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.

Antioxidant properties of hydroxycinnamic acids: a review of structure- activity relationships

Hydroxycinnamic acids (HCAs) are important phytochemicals possessing significant biological properties. Several investigators have studied in vitro antioxidant activity of HCAs in detail. In this review, we have gathered the studies focused on the structure-activity relationships (SARs) of these compounds that have used medicinal chemistry to generate more potent antioxidant molecules. Most of the reports indicated that the presence of an unsaturated bond on the side chain of HCAs is vital to their activity. The structural features that were reported to be of importance to the antioxidant activity were categorized as follows: modifications of the aromatic ring, which include alterations in the number and position of hydroxy groups and insertion of electron donating or withdrawing moieties as well as modifications of the carboxylic function that include esterification and amidation process. Furthermore, reports that have addressed the influence of physicochemical properties including redox potential, lipid solubility and dissociation constant on the antioxidant activity were also summarized. Finally, the pro-oxidant effect of HCAs in some test systems was addressed. Most of the investigations concluded that the presence of ortho-dihydroxy phenyl group (catechol moiety) is of significant importance to the antioxidant activity, while, the presence of three hydroxy groups does not necessarily improve the activity. Optimization of the structure of molecular leads is an important task of modern medicinal chemistry and its accomplishment relies on the careful assessment of SARs. SAR studies on HCAs can identify the most successful antioxidants that could be useful for management of oxidative stress-related diseases.

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.

S100A6 Amyloid Fibril Formation Is Calcium-modulated and Enhances Superoxide Dismutase-1 (SOD1) Aggregation

S100A6 is a small EF-hand calcium- and zinc-binding protein involved in the regulation of cell proliferation and cytoskeletal dynamics. It is overexpressed in neurodegenerative disorders and a proposed marker for Amyotrophic Lateral Sclerosis (ALS). Following recent reports of amyloid formation by S100 proteins, we investigated the aggregation properties of S100A6. Computational analysis using aggregation predictors Waltz and Zyggregator revealed increased propensity within S100A6 helices HI and HIV. Subsequent analysis of Thioflavin-T binding kinetics under acidic conditions elicited a very fast process with no lag phase and extensive formation of aggregates and stacked fibrils as observed by electron microscopy. Ca2+ exerted an inhibitory effect on the aggregation kinetics, which could be reverted upon chelation. An FT-IR investigation of the early conformational changes occurring under these conditions showed that Ca2+ promotes anti-parallel β-sheet conformations that repress fibrillation. At pH 7, Ca2+ rendered the fibril formation kinetics slower: time-resolved imaging showed that fibril formation is highly suppressed, with aggregates forming instead. In the absence of metals an extensive network of fibrils is formed. S100A6 oligomers, but not fibrils, were found to be cytotoxic, decreasing cell viability by up to 40%. This effect was not observed when the aggregates were formed in the presence of Ca2+. Interestingly, native S1006 seeds SOD1 aggregation, shortening its nucleation process. This suggests a cross-talk between these two proteins involved in ALS. Overall, these results put forward novel roles for S100 proteins, whose metal-modulated aggregation propensity may be a key aspect in their physiology and function.

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.