Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Endothelialization of chitosan porous conduits via immobilization of a recombinant fibronectin fragment (rhFNIII7–10)

The present study aimed to develop a pre-endothelialized chitosan (CH) porous hollowed scaffold for application in spinal cord regenerative therapies. CH conduits with different degrees of acetylation (DA; 4% and 15%) were prepared, characterized (microstructure, porosity and water uptake) and functionalized with a recombinant fragment of human fibronectin (rhFNIII7–10). Immobilized rhFNIII7–10 was characterized in terms of amount (125I-radiolabelling), exposure of cell-binding domains (immunofluorescence) and ability to mediate endothelial cell (EC) adhesion and cytoskeletal rearrangement. Functionalized conduits revealed a linear increase in immobilized rhFNIII7–10 with rhFNIII7–10 concentration, and, for the same concentration, higher amounts of rhFNIII7–10 on DA 4% compared with DA 15%. Moreover, rhFNIII7–10 concentrations as low as 5 and 20 lgml 1 in the coupling reaction were shown to provide DA 4% and 15% scaffolds, respectively, with levels of exposed cell-binding domains exceeding those observed on the control (DA 4% scaffolds incubated in a 20 lgml 1 human fibronectin solution). These grafting conditions proved to be effective in mediating EC adhesion/cytoskeletal organization on CH with DA 4% and 15%, without affecting the endothelial angiogenic potential. rhFNIII7–10 grafting to CH could be a strategy of particular interest in tissue engineering applications requiring the use of endothelialized porous matrices with tunable degradation rates.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

Chitosan/AuNPs Modified Graphene Electrochemical Sensor for Label-Free Human Chorionic Gonadotropin Detection

A new immunosensor is presented for human chorionic gonadotropin (hCG), made by electrodepositing chitosan/gold-nanoparticles over graphene screen-printed electrode (SPE). The antibody was covalently bound to CS via its Fc-terminal. The assembly was controlled by electrochemical Impedance Spectroscopy (EIS) and followed by Fourier Transformed Infrared (FTIR). The hCG-immunosensor displayed linear response against the logarithm-hCG concentration for 0.1–25 ng/mL with limit of detection of 0.016 ng/mL. High selectivity was observed in blank urine and successful detection of hCG was also achieved in spiked samples of real urine from pregnant woman. The immunosensor showed good detection capability, simplicity of fabrication, low-cost, high sensitivity and selectivity.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?