Search results for "linear system"
showing 10 items of 1558 documents
A logarithmic fourth-order parabolic equation and related logarithmic Sobolev inequalities
2006
A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions and some regularity results are shown. Furthermore, we prove that the solution converges exponentially fast to its mean value in the ``entropy norm'' and in the Fisher information, using a new optimal logarithmic Sobolev inequality for higher derivatives. In particular, the rate is independent of the solution and the constant depends only on the initial value of the entropy.
Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems
2002
AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.
Linear and nonlinear parametric model identification to assess granger causality in short-term cardiovascular interactions
2008
We assessed directional relationships between short RR interval and systolic arterial pressure (SAP) variability series according to the concept of Granger causality. Causality was quantified as the predictability improvement (PI) of a time series obtained when samples of the other series were used for prediction, i.e. moving from autoregressive (AR) to AR exogenous (ARX) prediction. AR and ARX predictions were performed both by linear and nonlinear parametric models. The PIs of RR given SAP and of SAP given RR, measuring baroreflex and mechanical couplings, were calculated in 15 healthy subjects in the resting supine and upright tilt positions. Using nonlinear models we found a bilateral i…
Analysis of neuronal networks in the visual system of the cat using statistical signals--simple and complex cells. Part II.
1978
Superimposing additively a two-dimensional noise process to deterministic input signals (bars) the neurons of area 17 show a class-specific reaction for the task of signal extraction. Moving both parts of the signals simultaneously and varying the signal to noise ratio (S/N) the simple cells achieve the same performance as resulted from the psychophysical experiment. Type I complex cells extract moving deterministic signals (i.e. bars) from the stationary noise, whereas in the answers of Type II complex cells the statistical parts of the signals predominate. Considering the different cell types each as a series of a linear and a nonlinear system one obtains the cell specific space-time freq…
System-theoretical analysis of the Clare Bishop Area in the cat
1980
The Clare Bishop Area (CBA) is a retinotopically organized cortical area in the cat brain connected to a great variety of visual areas in a very complex wax (Fig. 1). Experimental analysis is difficult because of the following aspects: 1. As the distance from the retina increases, the signal combinations necessary to analyse the system become more and more specific. 2. Feedback loops cannot be opened, so an unequivocal identification of CBA cell properties is impossible. 3. The nonlinear character seems to have a great influence on signal processing. To circumvent these problems, specific signal combinations leading to a separation of input subsystems have been developed (Hoffmann and v. Se…
Nonlinear pattern recognition correlators based on color-encoding single-channel systems.
2004
In color pattern recognition, color channels are normally processed separately and afterward the correlation outputs are combined. This is the definition of multichannel processing. We combine a single-channel method with nonlinear filtering based on nonlinear correlations. These nonlinear correlations yield better discrimination than common matched filtering. The method codes color information as amplitude and phase distributions and is followed by correlations related to binary decompositions. The technique is based on binary decompositions of the red, green, and blue and the hue, saturation, and intensity monochromatic channels of the reference and of the input scene, after which the bin…
Symbolic control for underactuated differentially flat systems
2006
In this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steer…
Analysis of neuronal networks in the visual system of the cat using statistical signals
1976
If the input signals of the visual system in the cat are statistical patterns in space and time, a complete system analysis can be carried out. What counts here as a system are the neuronal networks between retina and recording site. In the case of linearity, one obtains the temporal impulse response functions at every point in the receptive field with the aid of correlation methods. The measuring time is about one minute. Some aspects of the procedure are explained in terms of examples. The method of measurement also makes it possible to determine the characteristic function of the system in time and space between different recording sites within the cortex. It is possible to specialize th…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Application of Genetic Algorithm on Parameter Optimization of Three Vehicle Crash Scenarios
2017
Abstract This paper focuses on the development of mathematical models for vehicle frontal crashes. The models under consideration are threefold: a vehicle into barrier, vehicle-occupant and vehicle to vehicle frontal crashes. The first model is represented as a simple spring-mass-damper and the second case consists of a double-spring-mass-damper system, whereby the front mass and the rear mass represent the vehicle chassis and the occupant, respectively. The third model consists of a collision of two vehicles represented by two masses moving in opposite directions. The springs and dampers in the models are nonlinear piecewise functions of displacements and velocities respectively. More spec…