-activity relationships within this new series of compounds. Finally, the models of the interaction of NAMs with mGlu5 were extended to include important non-aryl alkyne mGlu5 NAMs taken from the literature. Overall, the results provide useful insights into the molecular interaction of negative allosteric modulators with mGlu5 and may facilitate the design of new modulators for this class of receptors.
Institute of Scientific and Technical Information of China (English)
DUJIN－ZHOU; LUCHANG－QING; 等
1994-01-01
Potentiometric experiments were carried out on the proton binding equilibria of FA extracted from a weathered coal and HA and Fa extracted from a dark loessial soil.The affinity spectrum model was employed to treat the experimental data.The affinity spectrum model technique could“magnify” the heterogeneity of the proton binding equilibria.so it was useful for comparing and studying the characteristics of humic substances with similar properties.According to the affinity spectra,we also found that the direction of the titration could affect the properties of the equilibria of FA from the weathered coal,and the acidic functional groups contained in FA from the weathered coal were larger in quantity than those contained in HA and FA from the dark loessial soil.
Lipin, Daniel I; Raj, Abhijeet; Lua, Linda H L; Middelberg, Anton P J
2009-07-24
Prokaryote-expressed polyomavirus structural protein VP1 with an N-terminal glutathione-S-transferase tag (GST-VP1) self-assembles into pentamer structures that further organize into soluble aggregates of variable size (3.4 x 10(2)-1.8 x 10(4)kDa) [D.I. Lipin, L.H.L. Lua, A.P.J. Middelberg, J. Chromatogr. A 1190 (2008) 204]. The adsorption mechanism for the full range of GST-VP1 soluble aggregates was described assuming a dual-component model [T.Y. Gu, G.J. Tsai, G.T. Tsao, AICHE J. 37 (1991) 1333], with components differentiated by size, and hence pore accessibility, rather than by protein identity. GST-VP1 protein was separated into two component groups: aggregates small enough to access resin pores (LMW: 3.4 x 10(2)-1.4 x 10(3)kDa) and aggregates excluded from the resin pores (HMW: 9.0 x 10(2)-1.8 x 10(4)kDa). LMW aggregates bound to resin at a higher saturation concentration (29.7 g L(-1)) than HMW aggregates (13.3 g L(-1)), while the rate of adsorption of HMW aggregates was an order of magnitude higher than for LMW aggregates. The model was used to predict both batch and packed bed adsorption of GST-VP1 protein in solutions with known concentrations of HMW and LMW aggregates to Glutathione Sepharose HP resin. Asymmetrical flow field flow fractionation with UV absorbance was utilized in conjunction with adsorption experimentation to show that binding of HMW aggregates to the resin was strong enough to withstand model-predicted displacement by LMW aggregates. High pore concentrations of LMW aggregates were also found to significantly inhibit the diffusion rate of further protein in the resin pores. Additional downstream processing experimentation showed that enzymatic cleavage of LMW aggregates to remove GST tags yields more un-aggregated VP1 pentamers than enzymatic cleavage of HMW aggregates. This model can be used to enhance the chromatographic capture of GST-VP1, and suggests an approach for modeling chromatographic purification of proteins that have a range
Stenroos, Matti
2016-01-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from standard formulation. The approach and resulting solver are verified in three ways, including comparison to finite element method (FEM). In a two-compartment split-sphere model with two spaced monopoles, the results obtained with high-resolution FEM and the BEMs were almost identical (relative difference < 0.003).
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
Nguyen, Trang Truc; Viet, Man Hoang; Li, Mai Suan
2014-01-01
The influence of water models SPC, SPC/E, TIP3P, and TIP4P on ligand binding affinity is examined by calculating the binding free energy ΔG(bind) of oseltamivir carboxylate (Tamiflu) to the wild type of glycoprotein neuraminidase from the pandemic A/H5N1 virus. ΔG(bind) is estimated by the Molecular Mechanic-Poisson Boltzmann Surface Area method and all-atom simulations with different combinations of these aqueous models and four force fields AMBER99SB, CHARMM27, GROMOS96 43a1, and OPLS-AA/L. It is shown that there is no correlation between the binding free energy and the water density in the binding pocket in CHARMM. However, for three remaining force fields ΔG(bind) decays with increase of water density. SPC/E provides the lowest binding free energy for any force field, while the water effect is the most pronounced in CHARMM. In agreement with the popular GROMACS recommendation, the binding score obtained by combinations of AMBER-TIP3P, OPLS-TIP4P, and GROMOS-SPC is the most relevant to the experiments. For wild-type neuraminidase we have found that SPC is more suitable for CHARMM than TIP3P recommended by GROMACS for studying ligand binding. However, our study for three of its mutants reveals that TIP3P is presumably the best choice for CHARMM.
Estimating affinities of calcium ions to proteins
Directory of Open Access Journals (Sweden)
Stefan Franke
2010-03-01
Full Text Available Stefan Franke, Julia Herfurth, Daniel HoffmannDepartment of Bioinformatics/Centre for Medical Biotechnology, University of Duisburg-Essen, Essen, GermanyAbstract: Ca2+-ions have a range of affinities to different proteins, depending on the various functions of these proteins. This makes the determination of Ca2+-protein affinities an interesting subject for functional studies. We have investigated the performance of two methods – Fold-X and AutoDock vina – in the prediction of Ca2+-protein affinities. Both methods, although based on different energy functions, showed virtually the same correlation with experimental affinities. Guided by insight from experiment, we further derived a simple linear model based on thesolvent accessible surface of Ca2+ that had practically the same performance in terms of absolute errors as the more complex docking methods.Keywords: metal ions, binding, free energy, crystal structure, solvent accessible surface
Estimating affinities of calcium ions to proteins
Franke, Stefan; Herfurth, Julia; Hoffmann, Daniel
2010-01-01
Ca2+-ions have a range of affinities to different proteins, depending on the various functions of these proteins. This makes the determination of Ca2+-protein affinities an interesting subject for functional studies. We have investigated the performance of two methods – Fold-X and AutoDock vina – in the prediction of Ca2+-protein affinities. Both methods, although based on different energy functions, showed virtually the same correlation with experimental affinities. Guided by insight from experiment, we further derived a simple linear model based on the solvent accessible surface of Ca2+ that had practically the same performance in terms of absolute errors as the more complex docking methods. PMID:21918621
Schlicker, E; Kathmann, M; Reidemeister, S; Stark, H; Schunack, W
1994-08-01
1. We determined the affinities of ten novel H3 receptor antagonists in an H3 receptor binding assay and their potencies in two functional H3 receptor models. The novel compounds differ from histamine in that the aminoethyl side chain is replaced by a propyl or butyl chain linked to a polar group (amide, thioamide, ester, guanidine, guanidine ester or urea) which, in turn, is connected to a hexocyclic ring or to an alicyclic ring-containing alkyl residue [corrected]. 2. The specific binding of [3H]-N alpha-methylhistamine to rat brain cortex membranes was monophasically displaced by each of the ten compounds at pKi values ranging from 7.56 to 8.68. 3. Inhibition by histamine of the electrically evoked tritium overflow from mouse brain cortex slices preincubated with [3H]-noradrenaline was antagonized by the ten compounds and the concentration-response curve was shifted to the right with apparent pA2 values ranging from 7.07 to 9.20. 4. The electrically induced contraction in guinea-pig ileum strips (which was abolished by atropine) was inhibited by the H3 receptor agonists R-(-)-alpha-methylhistamine (pEC50 7.76), N alpha-methylhistamine (7.90) and imetit (8.18). The concentration-response curve of R-(-)-alpha-methylhistamine was shifted to the right by thioperamide (apparent pA2 8.79) and by the ten novel compounds (range of pA2 values 6.64-8.81). 5. The affinities and potencies were compared by linear regression analysis. This analysis was extended to thioperamide, the standard H3 receptor antagonist, which is also capable of differentiating between H3A and H3B sites. Comparison of the apparent pA2 values in the two functional H3 receptor models yielded a regression coefficient of 0.77 (PH3 receptor antagonists,and the nature of the H3 receptors in the guinea-pig ileum and mouse brain, are considered.
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...
Affine Quantization and the Initial Cosmological Singularity
Fanuel, Michaël
2012-01-01
A toy model for quantum cosmology is suggested and quantized in the light of the Affine Coherent State Quantization procedure. The quantum corrections to the classical dynamics seem to provide a potential barrier term, as already suggested in other models studied in the literature. The possible application of this method to more realistic minisuperspace models is envisaged.
Bennett-Kennett, Ross; Herbots, Nicole; Murphy, Ashlee; Sell, David; Kutz, Tyler; Benitez, Sophia; Acharya, Ajjya; Hughes, Brett; Watson, Clarizza; Culbertson, Eric; Sell, Clive; Kwong, H.
2012-10-01
Surgical lenses in laparoscopes and arthroscopes ``fog'' during surgery. Fogging increases by up to 40% surgery duration, infection rates, and scarring due to exposure from repeated scopes withdrawal for cleaning. Modeling nucleation on surfaces shows that 2-D layer-by-layer condensation maintains transparency while 3-D droplets refract at gas/fluid interfaces leading to opacity or ``fogging.'' This ProteinKnoxmodel for lenses made from bio-compatible polymers, and silica led us to a nano-scale molecular mesh applied as a bio-identical emulsion. ProteinKnox[1-5] meets a 100% success rate in eliminating fogging for up to 240 minutes over 300 experiments. Twenty surgical trials in the OR yield a success rate of 90%, with loss of vision due to the presence of blood or blood proteins, not fogging. We studied the common blood protein, heparin, which prevents coagulation, with the ProteinKnoxmodel. Heparin behaves like H2O on hydrophobic surfaces. It does not prevent fogging nor interferes with 2-D condensatio. Next, we investigated fibrinogen as agonist agent because it causes coagulation. Fibrinogen applied to various surfaces in emulsions prepared in accordance with the ProteinKnoxmodel can prevent not only
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.
Stenroos, Matti
2016-11-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from the standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.
Volatility Components, Affine Restrictions and Non-Normal Innovations
DEFF Research Database (Denmark)
Christoffersen, Peter; Jacobs, Kris; Dorian, Christian
Recent work by Engle and Lee (1999) shows that allowing for long-run and short-run components greatly enhances a GARCH model's ability fit daily equity return dynamics. Using the risk-neutralization in Duan (1995), we assess the option valuation performance of the Engle-Lee model and compare...... it to the standard one-component GARCH(1,1) model. We also compare these non-affine GARCH models to one- and two- component models from the class of affine GARCH models developed in Heston and Nandi (2000). Using the option pricing methodology in Duan (1999), we then compare the four conditionally normal GARCH...... models to four conditionally non-normal versions. As in Hsieh and Ritchken (2005), we find that non-affine models dominate affine models both in terms of fitting return and in terms of option valuation. For the affine models we find strong evidence in favor of the component structure for both returns...
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...
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.
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.
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...
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.
Graph-Based Transform for 2D Piecewise Smooth Signals With Random Discontinuity Locations.
Zhang, Dong; Liang, Jie
2017-04-01
The graph-based block transform recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, in existing methods, overheads are required to describe the graph of the block, from which the decoder has to calculate the transform via time-consuming eigendecomposition. To address these problems, in this paper, we aim to develop a single graph-based transform for a class of 2D piecewise smooth signals with similar discontinuity patterns. We first consider the deterministic case with a known discontinuity location in each row. We propose a 2D first-order autoregression (2D AR1) model and a 2D graph for this type of signals. We show that the closed-form expression of the inverse of a biased Laplacian matrix of the proposed 2D graph is exactly the covariance matrix of the proposed 2D AR1 model. Therefore, the optimal transform for the signal are the eigenvectors of the proposed graph Laplacian. Next, we show that similar results hold in the random case, where the locations of the discontinuities in different rows are randomly distributed within a confined region, and we derive the closed-form expression of the corresponding optimal 2D graph Laplacian. The theory developed in this paper can be used to design both pre-computed transforms and signal-dependent transforms with low complexities. Finally, depth image coding experiments demonstrate that our methods can achieve similar performance to the state-of-the-art method, but our complexity is much lower.
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.
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.
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.
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...
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...
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).
Estellés, Angeles; Woischnig, Anne-Kathrin; Liu, Keyi; Stephenson, Robert; Lomongsod, Evelene; Nguyen, Da; Zhang, Jianzhong; Heidecker, Manfred; Yang, Yifan; Simon, Reyna J; Tenorio, Edgar; Ellsworth, Stote; Leighton, Anton; Ryser, Stefan; Gremmelmaier, Nina Khanna; Kauvar, Lawrence M
2016-04-01
Many serious bacterial infections are difficult to treat due to biofilm formation, which provides physical protection and induces a sessile phenotype refractory to antibiotic treatment compared to the planktonic state. A key structural component of biofilm is extracellular DNA, which is held in place by secreted bacterial proteins from the DNABII family: integration host factor (IHF) and histone-like (HU) proteins. A native human monoclonal antibody, TRL1068, has been discovered using single B-lymphocyte screening technology. It has low-picomolar affinity against DNABII homologs from important Gram-positive and Gram-negative bacterial pathogens. The disruption of established biofilm was observedin vitroat an antibody concentration of 1.2 μg/ml over 12 h. The effect of TRL1068in vivowas evaluated in a murine tissue cage infection model in which a biofilm is formed by infection with methicillin-resistantStaphylococcus aureus(MRSA; ATCC 43300). Treatment of the established biofilm by combination therapy of TRL1068 (15 mg/kg of body weight, intraperitoneal [i.p.] administration) with daptomycin (50 mg/kg, i.p.) significantly reduced adherent bacterial count compared to that after daptomycin treatment alone, accompanied by significant reduction in planktonic bacterial numbers. The quantification of TRL1068 in sample matrices showed substantial penetration of TRL1068 from serum into the cage interior. TRL1068 is a clinical candidate for combination treatment with standard-of-care antibiotics to overcome the drug-refractory state associated with biofilm formation, with potential utility for a broad spectrum of difficult-to-treat bacterial infections.
Kempkens, Ozlem; Médina, Emmanuelle; Fernandez-Ballester, Gregorio; Ozüyaman, Susann; Le Bivic, André; Serrano, Luis; Knust, Elisabeth
2006-08-01
Formation of multiprotein complexes is a common theme to pattern a cell, thereby generating spatially and functionally distinct entities at specialised regions. Central components of these complexes are scaffold proteins, which contain several protein-protein interaction domains and provide a platform to recruit a variety of additional components. There is increasing evidence that protein complexes are dynamic structures and that their components can undergo various interactions depending on the cellular context. However, little is known so far about the factors regulating this behaviour. One evolutionarily conserved protein complex, which can be found both in Drosophila and mammalian epithelial cells, is composed of the transmembrane protein Crumbs/Crb3 and the scaffolding proteins Stardust/Pals1 and DPATJ/PATJ, respectively, and localises apically to the zonula adherens. Here we show by in vitro analysis that, similar as in vertebrates, the single PDZ domain of Drosophila DmPar-6 can bind to the four C-terminal amino acids (ERLI) of the transmembrane protein Crumbs. To further evaluate the binding capability of Crumbs to DmPar-6 and the MAGUK protein Stardust, analysis of the PDZ structural database and modelling of the interactions between the C-terminus of Crumbs and the PDZ domains of these two proteins were performed. The results suggest that both PDZ domains bind Crumbs with similar affinities. These data are supported by quantitative yeast two-hybrid interactions. In vivo analysis performed in cell cultures and in the Drosophila embryo show that the cytoplasmic domain of Crumbs can recruit DmPar-6 and DaPKC to the plasma membrane. The data presented here are discussed with respect to possible dynamic interactions between these proteins.
Directory of Open Access Journals (Sweden)
Aimi Steven
2011-03-01
Full Text Available Abstract Background Inhaled short acting β2-agonists (SABA, e.g. albuterol, are used for quick reversal of bronchoconstriction in asthmatics. While SABA are not recommended for maintenance therapy, it is not uncommon to find patients who frequently use SABA over a long period of time and there is a suspicion that long term exposure to SABA could be detrimental to lung function. To test this hypothesis we studied the effect of long-term inhaled albuterol stereoisomers on immediate allergic response (IAR and airway hyperresponsiveness (AHR in mouse models of asthma. Methods Balb/C mice were sensitized and challenged with ovalbumin (OVA and then we studied the IAR to inhaled allergen and the AHR to inhaled methacholine. The mice were pretreated with nebulizations of either racemic (RS-albuterol or the single isomers (S- and (R-albuterol twice daily over 7 days prior to harvest. Results We found that all forms of albuterol produced a significant increase of IAR measured as respiratory elastance. Similarly, we found that AHR was elevated by albuterol. At the same time a mouse strain that is intrinsically hyperresponsive (A/J mouse was not affected by the albuterol isomers nor was AHR induced by epithelial disruption with Poly-L-lysine affected by albuterol. Conclusions We conclude that long term inhalation treatment with either isomer of albuterol is capable of precipitating IAR and AHR in allergically inflamed airways but not in intrinsically hyperresponsive mice or immunologically naïve mice. Because (S-albuterol, which lacks affinity for the β2-receptor, did not differ from (R-albuterol, we speculate that isomer-independent properties of the albuterol molecule, other than β2-agonism, are responsible for the effect on AHR.
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.
Volatility Components, Affine Restrictions and Non-Normal Innovations
DEFF Research Database (Denmark)
Christoffersen, Peter; Jacobs, Kris; Dorian, Christian;
Recent work by Engle and Lee (1999) shows that allowing for long-run and short-run components greatly enhances a GARCH model's ability fit daily equity return dynamics. Using the risk-neutralization in Duan (1995), we assess the option valuation performance of the Engle-Lee model and compare...... models to four conditionally non-normal versions. As in Hsieh and Ritchken (2005), we find that non-affine models dominate affine models both in terms of fitting return and in terms of option valuation. For the affine models we find strong evidence in favor of the component structure for both returns...
Institute of Scientific and Technical Information of China (English)
Xin Wen; Shi Jin
2008-01-01
We study the L1-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces.Here the interface condition is immersed into the upwind scheme.We prove that,for initial data with a bounded variation,the numerical solution of the immersed interface upwind scheme converges in L1-norm to the differential equation with the corresponding interface condition.We derive the one-halfth order L1-error bounds with explicit coefficients following a technique used in [25].We also use some inequalities on binomial coefficients proved in a consecutive paper[32].
Simulation of mineral dust aerosol with Piecewise Log-normal Approximation (PLA in CanAM4-PAM
Directory of Open Access Journals (Sweden)
Y. Peng
2012-08-01
Full Text Available A new size-resolved dust scheme based on the numerical method of piecewise log-normal approximation (PLA was developed and implemented in the fourth generation of the Canadian Atmospheric Global Climate Model with the PLA Aerosol Model (CanAM4-PAM. The total simulated annual global dust emission is 2500 Tg yr^{−1}, and the dust mass load is 19.3 Tg for year 2000. Both are consistent with estimates from other models. Results from simulations are compared with multiple surface measurements near and away from dust source regions, validating the generation, transport and deposition of dust in the model. Most discrepancies between model results and surface measurements are due to unresolved aerosol processes. Biases in long-range transport are also contributing. Radiative properties of dust aerosol are derived from approximated parameters in two size modes using Mie theory. The simulated aerosol optical depth (AOD is compared with satellite and surface remote sensing measurements and shows general agreement in terms of the dust distribution around sources. The model yields a dust AOD of 0.042 and dust aerosol direct radiative forcing (ADRF of −1.24 W m^{−2} respectively, which show good consistency with model estimates from other studies.
Jha, Preeti; Chaturvedi, Shubhra; Swastika; Pal, Sunil; Jain, Nidhi; Mishra, Anil K
2017-08-09
The subtype, 5-HT7R has been implicated in neurological disorders and presents itself as a promising target for antidepressant drugs. Design of targeted selective ligands, require a sound knowledge of 3D-receptor structure. In absence of receptor structure, structure-based design of targeted ligands relies on generation of 5-HT7R homology model. In this study, the impact of template choice, alignment, and model building methods on the homology model of 5-HT7R is addressed. The compactness and model quality due to the presence of cholesterol (lipidic receptor) have also been observed. The results suggest good stereochemical quality of the final model. Ramachandran Plot Analysis indicated more than 97.5% amino acid residues in the favorable region. The overall quality factor was 91.8% using ERRAT. The Z-score for backbone confirmation and packing quality were -1.248 and -1.427, respectively, using WHATCHECK. The RMS Z-score for side chain planarity was .711. Other validation results for the final model include binding site analysis in which Asp162, Val163, Phe343, Phe344, Arg350, Arg367, and Leu370 conserved residues were found in the active site, correlation coefficient of .82 in ligand-based screening and .85 in embrace minimization. Further, the model showed good correlation for agonist and antagonist in docking ([Formula: see text] ≈ .76, [Formula: see text] ≈ .82), embrace minimization ([Formula: see text] ≈ .73, [Formula: see text] ≈ .72), and MM-GBSA ([Formula: see text] ≈ .69, [Formula: see text] ≈ .75) studies. The model was subjected to Molecular Dynamics (MD) simulation of 20 ns both in ligand-free and ligand-bound receptor (agonist and antagonist) system in order to assess its stability.
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.
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...
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.
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.
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.
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.
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.
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
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.
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...
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.
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.
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.
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.
Simulation of mineral dust aerosol with piecewise log-normal approximation (PLA in CanAM4-PAM
Directory of Open Access Journals (Sweden)
Y. Peng
2011-09-01
Full Text Available A new size-resolved dust scheme based on the numerical method of piecewise log-normal approximation (PLA was developed and implemented in the fourth generation of the Canadian Atmospheric Global Climate Model with the PLA Aerosol Module (CanAM4-PAM. The total simulated annual mean dust burden is 37.8 mg m^{−2} for year 2000, which is consistent with estimates from other models. Results from simulations are compared with multiple surface measurements near and away from dust source regions, validating the generation, transport and deposition of dust in the model. Most discrepancies between model results and surface measurements are due to unresolved aerosol processes. Radiative properties of dust aerosol are derived from approximated parameters in two size modes using Mie theory. The simulated aerosol optical depth (AOD is compared with several satellite observations and shows good agreements. The model yields a dust AOD of 0.042 and total AOD of 0.126 for the year 2000. The simulated aerosol direct radiative forcings (ADRF of dust and total aerosol over ocean are −1.24 W m^{−2} and −4.76 W m^{−2} respectively, which show good consistency with satellite estimates for the year 2001.
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...
A HYBRID TECHNIQUE FOR PAPR REDUCTION OF OFDM USING DHT PRECODING WITH PIECEWISE LINEAR COMPANDING
Directory of Open Access Journals (Sweden)
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.
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.
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.
Autopilot Design Method for the Blended Missile Based on Model Predictive Control
Directory of Open Access Journals (Sweden)
Baoqing Yang
2015-01-01
Full Text Available This paper develops a novel autopilot design method for blended missiles with aerodynamic control surfaces and lateral jets. Firstly, the nonlinear model of blended missiles is reduced into a piecewise affine (PWA model according to the aerodynamics properties. Secondly, based on the equivalence between the PWA model and mixed logical dynamical (MLD model, the MLD model of blended missiles is proposed taking into account the on-off constraints of lateral pulse jets. Thirdly, a hybrid model predictive control (MPC method is employed to design autopilot. Finally, simulation results under different conditions are presented to show the effectiveness of the proposed method, which demonstrate that control allocation between aerodynamic control surfaces and lateral jets is realized by adjusting the weighting matrix in an index function.
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.
Affine Coherent States in Quantum Cosmology
Malkiewicz, Przemyslaw
2015-01-01
A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The implementation of coherent states based on the affine group resolves the hardest singularities, renders self-adjoint Hamiltonians without boundary conditions and provides a completely consistent semi-classical description of the involved quantum dynamics. We consider three examples: the closed Friedmann model, the anisotropic Bianchi Type I model and the deep quantum domain of the Bianchi Type IX model.
Kumbhar, Bajarang Vasant; Borogaon, Anubhaw; Panda, Dulal; Kunwar, Ambarish
2016-01-01
Tubulin isotypes are found to play an important role in regulating microtubule dynamics. The isotype composition is also thought to contribute in the development of drug resistance as tubulin isotypes show differential binding affinities for various anti-cancer agents. Tubulin isotypes αβII, αβIII and αβIV show differential binding affinity for colchicine. However, the origin of differential binding affinity is not well understood at the molecular level. Here, we investigate the origin of differential binding affinity of a colchicine analogue N-deacetyl-N-(2-mercaptoacetyl)-colchicine (DAMA-colchicine) for human αβII, αβIII and αβIV isotypes, employing sequence analysis, homology modeling, molecular docking, molecular dynamics simulation and MM-GBSA binding free energy calculations. The sequence analysis study shows that the residue compositions are different in the colchicine binding pocket of αβII and αβIII, whereas no such difference is present in αβIV tubulin isotypes. Further, the molecular docking and molecular dynamics simulations results show that residue differences present at the colchicine binding pocket weaken the bonding interactions and the correct binding of DAMA-colchicine at the interface of αβII and αβIII tubulin isotypes. Post molecular dynamics simulation analysis suggests that these residue variations affect the structure and dynamics of αβII and αβIII tubulin isotypes, which in turn affect the binding of DAMA-colchicine. Further, the binding free-energy calculation shows that αβIV tubulin isotype has the highest binding free-energy and αβIII has the lowest binding free-energy for DAMA-colchicine. The order of binding free-energy for DAMA-colchicine is αβIV ≃ αβII > αβIII. Thus, our computational approaches provide an insight into the effect of residue variations on differential binding of αβII, αβIII and αβIV tubulin isotypes with DAMA-colchicine and may help to design new analogues with higher
Directory of Open Access Journals (Sweden)
Bajarang Vasant Kumbhar
Full Text Available Tubulin isotypes are found to play an important role in regulating microtubule dynamics. The isotype composition is also thought to contribute in the development of drug resistance as tubulin isotypes show differential binding affinities for various anti-cancer agents. Tubulin isotypes αβII, αβIII and αβIV show differential binding affinity for colchicine. However, the origin of differential binding affinity is not well understood at the molecular level. Here, we investigate the origin of differential binding affinity of a colchicine analogue N-deacetyl-N-(2-mercaptoacetyl-colchicine (DAMA-colchicine for human αβII, αβIII and αβIV isotypes, employing sequence analysis, homology modeling, molecular docking, molecular dynamics simulation and MM-GBSA binding free energy calculations. The sequence analysis study shows that the residue compositions are different in the colchicine binding pocket of αβII and αβIII, whereas no such difference is present in αβIV tubulin isotypes. Further, the molecular docking and molecular dynamics simulations results show that residue differences present at the colchicine binding pocket weaken the bonding interactions and the correct binding of DAMA-colchicine at the interface of αβII and αβIII tubulin isotypes. Post molecular dynamics simulation analysis suggests that these residue variations affect the structure and dynamics of αβII and αβIII tubulin isotypes, which in turn affect the binding of DAMA-colchicine. Further, the binding free-energy calculation shows that αβIV tubulin isotype has the highest binding free-energy and αβIII has the lowest binding free-energy for DAMA-colchicine. The order of binding free-energy for DAMA-colchicine is αβIV ≃ αβII >> αβIII. Thus, our computational approaches provide an insight into the effect of residue variations on differential binding of αβII, αβIII and αβIV tubulin isotypes with DAMA-colchicine and may help to design new
A Mathematical Model for the Dynamics and Synchronization of Cows
Sun, Jie; Porter, Mason A; Dawkins, Marian S
2010-01-01
We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \\emph{less} when the coupling is increased.
Sun, Honglei; Pu, Juan; Wei, Yandi; Sun, Yipeng; Hu, Jiao; Liu, Litao; Xu, Guanlong; Gao, Weihua; Li, Chong; Zhang, Xuxiao; Huang, Yinhua; Chang, Kin-Chow; Liu, Xiufan; Liu, Jinhua
2016-07-15
Since May 2014, highly pathogenic avian influenza H5N6 virus has been reported to cause six severe human infections three of which were fatal. The biological properties of this subtype, in particular its relative pathogenicity and transmissibility in mammals, are not known. We characterized the virus receptor-binding affinity, pathogenicity, and transmissibility in mice and ferrets of four H5N6 isolates derived from waterfowl in China from 2013-2014. All four H5N6 viruses have acquired a binding affinity for human-like SAα2,6Gal-linked receptor to be able to attach to human tracheal epithelial and alveolar cells. The emergent H5N6 viruses, which share high sequence similarity with the human isolate A/Guangzhou/39715/2014 (H5N6), were fully infective and highly transmissible by direct contact in ferrets but showed less-severe pathogenicity than the parental H5N1 virus. The present results highlight the threat of emergent H5N6 viruses to poultry and human health and the need to closely track their continual adaptation in humans. Extended epizootics and panzootics of H5N1 viruses have led to the emergence of the novel 2.3.4.4 clade of H5 virus subtypes, including H5N2, H5N6, and H5N8 reassortants. Avian H5N6 viruses from this clade have caused three fatalities out of six severe human infections in China since the first case in 2014. However, the biological properties of this subtype, especially the pathogenicity and transmission in mammals, are not known. Here, we found that natural avian H5N6 viruses have acquired a high affinity for human-type virus receptor. Compared to the parental clade 2.3.4 H5N1 virus, emergent H5N6 isolates showed less severe pathogenicity in mice and ferrets but acquired efficient in-contact transmission in ferrets. These findings suggest that the threat of avian H5N6 viruses to humans should not be ignored. Copyright © 2016, American Society for Microbiology. All Rights Reserved.
Suriyanarayanan, Balasubramanian; Lakshmi, Praveena Pothuraju; Santhosh, Ramachandran Sarojini; Dhevendaran, Kandasamy; Priya, Balakrishnan; Krishna, Shivaani
2016-06-01
Streptomycin, an antibiotic used against microbial infections, inhibits the protein synthesis by binding to ribosomal protein S12, encoded by rpsL12 gene, and associated mutations cause streptomycin resistance. A streptomycin resistant, Lysinibacillus sphaericus DSLS5 (MIC >300 µg/mL for streptomycin), was isolated from a marine sponge (Tedania anhelans). The characterisation of rpsL12 gene showed a region having similarity to long terminal repeat sequences of murine lukemia virus which added 13 amino acids for loop formation in RpsL12; in addition, a K56R mutation which corresponds to K43R mutation present in streptomycin-resistant Escherichia coli is also present. The RpsL12 protein was modelled and compared with that of Lysinibacillus boronitolerans, Escherichia coli and Mycobacterium tuberculosis. The modelled proteins docked with streptomycin indicate compound had less affinity. The effect of loop on streptomycin resistance was analysed by constructing three different models of RpsL12 by, (i) removing both loop and mutation, (ii) removing the loop alone while retaining the mutation and (iii) without mutation having loop. The results showed that the presence of loop causes streptomycin resistance (decreases the affinity), and it further enhanced in the presence of mutation at 56th codon. Further study will help in understanding the evolution of streptomycin resistance in organisms.
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.
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.
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.
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.
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.
Risser, Laurent; Vialard, François-Xavier; Baluwala, Habib Y; Schnabel, Julia A
2013-02-01
In this paper, we propose a new strategy for modelling sliding conditions when registering 3D images in a piecewise-diffeomorphic framework. More specifically, our main contribution is the development of a mathematical formalism to perform Large Deformation Diffeomorphic Metric Mapping registration with sliding conditions. We also show how to adapt this formalism to the LogDemons diffeomorphic registration framework. We finally show how to apply this strategy to estimate the respiratory motion between 3D CT pulmonary images. Quantitative tests are performed on 2D and 3D synthetic images, as well as on real 3D lung images from the MICCAI EMPIRE10 challenge. Results show that our strategy estimates accurate mappings of entire 3D thoracic image volumes that exhibit a sliding motion, as opposed to conventional registration methods which are not capable of capturing discontinuous deformations at the thoracic cage boundary. They also show that although the deformations are not smooth across the location of sliding conditions, they are almost always invertible in the whole image domain. This would be helpful for radiotherapy planning and delivery.
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.
Nes, Erik B.; Yelkur, Rama; Silkoset, Ragnhild
2014-01-01
Purpose: Our purpose is to extend affinity theory in construct domain, scale development, model testing and by discerning affinity and animosity. Design/methodology/approach: We carry out exploratory and empirical research in order to explore the domain and to test the factor structure and the hypotheses through confirmatory analysis. Findings: We find (1) four target country affinity dimensions, (2) consumer affinity impacts micro country image, buying intentions and actual product own...
DEFF Research Database (Denmark)
Skjødt, Mette Louise
surface expression of various antibody formats in the generated knockout strain. Functional scFv and scFab fragments were efficiently displayed on yeast whereas impaired chain assembly and heavy chain degradation was observed for display of full-length IgG molecules. To identify the optimal polypeptide...... linker for yeast surface display of scFv and scFab fragments, we compared a series of different Gly-Ser-based linkers in display and antigen binding proficiency. We show that these formats of the model antibody can accommodate linkers of different lengths and that introduction of alanine or glutamate...... fragments by in vivo homologous recombination large combinatorial antibody libraries can easily be generated. We have optimized ordered assembly of three CDR fragments into a gapped vector and observed increased transformation efficiency in a yeast strain carrying a deletion of the SGS1 helicase...
DEFF Research Database (Denmark)
Skjødt, Mette Louise
fragments by in vivo homologous recombination large combinatorial antibody libraries can easily be generated. We have optimized ordered assembly of three CDR fragments into a gapped vector and observed increased transformation efficiency in a yeast strain carrying a deletion of the SGS1 helicase...... surface expression of various antibody formats in the generated knockout strain. Functional scFv and scFab fragments were efficiently displayed on yeast whereas impaired chain assembly and heavy chain degradation was observed for display of full-length IgG molecules. To identify the optimal polypeptide...... linker for yeast surface display of scFv and scFab fragments, we compared a series of different Gly-Ser-based linkers in display and antigen binding proficiency. We show that these formats of the model antibody can accommodate linkers of different lengths and that introduction of alanine or glutamate...
Directory of Open Access Journals (Sweden)
Tarique N Hasan
2011-03-01
Full Text Available Tarique N Hasan1,4, Leena Grace B2, Tariq A Masoodi3,5, Gowhar Shafi4 , Ali A. Alshatwi4, P Sivashanmugham31Department of Biotechnology, Bharathiar University, Coimbator, TN, India; 2Department of Biotechnology, V. M. K. V. College of Engineering, Salem, TN, India; 3Department of Bioinformatics, Jamal Mohammed College, Bharathidasan University, Tiruchirappalli, India; 4Molecular Cancer Biology Laboratory, Department of Food Science and Nutrition, College of Food and Agricultural Sciences; 5Department of Community Health Sciences, College of Applied Medical Sciences, King Saud University, Saudi ArabiaBackground: The human progesterone receptor (hPR belongs to the steroid receptor family. It may be found as monomers (A and B and or as a dimer (AB. hPR is regarded as the prognostic biomarker for breast cancer. In a cellular dimer system, AB is the dominant species in most cases. However, when a cell coexpresses all three isoforms of hPR, the complexity of the action of this receptor increases. For example, hPR A suppresses the activity of hPR B, and the ratio of hPR A to hPR B may determine the physiology of a breast tumor. Also, persistent exposure of hPRs to nonendogenous ligands is a common risk factor for breast cancer. Hence we aimed to study progesterone and some nonendogenous ligand interactions with hPRs and their molecular docking.Methods and results: A pool of steroid derivatives, namely, progesterone, cholesterol, testosterone, testolectone, estradiol, estrone, norethindrone, exemestane, and norgestrel, was used for this in silico study. Dockings were performed on AutoDock 4.2. We found that estrogens, including estradiol and estrone, had a higher affinity for hPR A and B monomers in comparison with the dimer, hPR AB, and that of the endogenous progesterone ligand. hPR A had a higher affinity to all the docked ligands than hPR B.Conclusion: This study suggests that the exposure of estrogens to hPR A as well as hPR B, and more
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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....
Shah, Mrudang; Rajagopalan, Subramanian; Xu, Liping; Voshavar, Chandrashekhar; Shurubor, Yevgeniya; Beal, Flint; Andersen, Julie K; Dutta, Aloke K
2014-10-01
In this study, in vitro and in vivo experiments were carried out with the high-affinity multifunctional D2/D3 agonist D-512 to explore its potential neuroprotective effects in models of Parkinson's disease and the potential mechanism(s) underlying such properties. Pre-treatment with D-512 in vitro was found to rescue rat adrenal Pheochromocytoma PC12 cells from toxicity induced by 6-hydroxydopamine administration in a dose-dependent manner. Neuroprotection was found to coincide with reductions in intracellular reactive oxygen species, lipid peroxidation, and DNA damage. In vivo, pre-treatment with 0.5 mg/kg D-512 was protective against neurodegenerative phenotypes associated with systemic administration of MPTP, including losses in striatal dopamine, reductions in numbers of DAergic neurons in the substantia nigra (SN), and locomotor dysfunction. These observations strongly suggest that the multifunctional drug D-512 may constitute a novel viable therapy for Parkinson's disease.
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)
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.
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.
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.
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...
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.