Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

Tonal Modulation and Subjective Time

This work investigated listeners` sense of the temporal expression of tonal modulation. One experiment described the effects on retrospective reproductions of sudden and gradual modulations to close and distant keys. The results showed that modulations elicit time underestimations as an inverse function of interkey distances, with a major impact for sudden modulations. A proposed vectorial model - ""Expected Development Fraction"" (EDF) - describes the development of expectations when an interkey distance is traversed during a certain time interval. This expected development is longer than the perceived duration, leading to underestimation of the time.

Chromatic spatial contrast sensitivity estimated by visual evoked cortical potential and psychophysics

The purpose of the present study was to measure contrast sensitivity to equiluminant gratings using steady-state visual evoked cortical potential (ssVECP) and psychophysics. Six healthy volunteers were evaluated with ssVECPs and psychophysics. The visual stimuli were red-green or blue-yellow horizontal sinusoidal gratings, 5° × 5°, 34.3 cd/m2 mean luminance, presented at 6 Hz. Eight spatial frequencies from 0.2 to 8 cpd were used, each presented at 8 contrast levels. Contrast threshold was obtained by extrapolating second harmonic amplitude values to zero. Psychophysical contrast thresholds were measured using stimuli at 6 Hz and static presentation. Contrast sensitivity was calculated as the inverse function of the pooled cone contrast threshold. ssVECP and both psychophysical contrast sensitivity functions (CSFs) were low-pass functions for red-green gratings. For electrophysiology, the highest contrast sensitivity values were found at 0.4 cpd (1.95 ± 0.15). ssVECP CSF was similar to dynamic psychophysical CSF, while static CSF had higher values ranging from 0.4 to 6 cpd (P < 0.05, ANOVA). Blue-yellow chromatic functions showed no specific tuning shape; however, at high spatial frequencies the evoked potentials showed higher contrast sensitivity than the psychophysical methods (P < 0.05, ANOVA). Evoked potentials can be used reliably to evaluate chromatic red-green CSFs in agreement with psychophysical thresholds, mainly if the same temporal properties are applied to the stimulus. For blue-yellow CSF, correlation between electrophysiology and psychophysics was poor at high spatial frequency, possibly due to a greater effect of chromatic aberration on this kind of stimulus.

El Nino-mean state-seasonal cycle interactions in a multi-model ensemble

The modelled El Nino-mean state-seasonal cycle interactions in 23 coupled ocean-atmosphere GCMs, including the recent IPCC AR4 models, are assessed and compared to observations and theory. The models show a clear improvement over previous generations in simulating the tropical Pacific climatology. Systematic biases still include too strong mean and seasonal cycle of trade winds. El Nino amplitude is shown to be an inverse function of the mean trade winds in agreement with the observed shift of 1976 and with theoretical studies. El Nino amplitude is further shown to be an inverse function of the relative strength of the seasonal cycle. When most of the energy is within the seasonal cycle, little is left for inter-annual signals and vice versa. An interannual coupling strength (ICS) is defined and its relation with the modelled El Nino frequency is compared to that predicted by theoretical models. An assessment of the modelled El Nino in term of SST mode (S-mode) or thermocline mode (T-mode) shows that most models are locked into a S-mode and that only a few models exhibit a hybrid mode, like in observations. It is concluded that several basic El Nino-mean state-seasonal cycle relationships proposed by either theory or analysis of observations seem to be reproduced by CGCMs. This is especially true for the amplitude of El Nino and is less clear for its frequency. Most of these relationships, first established for the pre-industrial control simulations, hold for the double and quadruple CO2 stabilized scenarios. The models that exhibit the largest El Nino amplitude change in these greenhouse gas (GHG) increase scenarios are those that exhibit a mode change towards a T-mode (either from S-mode to hybrid or hybrid to T-mode). This follows the observed 1976 climate shift in the tropical Pacific, and supports the-still debated-finding of studies that associated this shift to increased GHGs. In many respects, these models are also among those that best simulate the tropical Pacific climatology (ECHAM5/MPI-OM, GFDL-CM2.0, GFDL-CM2.1, MRI-CGM2.3.2, UKMO-HadCM3). Results from this large subset of models suggest the likelihood of increased El Nino amplitude in a warmer climate, though there is considerable spread of El Nino behaviour among the models and the changes in the subsurface thermocline properties that may be important for El Nino change could not be assessed. There are no clear indications of an El Nino frequency change with increased GHG.

PROCAPRI – Programa de gerenciamento de rebanhos caprinos: atualização e aprimoramento

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chromatic spatial contrast sensitivity estimated by visual evoked cortical potential and psychophysics

The purpose of the present study was to measure contrast sensitivity to equiluminant gratings using steady-state visual evoked cortical potential (ssVECP) and psychophysics. Six healthy volunteers were evaluated with ssVECPs and psychophysics. The visual stimuli were red-green or blue-yellow horizontal sinusoidal gratings, 5^° × 5^°, 34.3 cd/m2 mean luminance, presented at 6 Hz. Eight spatial frequencies from 0.2 to 8 cpd were used, each presented at 8 contrast levels. Contrast threshold was obtained by extrapolating second harmonic amplitude values to zero. Psychophysical contrast thresholds were measured using stimuli at 6 Hz and static presentation. Contrast sensitivity was calculated as the inverse function of the pooled cone contrast threshold. ssVECP and both psychophysical contrast sensitivity functions (CSFs) were low-pass functions for red-green gratings. For electrophysiology, the highest contrast sensitivity values were found at 0.4 cpd (1.95 ± 0.15). ssVECP CSF was similar to dynamic psychophysical CSF, while static CSF had higher values ranging from 0.4 to 6 cpd (P < 0.05, ANOVA). Blue-yellow chromatic functions showed no specific tuning shape; however, at high spatial frequencies the evoked potentials showed higher contrast sensitivity than the psychophysical methods (P < 0.05, ANOVA). Evoked potentials can be used reliably to evaluate chromatic red-green CSFs in agreement with psychophysical thresholds, mainly if the same temporal properties are applied to the stimulus. For blue-yellow CSF, correlation between electrophysiology and psychophysics was poor at high spatial frequency, possibly due to a greater effect of chromatic aberration on this kind of stimulus.

Sobre o Teorema da Função Inversa

Pós-graduação em Matemática em Rede Nacional - IBILCE

Direct estimation of the backward flow

[EN] The aim of this work is to propose a new method for estimating the backward flow directly from the optical flow. We assume that the optical flow has already been computed and we need to estimate the inverse mapping. This mapping is not bijective due to the presence of occlusions and disocclusions, therefore it is not possible to estimate the inverse function in the whole domain. Values in these regions has to be guessed from the available information. We propose an accurate algorithm to calculate the backward flow uniquely from the optical flow, using a simple relation. Occlusions are filled by selecting the maximum motion and disocclusions are filled with two different strategies: a min-fill strategy, which fills each disoccluded region with the minimum value around the region; and a restricted min-fill approach that selects the minimum value in a close neighborhood. In the experimental results, we show the accuracy of the method and compare the results using these two strategies.

A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.

On arterial contractility, energetic requirements of the cardiovascular system, and the formation of arterial sclerosis

The aorta has been viewed as a passive distribution manifold for blood whose elasticity allows it to store blood during cardiac ejection (systole), and release it during relaxation (diastole). This capacitance, or compliance, lowers peak cardiac work input and maintains peripheral sanguine irrigation throughout the cardiac cycle. The compliance of the human and canine circulatory systems have been described either as constant throughout the cycle (Toy et al. 1985) or as some inverse function of pressure (Li et al. 1990, Cappelo et al. 1995). This work shows that a compliance value that is higher during systole than diastole (equivalent to a direct function of pressure) leads to a reduction in the energetic input to the cardiovascular system (CV), even when accounting for the energy required to change compliance. This conclusion is obtained numerically, based on a 3-element lumped-parameter model of the CV, then demonstrated in a physical model built for the purpose. It is then shown, based on the numerical and physical models, on analytical considerations of elastic tubes, and on the analysis of arterial volume as a function of pressure measured in vivo (Armentano et al. 1995), that the mechanical effects of a presupposed arterial contraction are consistent with those of energetically beneficial changes in compliance during the cardiac cycle. Although the amount of energy potentially saved with rhythmically contracting arteries is small (mean 0.55% for the cases studied) the importance of the phenomenon lies in its possible relation to another function of the arterial smooth muscle (ASM): synthesis of wall matrix macromolecules. It is speculated that a reduction in the rate of collagen synthesis by the ASM is implicated in the formation of arteriosclerosis. ^

New evidence for the zoom lens model using the RSVP technique

A main prediction from the zoom lens model for visual attention is that performance is an inverse function of the size of the attended area. The "attention shift paradigm" developed by Sperling and Reeves (1980) was adapted here to study predictions from the zoom lens model. In two experiments two lists of items were simultaneously presented using the rapid serial visual presentation technique. Subjects were to report the first item he/she was able to identify in the series that did not include the target (the letter T) after he/she saw the target. In one condition, subjects knew in which list the target would appear, in another condition, they did not have this knowledge, having to attend to both positions in order to detect the target. The zoom lens model predicts an interaction between this variable and the distance separating the two positions where the lists are presented. In both experiments, this interaction was observed. The results are also discussed as a solution to the apparently contradictory results with regard to the analog movement model.

Up-regulation of the levels of expression and function of a constitutively active mutant of the hamster alpha1B-adrenoceptor by ligands that act as inverse agonists.

The alpha1-adrenergic agonist phenylephrine stimulated phospholipase D (PLD) activity in Rat 1 fibroblasts transfected to express either the wild-type hamster alpha1B-adrenoceptor or a constitutively active mutant (CAM) form of this receptor. The EC50 for agonist stimulation of PLD activity was substantially lower at the CAM receptor than at the wild-type receptor as previously noted for phenylephrine stimulation of phosphoinositidase C activity. Sustained treatment of cells expressing the CAM alpha1B-adrenoceptor with phentolamine resulted in a marked up-regulation in levels of this receptor with half-maximal effects produced within 24 h and with an EC50 of approx. 40 nM. Such an up-regulation could be produced with a range of other ligands generally viewed as alpha1-adrenoceptor antagonists but equivalent treatment of cells expressing the wild-type alpha1B-adrenoceptor was unable to mimic these effects. After sustained treatment of the CAM alpha1B-adrenoceptor expressing cells with phentolamine, basal PLD activity was increased and phenylephrine was now able to stimulate PLD activity to greater levels than in vehicle-treated CAM alpha1B-adrenoceptor-expressing cells. The EC50 for phenylephrine stimulation of PLD activity was not altered, however, by phentolamine pretreatment and the associated up-regulation of the receptor. After phentolamine-induced up-regulation of basal PLD activity, a range of alpha1-antagonists were shown to possess the characteristics of inverse agonists of the CAM alpha1B-adrenoceptor as they were able to substantially decrease the elevated basal PLD activity.

Impact of reduced complexity inverse Volterra series transfer function-based nonlinear equalizer in coherent OFDM systems for next-generation core networks

A modern electronic nonlinearity equalizer (NLE) based on inverse Volterra series transfer function (IVSTF) with reduced complexity is applied on coherent optical orthogonal frequency-division multiplexing (CO-OFDM) signals for next-generation long- and ultra-long-haul applications. The OFDM inter-subcarrier crosstalk effects are explored thoroughly using the IVSTF-NLE and compared with the case of linear equalization (LE) for transmission distances of up to 7000 km. © 2013 IEEE.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.