On the differential evolution algorithm and its appliation to training radial basis function networks

The parameter setting of a differential evolution algorithm must meet several requirements: efficiency, effectiveness, and reliability. Problems vary. The solution of a particular problem can be represented in different ways. An algorithm most efficient in dealing with a particular representation may be less efficient in dealing with other representations. The development of differential evolution-based methods contributes substantially to research on evolutionary computing and global optimization in general. The objective of this study is to investigatethe differential evolution algorithm, the intelligent adjustment of its controlparameters, and its application. In the thesis, the differential evolution algorithm is first examined using different parameter settings and test functions. Fuzzy control is then employed to make control parameters adaptive based on an optimization process and expert knowledge. The developed algorithms are applied to training radial basis function networks for function approximation with possible variables including centers, widths, and weights of basis functions and both having control parameters kept fixed and adjusted by fuzzy controller. After the influence of control variables on the performance of the differential evolution algorithm was explored, an adaptive version of the differential evolution algorithm was developed and the differential evolution-based radial basis function network training approaches were proposed. Experimental results showed that the performance of the differential evolution algorithm is sensitive to parameter setting, and the best setting was found to be problem dependent. The fuzzy adaptive differential evolution algorithm releases the user load of parameter setting and performs better than those using all fixedparameters. Differential evolution-based approaches are effective for training Gaussian radial basis function networks.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Activation function study for wavelet network

The main purpose of this paper is to investigate theoretically and experimentally the use of family of Polynomial Powers of the Sigmoid (PPS) Function Networks applied in speech signal representation and function approximation. This paper carries out practical investigations in terms of approximation fitness (LSE), time consuming (CPU Time), computational complexity (FLOP) and representation power (Number of Activation Function) for different PPS activation functions. We expected that different activation functions can provide performance variations and further investigations will guide us towards a class of mappings associating the best activation function to solve a class of problems under certain criteria.

Radial basis function networks with quantized parameters

A RBFN implemented with quantized parameters is proposed and the relative or limited approximation property is presented. Simulation results for sinusoidal function approximation with various quantization levels are shown. The results indicate that the network presents good approximation capability even with severe quantization. The parameter quantization decreases the memory size and circuit complexity required to store the network parameters leading to compact mixed-signal circuits proper for low-power applications. ©2008 IEEE.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope. (C) 2014 Elsevier Ltd. All rights reserved.

Terahertz Response of Excitons in Nanorod Heterostructures

Quantum-confined systems are one of the most promising ways to enable us to control a material's interactions with light. Nanorods in particular offer the right dimensions for exploring and manipulating the terahertz region of the spectrum. In this thesis, we model excitons confined inside a nanorod using the envelope function approximation. A region-matching transfer matrix method allows us to simulate excitonic states inside arbitrary heterostructures grown along the length of the rod. We apply the method to colloidal CdSe rods 70 nm in length and under 10 nm in diameter, capped with ligands of DDPA and pyridine. We extend past studies on these types of rods by taking into account their dielectric permittivity mismatch. Compared to previous calculations and experimentally measured terahertz absorption, we predict a higher energy main 1S$z$ to 2P$z$ transition peak. This indicates that the rods are likely larger in diameter than previously thought. We also investigate a nanorod with GaAs/Al$_{0.3}$Ga$_{0.7}$As coupled double dots. The excitonic transitions were found to be manipulable by varying the strength of an applied electric field. We employ quasi-static state population distributions to simulate the effects of exciton relaxation from optically active states to dim ground states. A critical value of the applied field, corresponding to the exciton binding energy of ~18 meV, was found to dramatically alter the terahertz absorption due to state mixing. Above this critical field, more nuanced shifts in transition energies were observed, and gain from radiative relaxation to the ground state is predicted.

Contributions to Physics-Based Aeroservoelastic Uncertainty Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

QSAR Modeling of a Set of Pyrazinoate Esters as Antituberculosis Prodrugs

Tuberculosis is an infection caused mainly by Mycobacterium tuberculosis. A first-line antimycobacterial drug is pyrazinamide (PZA), which acts partially as a prodrug activated by a pyrazinamidase releasing the active agent, pyrazinoic acid (POA). As pyrazinoic acid presents some difficulty to cross the mycobacterial cell wall, and also the pyrazinamide-resistant strains do not express the pyrazinamidase, a set of pyrazinoic acid esters have been evaluated as antimycobacterial agents. In this work, a QSAR approach was applied to a set of forty-three pyrazinoates against M. tuberculosis ATCC 27294, using genetic algorithm function and partial least squares regression (WOLF 5.5 program). The independent variables selected were the Balaban index (I), calculated n-octanol/water partition coefficient (ClogP), van-der-Waals surface area, dipole moment, and stretching-energy contribution. The final QSAR model (N = 32, r(2) = 0.68, q(2) = 0.59, LOF = 0.25, and LSE = 0.19) was fully validated employing leave-N-out cross-validation and y-scrambling techniques. The test set (N = 11) presented an external prediction power of 73%. In conclusion, the QSAR model generated can be used as a valuable tool to optimize the activity of future pyrazinoic acid esters in the designing of new antituberculosis agents.

Molecular modeling and QSAR studies of a set of indole and benzimidazole derivatives as H(4) receptor antagonists

Histamine is an important biogenic amine, which acts with a group of four G-protein coupled receptors (GPCRs), namely H(1) to H(4) (H(1)R - H(4)R) receptors. The actions of histamine at H(4)R are related to immunological and inflammatory processes, particularly in pathophysiology of asthma, and H(4)R ligands having antagonistic properties could be helpful as antiinflammatory agents. In this work, molecular modeling and QSAR studies of a set of 30 compounds, indole and benzimidazole derivatives, as H(4)R antagonists were performed. The QSAR models were built and optimized using a genetic algorithm function and partial least squares regression (WOLF 5.5 program). The best QSAR model constructed with training set (N = 25) presented the following statistical measures: r (2) = 0.76, q (2) = 0.62, LOF = 0.15, and LSE = 0.07, and was validated using the LNO and y-randomization techniques. Four of five compounds of test set were well predicted by the selected QSAR model, which presented an external prediction power of 80%. These findings can be quite useful to aid the designing of new anti-H(4) compounds with improved biological response.

Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

Recent advances in remote sensing image processing

Remote sensing image processing is nowadays a mature research area. The techniques developed in the field allow many real-life applications with great societal value. For instance, urban monitoring, fire detection or flood prediction can have a great impact on economical and environmental issues. To attain such objectives, the remote sensing community has turned into a multidisciplinary field of science that embraces physics, signal theory, computer science, electronics, and communications. From a machine learning and signal/image processing point of view, all the applications are tackled under specific formalisms, such as classification and clustering, regression and function approximation, image coding, restoration and enhancement, source unmixing, data fusion or feature selection and extraction. This paper serves as a survey of methods and applications, and reviews the last methodological advances in remote sensing image processing.

Not the outside but the inside matters : functional analysis of Capricious and Tartan during Drosophila tracheal morphogenesis

The tubular structures, which transport essential gases, liquids, or cells from one site to another, are shared among various divergent organisms. These highly organized tubular networks include lung, kidney, vasculature and mammary gland in mammals as well as trachea and salivary gland in Drosophila melanogaster. Many questions regarding the tubular morphogenesis cannot be addressed sufficiently by investigating the mammalian organs because their structures are extremely complex and therefore, systematic analyses of genetic and cellular programs guiding the development is not possible. In contrast, the Drosophila tracheal development provides an excellent model system since many molecular markers and powerful tools for genetic manipulations are available. Two mechanisms were shown to be important for the outgrowth of tracheal cells: the FGF signaling pathway and the interaction between the tracheal cells and the surrounding mesodermal cells. The Drosophila FGF ligand encoded by branchless (bnl) is localized in groups of cells near tracheal metameres. The tracheal cells expressing the FGF receptor breathless (btl) respond to these sources of FGF ligand and extend towards them. However, this FGF signaling pathway is not sufficient for the formation of continuous dorsal trunk, the only muticellular tube in tracheal system. Recently, it was found out that single mesodermal cells called bridge-cells are essential for the formation of continuous dorsal trunk as they direct the outgrowth of dorsal trunk cells towards the correct targets. The results in this PhD thesis demonstrate that a cell adhesion molecule Capricious (Caps), which is specifically localized on the surface of bridge-cells, plays an essential role in guiding the outgrowing dorsal trunk cells towards their correct targets. When caps is lacking, some bridge-cells cannot stretch properly towards the adjacent posterior tracheal metameres and thus fail to interconnect the juxtaposing dorsal trunk cells. Consequently, discontinuous dorsal trunks containing interruptions at several positions are formed. On the other hand, when caps is ectopically expressed in the mesodermal cells through a twi-GAL4 driver, these mesodermal cells acquire a guidance function through ectopic caps and misguide the outgrowing dorsal trunk cells in abnormal directions. As a result, disconnected dorsal trunks are formed. These loss- and gain-of-function studies suggest that Caps presumably establishes the cell-to-cell contact between the bridge-cells and the tracheal cells and thereby mediates directly the guidance function of bridge-cells. The most similar protein known to Caps is another cell adhesion molecule called Tartan (Trn). Interestingly, trn is expressed in the mesodermal cells but not in the bridge-cells. When trn is lacking, the outgrowth of not only the dorsal trunks but also the lateral trunks are disrupted. However, in contrast to the ectopic expression of caps, the misexpression of trn does not affect tracheal development. Whereas Trn requires only its extracellular domain to mediate the matrix function, Caps requires both its extracellular and intracellular domains to function as a guidance molecule in the bridge-cells. These observations suggest that Trn functions differently from Caps during tracheal morphogenesis. Presumably, Trn mediates a matrix function of mesodermal cells, which support the tracheal cells to extend efficiently through the surrounding mesodermal tissue. In order to determine which domains dictate the functional specificity of Caps, two hybrid proteins CapsEdTrnId, which contains the Caps extracellular domain and the Trn intracellular domain, and TrnEdCapsId, which consists of the Trn extracellular domain and the Caps intracellular domain, were constructed. Gain of function and rescue experiments with these hybrid proteins suggest on one hand that the extracellular domains of Caps and Trn are functionally redundant and on the other hand that the intracellular domain dictates the functional specificity of Caps. In order to identify putative interactors of Caps, yeast two-hybrid screening was performed. An in vivo interaction assay in yeast suggests that Ras64B interacts specifically with the Caps intracellular domain. In addition, an in vitro binding assay reveals a direct interaction between an inactive form of Ras64B and the Caps intracellular domain. ras64B, which encodes a small GTPase, is expressed in the mesodermal cells concurrently as caps. Finally, a gain-of-function study with the constitutively active Ras64B suggests that Ras64B presumably functions downstream of Caps. All these results suggest consistently that the small GTPase Ras64B binds specifically to the Caps intracellular domain and may thereby mediate the guidance function of Caps.

Sequential Optimal Recovery: A Paradigm for Active Learning

In most classical frameworks for learning from examples, it is assumed that examples are randomly drawn and presented to the learner. In this paper, we consider the possibility of a more active learner who is allowed to choose his/her own examples. Our investigations are carried out in a function approximation setting. In particular, using arguments from optimal recovery (Micchelli and Rivlin, 1976), we develop an adaptive sampling strategy (equivalent to adaptive approximation) for arbitrary approximation schemes. We provide a general formulation of the problem and show how it can be regarded as sequential optimal recovery. We demonstrate the application of this general formulation to two special cases of functions on the real line 1) monotonically increasing functions and 2) functions with bounded derivative. An extensive investigation of the sample complexity of approximating these functions is conducted yielding both theoretical and empirical results on test functions. Our theoretical results (stated insPAC-style), along with the simulations demonstrate the superiority of our active scheme over both passive learning as well as classical optimal recovery. The analysis of active function approximation is conducted in a worst-case setting, in contrast with other Bayesian paradigms obtained from optimal design (Mackay, 1992).