Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

Controle de sistemas lineares incertos via realimentação derivativa utilizando Funções de Lyapunov dependentes de parâmetros

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Development and validation of first derivative spectrophotometric method for quantification of darunavir in tablets

Aims: Darunavir is widely used in HIV/AIDS therapy. It is a HIV protease inhibitor that has excellent efficacy against the virus. The aim of this study is to develop and validate an analytical method fast and free of interferences for determination of darunavir ethanolate as raw material and tablet dosage form. Methodology: As the formulation excipients show high interference in darunavir determination by a direct UV absorption measurement a derivative spectrophotometry was applied. A selective, easy and fast method was achieved employing simple and cheap instrumentation by using first-order derivative spectrophotometry. Results: The first-derivation of spectrum of the drug measured between 200 and 400 nm allowed identification of the analyte and showed absence of placebo interference. The assay was based on the absorbance at 276nm. The linear concentration range was established from 11 to 21 μg/mL. The intra-day and inter-day precision expressed as RSD was 0.06% and 3.75% respectively with mean recovery of 99.84%. Conclusion: The proposed analytical method is able to quantify darunavir as raw material and tablets and can be used routinely by any laboratory applying a spectrophotometer with a derivative accessory. The great difference of the method proposed here is that it proves to be free of placebo interferences as well as simple, fast and low cost.

Alternative derivative expansion in Functional RG and application

We give a brief review of the Functional Renormalization method in quantum field theory, which is intrinsically non perturbative, in terms of both the Polchinski equation for the Wilsonian action and the Wetterich equation for the generator of the proper verteces. For the latter case we show a simple application for a theory with one real scalar field within the LPA and LPA' approximations. For the first case, instead, we give a covariant "Hamiltonian" version of the Polchinski equation which consists in doing a Legendre transform of the flow for the corresponding effective Lagrangian replacing arbitrary high order derivative of fields with momenta fields. This approach is suitable for studying new truncations in the derivative expansion. We apply this formulation for a theory with one real scalar field and, as a novel result, derive the flow equations for a theory with N real scalar fields with the O(N) internal symmetry. Within this new approach we analyze numerically the scaling solutions for N=1 in d=3 (critical Ising model), at the leading order in the derivative expansion with an infinite number of couplings, encoded in two functions V(phi) and Z(phi), obtaining an estimate for the quantum anomalous dimension with a 10% accuracy (confronting with Monte Carlo results).

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

FTIR-spektroskopia kasviuutteiden analysoinnissa

FTIR-spektroskopia (Fourier-muunnosinfrapunaspektroskopia) on nopea analyysimenetelmä. Fourier-laitteissa interferometrin käyttäminen mahdollistaa koko infrapunataajuusalueen mittaamisen muutamassa sekunnissa. ATR-liitännäisellä varustetun FTIR-spektrometrin käyttö ei edellytä juuri näytteen valmistusta ja siksi menetelmä on käytössä myös helppo. ATR-liitännäinen mahdollistaa myös monien erilaisten näytteiden analysoinnin. Infrapunaspektrin mittaaminen onnistuu myös sellaisista näytteistä, joille perinteisiä näytteenvalmistusmenetelmiä ei voida käyttää. FTIR-spektroskopian avulla saatu tieto yhdistetään usein tilastollisiin monimuuttuja-analyyseihin. Klusterianalyysin avulla voidaan spektreistä saatu tieto ryhmitellä samanlaisuuteen perustuen. Hierarkkisessa klusterianalyysissa objektien välinen samanlaisuus määritetään laskemalla niiden välinen etäisyys. Pääkomponenttianalyysin avulla vähennetään datan ulotteisuutta ja luodaan uusia korreloimattomia pääkomponentteja. Pääkomponenttien tulee säilyttää mahdollisimman suuri määrä alkuperäisen datan variaatiosta. FTIR-spektroskopian ja monimuuttujamenetelmien sovellusmahdollisuuksia on tutkittu paljon. Elintarviketeollisuudessa sen soveltuvuutta esimerkiksi laadun valvontaan on tutkittu. Menetelmää on käytetty myös haihtuvien öljyjen kemiallisten koostumusten tunnistukseen sekä öljykasvien kemotyyppien havaitsemiseen. Tässä tutkimuksessa arvioitiin menetelmän käyttöä suoputken uutenäytteiden luokittelussa. Tutkimuksessa suoputken eri kasvinosien uutenäytteiden FTIR-spektrejä vertailtiin valikoiduista puhdasaineista mitattuihin FTIR-spektreihin. Puhdasaineiden FTIR-spektreistä tunnistettiin niiden tyypilliset absorptiovyöhykkeet. Furanokumariinien spektrien intensiivisten vyöhykkeiden aaltolukualueet valittiin monimuuttuja-analyyseihin. Monimuuttuja-analyysit tehtiin myös IR-spektrin sormenjälkialueelta aaltolukualueelta 1785-725 cm-1. Uutenäytteitä pyrittiin luokittelemaan niiden keräyspaikan ja kumariinipitoisuuden mukaan. Keräyspaikan mukaan ryhmittymistä oli havaittavissa, mikä selittyi vyöhykkeiden aaltolukualueiden mukaan tehdyissä analyyseissa pääosin kumariinipitoisuuksilla. Näissä analyyseissa uutenäytteet pääosin ryhmittyivät ja erottuivat kokonaiskumariinipitoisuuksien mukaan. Myös aaltolukualueen 1785-725 cm-1 analyyseissa havaittiin keräyspaikan mukaan ryhmittymistä, mitä kumariinipitoisuudet eivät kuitenkaan selittäneet. Näihin ryhmittymisiin vaikuttivat mahdollisesti muiden yhdisteiden samanlaiset pitoisuudet näytteissä. Analyyseissa käytettiin myös muita aaltolukualueita, mutta tulokset eivät juuri poikenneet aiemmista. 2. kertaluvun derivaattaspektrien monimuuttuja-analyysit sormenjälkialueelta eivät myöskään muuttaneet tuloksia havaittavasti. Jatkotutkimuksissa nyt käytettyä menetelmää on mahdollista edelleen kehittää esimerkiksi tutkimalla monimuuttuja-analyyseissa 2. kertaluvun derivaattaspektreistä suppeampia, tarkkaan valittuja aaltolukualueita.

Time-Instant Sampling Based Encoding of Time-Varying Acoustic Spectrum

The inner ear has been shown to characterize an acoustic stimuli by transducing fluid motion in the inner ear to mechanical bending of stereocilia on the inner hair cells (IHCs). The excitation motion/energy transferred to an IHC is dependent on the frequency spectrum of the acoustic stimuli, and the spatial location of the IHC along the length of the basilar membrane (BM). Subsequently, the afferent auditory nerve fiber (ANF) bundle samples the encoded waveform in the IHCs by synapsing with them. In this work we focus on sampling of information by afferent ANFs from the IHCs, and show computationally that sampling at specific time instants is sufficient for decoding of time-varying acoustic spectrum embedded in the acoustic stimuli. The approach is based on sampling the signal at its zero-crossings and higher-order derivative zero-crossings. We show results of the approach on time-varying acoustic spectrum estimation from cricket call signal recording. The framework gives a time-domain and non-spatial processing perspective to auditory signal processing. The approach works on the full band signal, and is devoid of modeling any bandpass filtering mimicking the BM action. Instead, we motivate the approach from the perspective of event-triggered sampling by afferent ANFs on the stimuli encoded in the IHCs. Though the approach gives acoustic spectrum estimation but it is shallow on its complete understanding for plausible bio-mechanical replication with current mammalian auditory mechanics insights.

A SINGULAR EXACT SOLUTION FOR NONLINEAR SHALLOW-WATER ON A ROTATING EARTH

In this paper, we present an exact solution for nonlinear shallow water on a rotating planet. It is a kind of solitary waves with always negative wave height and a celerity smaller than linear shallow water propagation speed square-root gh. In fact, it propagates with a speed equal to (1 + a/h) square-root gh(1 + a/h) where a is the negative wave height. The lowest point of the water surface is a singular point where the first order derivative has a discontinuity of the first kind. The horizontal scale of the wave has actually no connection with the water depth.

An efficient neural network approach for nanoscale FinFET modelling and circuit simulation

The present paper demonstrates the suitability of artificial neural network (ANN) for modelling of a FinFET in nano-circuit simulation. The FinFET used in this work is designed using careful engineering of source-drain extension, which simultaneously improves maximum frequency of oscillation f(max) because of lower gate to drain capacitance, and intrinsic gain A(V0) = g(m)/g(ds), due to lower output conductance g(ds). The framework for the ANN-based FinFET model is a common source equivalent circuit, where the dependence of intrinsic capacitances, resistances and dc drain current I-d on drain-source V-ds and gate-source V-gs is derived by a simple two-layered neural network architecture. All extrinsic components of the FinFET model are treated as bias independent. The model was implemented in a circuit simulator and verified by its ability to generate accurate response to excitations not used during training. The model was used to design a low-noise amplifier. At low power (J(ds) similar to 10 mu A/mu m) improvement was observed in both third-order-intercept IIP3 (similar to 10 dBm) and intrinsic gain A(V0) (similar to 20 dB), compared to a comparable bulk MOSFET with similar effective channel length. This is attributed to higher ratio of first-order to third-order derivative of I-d with respect to gate voltage and lower g(ds), in FinFET compared to bulk MOSFET. Copyright (C) 2009 John Wiley & Sons, Ltd.

Learning from time series:Supervised Aggregative Feature Extraction

Many modeling problems require to estimate a scalar output from one or more time series. Such problems are usually tackled by extracting a fixed number of features from the time series (like their statistical moments), with a consequent loss in information that leads to suboptimal predictive models. Moreover, feature extraction techniques usually make assumptions that are not met by real world settings (e.g. uniformly sampled time series of constant length), and fail to deliver a thorough methodology to deal with noisy data. In this paper a methodology based on functional learning is proposed to overcome the aforementioned problems; the proposed Supervised Aggregative Feature Extraction (SAFE) approach allows to derive continuous, smooth estimates of time series data (yielding aggregate local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The SAFE paradigm enjoys several properties like closed form solution, incorporation of first and second order derivative information into the regressor matrix, interpretability of the generated functional predictor and the possibility to exploit Reproducing Kernel Hilbert Spaces setting to yield nonlinear predictive models. Simulation studies are provided to highlight the strengths of the new methodology w.r.t. standard unsupervised feature selection approaches. © 2012 IEEE.