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.

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.

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.

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.