Entropy and Hausdorff Dimension in Random Growing Trees

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution of the already existing tree. The so-called weight function, in terms of which the rule of attachment is formulated, is such that each vertex in the tree can have at most K children. We define the concept of a certain random measure mu on the leaves of the limiting tree, which captures a global property of the tree growth in a natural way. We prove that the Hausdorff and the packing dimension of this limiting measure is equal and constant with probability one. Moreover, the local dimension of mu equals the Hausdorff dimension at mu-almost every point. We give an explicit formula for the dimension, given the rule of attachment

A remote sensing approach to assess algal beta-carotene content in solar salt evaporation ponds

The present research attempts to calibrate satellite images against field data on D. salina ß-carotene concentration expressed per 1 L of brine. We found the empirical relation between ß-carotene quantity and the index based on two infrared reflectance bands (NIR and SWIR)

Simple Geometric Approach of Identification and Control Using Floating Basis Vectors for Representation

As a plausible alternative of certain sophisticated soft computing approaches trying to identify complete and static system models, a simple adaptive controller is outlined that creates only a temporal model. This model can be built up and maintained step-by-step on the basis of slowly fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation. The method may be used for filling in the lookup tables or rule bases of the above representations experimentally. The method is tested by the use of a simple dynamic system as a typical paradigm via simulation.N/

Adaptive vibration damping based on casual time-invariant green-functions and fractional order derivates

In this paper a simple nonlinear, adaptive control using causal time-invariant Green-functions and fractional order derivatives is applied for damping the vibration of a car forced during passing along a bumpy road. Its key idea is the replacement of the integer order derivates in a Green-functions-based nonlinear controller with a time-shift invariant, causal approximation of the Riemann-Liouville fractional derivative that also behaves like a Green-function. Since its physical essence is rather frequency filtering than providing inter order derivatives in limit cases, the approximation applied numerically is quite convinent. In this way simple kinematic design of the desired damping becomes possible. The adaptive part of the controller guarantees the realization of this kinematic design without making it necessary for the designer to have accurate and complete dynamic model of the system to be controlled or to design a sophisticated linear "CRONE" controller that has to take the responsability for the unknown dynamics of the system. The applicability of the approach is illustrated via simulations for a paradigm that is a rough model of a car. It was found that both adaptivity and the use of fractional order derivatives in the control are essential parts of the success of the method.info:eu-repo/semantics/publishedVersio

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution

Neural mechanisms for voice recognition

We investigated neural mechanisms that support voice recognition in a training paradigm with fMRI. The same listeners were trained on different weeks to categorize the mid-regions of voice-morph continua as an individual's voice. Stimuli implicitly defined a voice-acoustics space, and training explicitly defined a voice-identity space. The predefined centre of the voice category was shifted from the acoustic centre each week in opposite directions, so the same stimuli had different training histories on different tests. Cortical sensitivity to voice similarity appeared over different time-scales and at different representational stages. First, there were short-term adaptation effects: Increasing acoustic similarity to the directly preceding stimulus led to haemodynamic response reduction in the middle/posterior STS and in right ventrolateral prefrontal regions. Second, there were longer-term effects: Response reduction was found in the orbital/insular cortex for stimuli that were most versus least similar to the acoustic mean of all preceding stimuli, and, in the anterior temporal pole, the deep posterior STS and the amygdala, for stimuli that were most versus least similar to the trained voice-identity category mean. These findings are interpreted as effects of neural sharpening of long-term stored typical acoustic and category-internal values. The analyses also reveal anatomically separable voice representations: one in a voice-acoustics space and one in a voice-identity space. Voice-identity representations flexibly followed the trained identity shift, and listeners with a greater identity effect were more accurate at recognizing familiar voices. Voice recognition is thus supported by neural voice spaces that are organized around flexible ‘mean voice’ representations

Simple Kinematic Design for Evading the Forced Oscillation of a Car-Wheel Suspension System

An adaptive control damping the forced vibration of a car while passing along a bumpy road is investigated. It is based on a simple kinematic description of the desired behavior of the damped system. A modified PID controller containing an approximation of Caputo’s fractional derivative suppresses the high-frequency components related to the bumps and dips, while the low frequency part of passing hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a priori’ information on the surface of the road is needed. The adaptive control realizes this kinematic design in spite of the existence of dynamically coupled, excitable internal degrees of freedom. The method is investigated via Scicos-based simulation in the case of a paradigm. It was found that both adaptivity and fractional order derivatives are essential parts of the control that can keep the vibration of the load at bay without directly controlling its motion

Scicos Based Investigation of an Adaptive Vibration Damping Technique Using Fractional Order Derivatives

Detailed investigation of a simple nonlinear, active, adaptive approach of controlling the oscillation of a car proceeding on a bumpy road is presented. Its key idea is a frequency dependent control of the strictness of a traditional PID controller by applying fractional order derivatives in a simple kinematic design without any respect to the dynamic model of the system. The adaptive part of the controller relieves the designer of dealing with the system’s dynamics within the frames of some linear control, and guarantees the implementation of this design. The operation of the approach is illustrated by the use of INRIA’s scientific co-simulator Scicos for a rough model of a car. Well interpretable trends were revealed regarding the effect of the variation of the order of derivation, and that of the sampling time of the adaptive loop. These results seem to be promising for actively damping the vibration of systems having unmodeled, uncontrolled internal degrees of freedom.N/

Adaptive nonlinear vibration control based on causal time-invariant green functions and on a novel branch of soft computing

In this paper a simple nonlinear, adaptive approach inspired by the fractional derivatives based CRONE control is presented for vibration damping. Its key idea is replacement of the fractional derivatives with the mathematically less restricted concept of time-invariant Green functions. Instead of the traditional PID feedback terms it applies positive definite weighted moving average of the square of the error plus a nonlinear term making the error converge to zero. In this way simple kinematic design of the desired damping becomes possible. The adaptive part of the controller guarantees the realization of this kinematic design without making it necessary to the designer to have an accurate and complete dynamic model of the system to be controlled or to design sophisticated linear controller. The applicability of the approach is illustrated via simulations for a paradigm consisting of a pair of coupled damper linear oscillators under external excitation. One of the oscillators is not modeled by the controller. The adaptive loop successively maps the observed system behavior to the desired one without exerting any effort to identify the reasons of the differences. The approach was found be useful for solving vibration damping problems with unmodeled and uncontrolled internal degrees of freedom.N/

Centralized and Decentralized Applications of a Novel Adaptive Control

An adaptive control based on the combination of a novel branch of Soft Computing and fractional order derivatives was applied to control two incompletely modeled, nonlinear, coupled dynamic systems. Each of them contained one internal degree of freedom neither directly modeled/observed nor actuated. As alternatives the decentralized and the centralized control approaches were considered. In each case, as a starting point, a simple, incomplete dynamic model predicting the state-propagation of the modeled axes was applied. In the centralized approach this model contained all the observable and controllable joints. In the decentralized approach two similar initial models were applied for the two coupled subsystems separately. The controllers were restricted to the observation of the generalized coordinates modeled by them. It was expected that both approaches had to be efficient and successful. Simulation examples are resented for the control of two double pendulum-cart systems coupled by a spring and two bumpers modeled by a quasi-singular potential. It was found that both approaches were able to “learn” and to manage this control task with a very similar efficiency. In both cases the application of near integer order derivatives means serious factor of stabilization and elimination of undesirable fluctuations. Since in many technical fields the application of simple decentralized controllers is desirable the present approach seems to be promising and deserves further attention and research.N/