Solving MPCC problem with the hyperbolic penalty function

The main goal of this work is to solve mathematical program with complementarity constraints (MPCC) using nonlinear programming techniques (NLP). An hyperbolic penalty function is used to solve MPCC problems by including the complementarity constraints in the penalty term. This penalty function [1] is twice continuously differentiable and combines features of both exterior and interior penalty methods. A set of AMPL problems from MacMPEC [2] are tested and a comparative study is performed.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Fitness function evaluation through fractional algorithms

This paper proposes a Genetic Algorithm (GA) for the design of combinational logic circuits. The fitness function evaluation is calculated using Fractional Calculus. This approach extends the classical fitness function by including a fractional-order dynamical evaluation. The experiments reveal superior results when comparing with the classical method.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

Describing function of two masses with backlash

This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.

Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.

Executive Function Impairments in Patients with Depression

Depression, the most prevalent psychiatric disorder, has a lifelong risk of 20% and is related to high rates of death among the patients. Thus, this study aims to conduct a systematic review of changes in executive functions of adult patients diagnosed with depression. We found 1381 articles; however, only 28 were selected and recovered. The inclusion criteria was the assessment of executive functions with at least one neuropsychological test, and articles that evaluated primarily adult individuals with depression, without comparison to other psychiatric disorders. Although most of the studies (25 out of 28 analyzed) have shown deficits in some executive subcomponents, these findings are not conclusive because they used different parameters of assessment. Moreover, many variables were not controlled, such as the different subtypes of the disorder, the high level of severity, comorbidity and the use of drugs. Most studies showed different deficits in executive functions in depressed patients, but further longitudinal studies are needed in order to confirm these findings.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Descending pain modulation in a Kaolin-induced hydrocephalus rat model

Pain transmission at the spinal cord is modulated by descending actions that arise from supraspinal areas which collectively form the endogenous pain control system. Two key areas involved of the endogenous pain control system have a circunventricular location, namely the periaqueductal grey (PAG) and the locus coeruleus (LC). The PAG plays a crucial role in descending pain modulation as it conveys the input from higher brain centers to the spinal cord. As to the LC, it is involved in descending pain inhibition by direct noradrenergic projections to the spinal cord. In the context of neurological defects, several diseases may affect the structure and function of the brain. Hydrocephalus is a congenital or acquired disease characterized by an enlargement of the ventricles which leads to a distortion of the adjacent tissues, including the PAG and LC. Usually, patients suffering from hydrocephalus present dysfunctions in learning and memory and also motor deficits. It remains to be evaluated if lesions of the periventricular brain areas involved in pain control during hydrocephalus may affect descending pain control and, herein, affect pain responses. The studies included in the present thesis used an experimental model of hydrocephalus (the rat injected in the cisterna magna with kaolin) to study descending modulation of pain, focusing on the two circumventricular regions referred above (the PAG and the LC). In order to evaluate the effects of kaolin injection into the cisterna magna, we measured the degree of ventricular dilatation in sections encompassing the PAG by standard cytoarquitectonic stanings (thionin staining). For the LC, immunodetection of the noradrenaline-synthetizing enzyme tyrosine hydroxylase (TH) was performed, due to the noradrenergic nature of the LC neurons. In general, rats with kaolin-induced hydrocephalus presented a higher dilatation of the 4th ventricle, along with a tendency to a higher area of the PAG. Due to the validated role of detection the c-fos protooncogene as a marker of neuronal activation, we also studied neuronal activation in the several subnuclei which compose the PAG, namely the dorsomedial, dorsolateral, lateral and ventrolateral (VLPAG) parts. A decrease in the numbers of neurons immunoreactive for Fos protein (the product of activation of the c-fos protooncogene) was detected in rats injected with kaolin, whereas the remaining PAG subnuclei did not present changes in Fos-immunoreactive nuclei. Increases in the levels of TH in the LC, namely at the rostral parts of the nucleus, were detected in hydrocephalic animals. The following pain-related parameters were measured, namely 1) pain behavioural responses in a validated pain inflammatory test (the formalin test) and 2) the nociceptive activation of spinal cord neurons. A decrease in behavioral responses was detected in rats with kaolin-induced hydrocephalus was detected, namely in the second phase of the test (inflammatory phase). This is the phase of the formalin test in which the motor behaviour is less important, which is important since a semi-quantitative analysis of the motor performance of rats injected with kaolin indicates that these animals may present some motor impairments. Collectively, the results of the behavioral studies indicate that rats with kaolin-induced hydrocephalus exhibit hypoalgesia. A decrease in Fos expression was detected at the superficial dorsal layers of the spinal cord in rats with kaolin-induced hydrocephalus, further indicating that hydrocephalus decreases nociceptive responses. It remains to be ascertained if this is due to alterations in the PAG and LC in the rats with kaolin-induced hydrocephalus, which may affect descending pain modulation. It remains to be evaluated what are the mechanisms underlying the increased pain inhibition at the spinal dorsal horn in the hydrocephalus rats. Regarding the VLPAG, the decrease in neuronal activity may impair descending modulation. Since the LC has higher levels of TH in rats with kaolininduced hydrocephalus, which also appears to increase the noradrenergic innervation in the spinal dorsal horn, it is possible that an increase in the release of noradrenaline at the spinal cord accounts for pain inhibition. Our studies also determine the need to study in detail patients with hydrocephalus namely in what concerns their thresholds to pain and to perform imaging studies focused on the structure and function of pain control areas in the brain.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Analysis of Systems with Backlash and Impacts through the Describing Function

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. The dynamics is illustrated using the Nyquist and Bode plots and the results are compared with those of standard models.