Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Produção de ovinos de corte em sistemas integrados.

O primeiro registro de ovinos no Brasil data de 1556, sendo estes animais trazidos pelos portugueses à época do descobrimento. Originários da Península Ibérica, eram raças lanadas de pequeno porte e extremamente rústicas (SANTOS, 2003). Por cinco séculos multiplicaram-se com mínima interferência do homem, sendo fortemente influenciados pelo processo de seleção natural, adquirindo características adaptativas e de produção para as diversas regiões do país, ficando conhecidos como raças ?locais?, ?crioulas? ou naturalizadas (MARIANTE; EGITO, 2002). A expansão da ovinocultura, que inicialmente esteve mais ligada à subsistência, exceção no Rio Grande do Sul em que se desenvolveu baseada na produção de lã, atualmente tem objetivos comerciais.bitstream/item/202758/1/CNPC-2019-Producao-de-ovinos.pd

25th Annual Computational Neuroscience Meeting: CNS-2016

Abstracts of the 25th Annual Computational Neuroscience Meeting: CNS-2016 Seogwipo City, Jeju-do, South Korea. 2–7 July 201

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

Nonlinear Analysis of Interaction with SVC in Stressed Power Systems: Effect of SVC Controller Parameters

In this paper, the effect of Static VAr Compensator (SVC) parameters on the nonlinear interaction of steam power plant turbine-generator set is studied using the Modal Series (MS) method. A second order representation of a power system equipped with SVC is developed and then by MS method the nonlinear interaction of torsional modes is assessed under various conditions and the most influencing factors are determined. The results show that the stress conditions and some SVC control parameters will adversely affect the dynamic performance of a power system by increasing the nonlinear interaction of torsional modes. In this situation, the MS method can precisely provide a reliable prediction of the torsional oscillations amplitudes and the frequency content of the output system response. As the angle and speed of turbine-generator segments are used as input signals in several controllers, the frequency content of these signals are quite important in designing such controllers. This analysis is performed on a 4-areas WSCC system, which is equipped with a SVC. The obtained results can provide some important guidelines for coordinate operation and design of FACTS controllers to reduce the risk of shaft failure arising from torsional interaction in long term

Kalman filters for fractional discrete-time stochastic systems along with time-delay in the observation signal

This paper investigates fractional Kalman filters when time-delay is entered in the observation signal in the discrete-time stochastic fractional order state-space representation. After investigating the common fractional Kalman filter, we try to derive a fractional Kalman filter for time-delay fractional systems. A detailed derivation is given. Fractional Kalman filters will be used to estimate recursively the states of fractional order state-space systems based on minimizing the cost function when there is a constant time delay (d) in the observation signal. The problem will be solved by converting the filtering problem to a usual d-step prediction problem for delay-free fractional systems

A new switching strategy for exponential stabilization of uncertain discrete-time switched linear systems in guaranteed cost control problem

Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and its stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, a new switching strategy and a state-feedback control law are designed to exponentially stabilize Uncertain Discrete-Time Switched Linear Systems (UDSLS), considering a given infinite-horizon cost function. Our design procedure consists of three steps. First, we generalize the exponential stabilization theorem of nonlinear systems to UDSLS. Second, based on the Common Lyapunov Function technique, a new stabilizing switching strategy is presented. Third, a sufficient condition on the existence of state-feedback controller is provided in the form of Linear Matrix Inequality. Besides, convergence rate is obtained and the upper bound of the cost is calculated. Finally, effectiveness of the proposed method is verified via numerical example

Bezier Curves Based Numerical Solutions of Delay Systems with Inverse Time

This paper applied, for the first time, the Bernstein’s approximation on delay differential equations and delay systems with inverse delay that models these problems. The direct algorithm is given for solving this problem. The delay function and inverse time function are expanded by the Bézier curves. The Bézier curves are chosen as piecewise polynomials of degree n, and the Bézier curves are determined on any subinterval by n+1 control points. The approximated solution of delay systems containing inverse time is derived. To validate accuracy of the present algorithm, some examples are solved