Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

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?

Analysis of panoramio photo tags in order to extract land use information

In the recent past, hardly anyone could predict this course of GIS development. GIS is moving from desktop to cloud. Web 2.0 enabled people to input data into web. These data are becoming increasingly geolocated. Big amounts of data formed something that is called "Big Data". Scientists still don't know how to deal with it completely. Different Data Mining tools are used for trying to extract some useful information from this Big Data. In our study, we also deal with one part of these data - User Generated Geographic Content (UGGC). The Panoramio initiative allows people to upload photos and describe them with tags. These photos are geolocated, which means that they have exact location on the Earth's surface according to a certain spatial reference system. By using Data Mining tools, we are trying to answer if it is possible to extract land use information from Panoramio photo tags. Also, we tried to answer to what extent this information could be accurate. At the end, we compared different Data Mining methods in order to distinguish which one has the most suited performances for this kind of data, which is text. Our answers are quite encouraging. With more than 70% of accuracy, we proved that extracting land use information is possible to some extent. Also, we found Memory Based Reasoning (MBR) method the most suitable method for this kind of data in all cases.

How to optimize Lipton’s business model in order to stimulate tea consumption in Portugal and increase Lipton Leaf tea market share?: The importance of distribution and sales channels management in a B2B2C market

Field Lab Entrepreneurial Innovative Ventures

Quadratic programming versus second order con programming in portfolio optimization

Despite the extensive literature in finding new models to replace the Markowitz model or trying to increase the accuracy of its input estimations, there is less studies about the impact on the results of using different optimization algorithms. This paper aims to add some research to this field by comparing the performance of two optimization algorithms in drawing the Markowitz Efficient Frontier and in real world investment strategies. Second order cone programming is a faster algorithm, appears to be more efficient, but is impossible to assert which algorithm is better. Quadratic Programming often shows superior performance in real investment strategies.

What should Fundação Calouste Gulbenkian do in order to attract the National Millennials?

Branding Lab

Which communication strategy should a male luxury (fashion) brand – associated with a luxury car brand – develop, in order to increase its awareness in Europe

This work project explores how a male luxury (fashion) brand (subsidiary) that is associated with a luxury car brand (parent company) should develop its communication strategy in order to increase awareness in Europe. For this purpose a quantitative research was conducted. The aim was to find out whether the company in question had low brand awareness among European luxury consumers. Hereafter, a qualitative research revealed important insights in regard to luxury communication among male luxury consumers. Both the results of the research and the recommendations of luxury experts laid the foundation for the development of a solution-oriented communication strategy. The result of the analysis crystallizes the importance of the shared heritage and the synergistic effects, of which the subsidiary should make vast use when communicating.

Fatigue life assessment of endodontic instruments subjected to multi planar curvature

This present study aimed to investigate the fatigue life of unused (new) endodontic instruments made of NiTi with control memory by Coltene™ and subjected to the multi curvature of a mandibular first molar root canal. Additionally, the instrument‟s structural behaviour was analysed through non-linear finite element analysis (FEA). The fatigue life of twelve Hyflex™ CM files was assessed while were forced to adopt a stance with multiple radius of curvature, similar to the ones usually found in a mandibular first molar root canal; nine of them were subjected to Pecking motion, a relative movement of axial type. To achieve this, it was designed an experimental setup with the aim of timing the instruments until fracture while worked inside a stainless steel mandibular first molar model with relative axial motion to simulate the pecking motion. Additionally, the model‟s root canal multi-curvature was confirmed by radiography. The non-linear finite element analysis was conducted using the computer aided design software package SolidWorks™ Simulation, in order to define the imposed displacement required by the FEA, it was necessary to model an endodontic instrument with simplified geometry using SolidWorks™ and subsequently analyse the geometry of the root canal CAD model. The experimental results shown that the instruments subjected to pecking motion displayed higher fatigue life values and higher lengths of fractured tips than those with only rotational relative movement. The finite element non-linear analyses shown, for identical conditions, maximum values for the first principal stress lower than the yield strength of the material and those were located in similar positions to the instrument‟s fracture location determined by the experimental testing results.

Plastic brain mechanisms for attaining auditory temporal order judgment proficiency.

Accurate perception of the order of occurrence of sensory information is critical for the building up of coherent representations of the external world from ongoing flows of sensory inputs. While some psychophysical evidence reports that performance on temporal perception can improve, the underlying neural mechanisms remain unresolved. Using electrical neuroimaging analyses of auditory evoked potentials (AEPs), we identified the brain dynamics and mechanism supporting improvements in auditory temporal order judgment (TOJ) during the course of the first vs. latter half of the experiment. Training-induced changes in brain activity were first evident 43-76 ms post stimulus onset and followed from topographic, rather than pure strength, AEP modulations. Improvements in auditory TOJ accuracy thus followed from changes in the configuration of the underlying brain networks during the initial stages of sensory processing. Source estimations revealed an increase in the lateralization of initially bilateral posterior sylvian region (PSR) responses at the beginning of the experiment to left-hemisphere dominance at its end. Further supporting the critical role of left and right PSR in auditory TOJ proficiency, as the experiment progressed, responses in the left and right PSR went from being correlated to un-correlated. These collective findings provide insights on the neurophysiologic mechanism and plasticity of temporal processing of sounds and are consistent with models based on spike timing dependent plasticity.

Order and membrane organization in chlorhexidine-lipid mixtures /

Formulations of a general bactericidal agent, chlorhexidine, mixed with a phospholipid at different concentrations are investigated using ^H NMR spectroscopy on a chain-deuterated lipid analog. Lipid-chlorhexidine formulation is known to release the drug into an aqueous medium slowly, maintaining a comparable concentration of the drug for up to four times longer than a direct aqueous solution. The NMR data does not support the proposed liposomal entrapment of chlorhexidine in lipid compartments. Complex thermal history of the lipid-chlorhexidine preparations is investigated in detail. In preparation for a counterpart measurement, using ^H NMR of deuterated chlorhexidine mixed with protonated lipid, the synthesis of a deuterated analog of chlorhexidine is performed.