A Java expression evaluator for nonlinear programming

Finding the optimal value for a problem is usual in many areas of knowledge where in many cases it is needed to solve Nonlinear Optimization Problems. For some of those problems it is not possible to determine the expression for its objective function and/or its constraints, they are the result of experimental procedures, might be non-smooth, among other reasons. To solve such problems it was implemented an API contained methods to solve both constrained and unconstrained problems. This API was developed to be used either locally on the computer where the application is being executed or remotely on a server. To obtain the maximum flexibility both from the programmers’ and users’ points of view, problems can be defined as a Java class (because this API was developed in Java) or as a simple text input that is sent to the API. For this last one to be possible it was also implemented on the API an expression evaluator. One of the drawbacks of this expression evaluator is that it is slower than the Java native code. In this paper it is presented a solution that combines both options: the problem can be expressed at run-time as a string of chars that are converted to Java code, compiled and loaded dynamically. To wide the target audience of the API, this new expression evaluator is also compatible with the AMPL format.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Calculation of fractional derivatives of noisy data with genetic algorithms

This paper addresses the calculation of derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes, a hierarchical GA composed by a series of two GAs, each one with a distinct fitness function, is established.

O alisamento dos resultados numa empresa: o caso do Grupo SONANGOL

Dissertação de Mestrado apresentada ao Instituto de Contabilidade e Administração do Porto para a obtenção do grau de Mestre em Contabilidade e Finanças sob orientação de Professor Doutor Adalmiro Alvaro Malheiro de Castro Andrade Pereira

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Towards a Mobile Three-dimensional Modelling System for Underground Structures

Robotica 2012: 12th International Conference on Autonomous Robot Systems and Competitions April 11, 2012, Guimarães, Portugal

Application of Visual-Inertial SLAM for 3D Mapping of Underground Environments

The underground scenarios are one of the most challenging environments for accurate and precise 3d mapping where hostile conditions like absence of Global Positioning Systems, extreme lighting variations and geometrically smooth surfaces may be expected. So far, the state-of-the-art methods in underground modelling remain restricted to environments in which pronounced geometric features are abundant. This limitation is a consequence of the scan matching algorithms used to solve the localization and registration problems. This paper contributes to the expansion of the modelling capabilities to structures characterized by uniform geometry and smooth surfaces, as is the case of road and train tunnels. To achieve that, we combine some state of the art techniques from mobile robotics, and propose a method for 6DOF platform positioning in such scenarios, that is latter used for the environment modelling. A visual monocular Simultaneous Localization and Mapping (MonoSLAM) approach based on the Extended Kalman Filter (EKF), complemented by the introduction of inertial measurements in the prediction step, allows our system to localize himself over long distances, using exclusively sensors carried on board a mobile platform. By feeding the Extended Kalman Filter with inertial data we were able to overcome the major problem related with MonoSLAM implementations, known as scale factor ambiguity. Despite extreme lighting variations, reliable visual features were extracted through the SIFT algorithm, and inserted directly in the EKF mechanism according to the Inverse Depth Parametrization. Through the 1-Point RANSAC (Random Sample Consensus) wrong frame-to-frame feature matches were rejected. The developed method was tested based on a dataset acquired inside a road tunnel and the navigation results compared with a ground truth obtained by post-processing a high grade Inertial Navigation System and L1/L2 RTK-GPS measurements acquired outside the tunnel. Results from the localization strategy are presented and analyzed.

Role of oxidative stress-induced systemic and cavernosal molecular alterations in the progression of diabetic erectile dysfunction

Background Erectile dysfunction (ED) is a prevalent complication of diabetes, and oxidative stress is an important feature of diabetic ED. Oxidative stress-induced damage plays a pivotal role in the development of tissue alterations. However, the deleterious effects of oxidative stress in the corpus cavernosum with the progression of diabetes remain unclear. The aim of this study was to evaluate systemic and penile oxidative stress status in the early and late stages of diabetes. Methods Male Wistar streptozotocin-diabetic rats (and age-matched controls) were examined 2 (early) and 8 weeks (late) after the induction of diabetes. Systemic oxidative stress was evaluated by urinary H2O2 and the ratio of circulating reduced/oxidized glutathione (GSH/GSSG). Penile oxidative status was assessed by H2O2 production and 3-nitrotyrosine (3-NT) formation. Cavernosal endothelial nitric oxide synthase (eNOS) was analyzed by quantitative immunohistochemistry. Dual immunofluorescence was also performed for 3-NT and α-smooth muscle actin (α-SMA) and eNOS–α-SMA. Results There was a significant increase in urinary H2O2 levels in both diabetic groups. The plasma GSH/GSSG ratio was significantly augmented in late diabetes. In cavernosal tissue, H2O2 production was significantly increased in late diabetes. Reactivity for 3-NT was located predominantly in cavernosal smooth muscle (SM) and was significantly reduced in late diabetes. Quantitative immunohistochemistry revealed a significant decrease in eNOS levels in cavernosal SM and endothelium in late diabetes. Conclusions The findings indicate that the noxious effects of oxidative stress are more prominent in late diabetes. Increased penile protein oxidative modifications and decreased eNOS expression may be responsible for structural and/or functional deregulation, contributing to the progression of diabetes-associated ED.

Calcium signaling and the novel anti-proliferative effect of the UTP-sensitive P2Y11 receptor in rat cardiac myofibroblasts

During myocardial ischemia and reperfusion both purines and pyrimidines are released into the extracellular milieu, thus creating a signaling wave that propagates to neighboring cells via membrane-bound P2 purinoceptors activation. Cardiac fibroblasts (CF) are important players in heart remodeling, electrophysiological changes and hemodynamic alterations following myocardial infarction. Here, we investigated the role UTP on calcium signaling and proliferation of CF cultured from ventricles of adult rats. Co-expression of discoidin domain receptor 2 and -smooth muscle actin indicate that cultured CF are activated myofibroblasts. Intracellular calcium ([Ca2+]i) signals were monitored in cells loaded with Fluo-4 NW. CF proliferation was evaluated by the MTT assay. UTP and the selective P2Y4 agonist, MRS4062, caused a fast desensitizing [Ca2+]i rise originated from thapsigargin-sensitive internal stores, which partially declined to a plateau providing the existence of Ca2+ in the extracellular fluid. The biphasic [Ca2+]i response to UTP was attenuated respectively by P2Y4 blockers, like reactive blue-2 and suramin, and by the P2Y11 antagonist, NF340. UTP and the P2Y2 receptor agonist MRS2768 increased, whereas the selective P2Y11 agonist NF546 decreased, CF growth; MRS4062 was ineffective. Blockage of the P2Y11receptor or its coupling to adenylate cyclase boosted UTP-induced CF proliferation. Confocal microscopy and Western blot analysis confirmed the presence of P2Y2, P2Y4 and P2Y11 receptors. Data indicate that besides P2Y4 and P2Y2 receptors which are responsible for UTP-induced [Ca2+]i transients and growth of CF, respectively, synchronous activation of the previously unrecognized P2Y11 receptor may represent an important target for anti-fibrotic intervention in cardiac remodeling.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.