Stability of multistep second derivative methods for integro-differential equations

The stability of multistep second derivative methods for integro-differential equations is examined through a test equation which allows for the construction of the associated characteristic polynomial and its region of stability (roots in the unit circle) at a proper parameter space. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

Flow analysis-hydride generation-gas phase derivative molecular absorption spectrophotometric determination of antimony in antileishmanial drugs

In the present work, the development of a method based on the coupling of flow analysis (FA), hydride generation (HG), and derivative molecular absorption spectrophotometry (D-EAM) in gas phase (GP), is described in order to determine total antimony in antileishmanial products. Second derivative order (D²224nm) of the absorption spectrum (190 - 300 nm) is utilized as measurement criterion. Each one of the parameters involved in the development of the proposed method was examined and optimized. The utilization of the EAM in GP as detection system in a continuous mode instead of atomic absorption spectrometry represents the great potential of the analytic proposal.

Development and Validation of an UV-Derivative Spectrophotometric Method for Determination of Glimepiride in Tablets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Students’ understanding of the function-derivative relationship when learning economic concepts

The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.

Automated Analysis of the Auditory Brainstem Response Using Derivative Estimation Wavelets

In this paper, we describe an algorithm that automatically detects and labels peaks I - VII of the normal, suprathreshold auditory brainstem response (ABR). The algorithm proceeds in three stages, with the option of a fourth: ( 1) all candidate peaks and troughs in the ABR waveform are identified using zero crossings of the first derivative, ( 2) peaks I - VII are identified from these candidate peaks based on their latency and morphology, ( 3) if required, peaks II and IV are identified as points of inflection using zero crossings of the second derivative and ( 4) interpeak troughs are identified before peak latencies and amplitudes are measured. The performance of the algorithm was estimated on a set of 240 normal ABR waveforms recorded using a stimulus intensity of 90 dBnHL. When compared to an expert audiologist, the algorithm correctly identified the major ABR peaks ( I, III and V) in 96 - 98% of the waveforms and the minor ABR peaks ( II, IV, VI and VII) in 45 - 83% of waveforms. Whilst peak II was correctly identified in only 83% and peak IV in 77% of waveforms, it was shown that 5% of the peak II identifications and 31% of the peak IV identifications came as a direct result of allowing these peaks to be found as points of inflection. Copyright (C) 2005 S. Karger AG, Basel.

Mach edges: a key role for 3rd derivative filters in spatial vision

Edges are key points of information in visual scenes. One important class of models supposes that edges correspond to the steepest parts of the luminance profile, implying that they can be found as peaks and troughs in the response of a gradient (first-derivative) filter, or as zero-crossings (ZCs) in the second-derivative. A variety of multi-scale models are based on this idea. We tested this approach by devising a stimulus that has no local peaks of gradient and no ZCs, at any scale. Our stimulus profile is analogous to the classic Mach-band stimulus, but it is the local luminance gradient (not the absolute luminance) that increases as a linear ramp between two plateaux. The luminance profile is a smoothed triangle wave and is obtained by integrating the gradient profile. Subjects used a cursor to mark the position and polarity of perceived edges. For all the ramp-widths tested, observers marked edges at or close to the corner points in the gradient profile, even though these were not gradient maxima. These new Mach edges correspond to peaks and troughs in the third-derivative. They are analogous to Mach bands - light and dark bars are seen where there are no luminance peaks but there are peaks in the second derivative. Here, peaks in the third derivative were seen as light-to-dark edges, troughs as dark-to-light edges. Thus Mach edges are inconsistent with many standard edge detectors, but are nicely predicted by a new model that uses a (nonlinear) third-derivative operator to find edge points.

The primal sketch revisited: locating and representing edges in human vision via Gaussian-derivative filtering

Marr's work offered guidelines on how to investigate vision (the theory - algorithm - implementation distinction), as well as specific proposals on how vision is done. Many of the latter have inevitably been superseded, but the approach was inspirational and remains so. Marr saw the computational study of vision as tightly linked to psychophysics and neurophysiology, but the last twenty years have seen some weakening of that integration. Because feature detection is a key stage in early human vision, we have returned to basic questions about representation of edges at coarse and fine scales. We describe an explicit model in the spirit of the primal sketch, but tightly constrained by psychophysical data. Results from two tasks (location-marking and blur-matching) point strongly to the central role played by second-derivative operators, as proposed by Marr and Hildreth. Edge location and blur are evaluated by finding the location and scale of the Gaussian-derivative `template' that best matches the second-derivative profile (`signature') of the edge. The system is scale-invariant, and accurately predicts blur-matching data for a wide variety of 1-D and 2-D images. By finding the best-fitting scale, it implements a form of local scale selection and circumvents the knotty problem of integrating filter outputs across scales. [Supported by BBSRC and the Wellcome Trust]

Metodologia para a suavização de dados biomecanicos por função não parametrica ponderada local robusta

Universidade Estadual de Campinas. Faculdade de Educação Física

Determinação de ácido acéttico em amostra de vinagre adulterada com ácido clorídrico - um experimento integrado de titulação potenciométrica e condutométrica

The determination of acetic acid in vinegar adulterated sample using simultaneous potentiometric and condutometric titrations was used as an example of integrated experiment in instrumental analysis. An Excel® spreadsheet, which allows the entry of simultaneous data and the construction of the superimposed experimental curves (condutometric, potentiometric, first and second derivative potentiometric curve and, distribution diagrama of the acetic species as function of pH), was used as powerful tool to discuss the fundamental concepts involved in each technique and choose the best of them to quantify, without mutual interference, H3CCOOH and HCl in vinegar adulterated sample.

Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

Whether at the zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we explicitly compute the stiffness at m = 0 and find strong evidence that it vanishes. In particular, we derive an upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m that is proportional to m2L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature, which implies the absence of ballistic transport for T > 0 for m = 0. Although our method relies in part on the thermodynamic Bethe ansatz (TBA), it does not evaluate the stiffness through the second derivative of the TBA energy eigenvalues relative to a uniform vector potential. Moreover, we provide strong evidence that in the thermodynamic limit the upper bounds on the spin current and stiffness used in our derivation remain valid under string deviations. Our results also provide strong evidence that in the thermodynamic limit the TBA method used by X. Zotos [Phys. Rev. Lett. 82, 1764 (1999)] leads to the exact stiffness values at finite temperature T > 0 for models whose stiffness is finite at T = 0, similar to the spin stiffness of the spin-1/2 Heisenberg chain but unlike the charge stiffness of the half-filled 1D Hubbard model.

Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

Investigation and data adaptive analysis of CARS spectra

In this diploma work advantages of coherent anti-Stokes Raman scattering spectrometry (CARS) and various methods of the quantitative analysis of substance structure with its help are considered. The basic methods and concepts of the adaptive analysis are adduced. On the basis of these methods the algorithm of automatic measurement of a scattering strip size of a target component in CARS spectrum is developed. The algorithm uses known full spectrum of target substance and compares it with a CARS spectrum. The form of a differential spectrum is used as a feedback to control the accuracy of matching. To exclude the influence of a background in CARS spectra the differential spectrum is analysed by means of its second derivative. The algorithm is checked up on the simulated simple spectra and on the spectra of organic compounds received experimentally.

Determinação de ácido acéttico em amostra de vinagre adulterada com ácido clorídrico - um experimento integrado de titulação potenciométrica e condutométrica

The determination of acetic acid in vinegar adulterated sample using simultaneous potentiometric and condutometric titrations was used as an example of integrated experiment in instrumental analysis. An Excel® spreadsheet, which allows the entry of simultaneous data and the construction of the superimposed experimental curves (condutometric, potentiometric, first and second derivative potentiometric curve and, distribution diagrama of the acetic species as function of pH), was used as powerful tool to discuss the fundamental concepts involved in each technique and choose the best of them to quantify, without mutual interference, H3CCOOH and HCl in vinegar adulterated sample.

Estudo espectroscópico de compósito obtido da reação no estado sólido entre um complexo mononuclear de vanádio(IV) e caulinita

The use of probes, such as paramagnetic species diluted in diamagnetic materials in EPR spectroscopy, and mathematical tools such, as the Kubelka-Munk function in DRUV-VIS spectroscopy are strategies in the analysis of complex mixtures of solid materials. The results obtained here show that the solid state reaction between the complex, [VO(acac)(BMIMAPY)] [ClO4], BMIMAPY = [(bis(1-methylimidazole-2-yl)methyl)(2-(pyridyl-2-yl)ethyl) amine] and acac = acetilacetonate, with kaolinite turns possible to obtain anisotropic EPR spectrum of the complex with a reasonable level of resolution. The study by DRUV-VIS using the method of second derivative mode of the Kubelka-Munk function revealed new complex structural arrangements, a solid hitherto unknown.