Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

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.