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 Many of the latter have inevitably been superseded, but the approach was inspirational and remains so.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]

The interrogation and multiplexing of long period grating curvature sensors using a Bragg grating based, derivative spectroscopy technique

A long period grating is interrogated with a fibre Bragg grating using a derivative spectroscopy technique. A quasi-linear relationship between the output of the sensing scheme and the curvature experienced by the long period grating is demonstrated, with a sensitivity of 5.05 m and with an average curvature resolution of 2.9 × 10-2 m-1. In addition, the feasibility of multiplexing an in-line series of long period gratings with this interrogation scheme is demonstrated with two pairs of fibre Bragg gratings and long period gratings. With this arrangement the cross-talk error between channels was less than ± 2.4 × 10-3 m-1.

The interrogation and multiplexing of long period grating curvature sensors using a Bragg grating based, derivative spectroscopy technique

A long period grating is interrogated with a fibre Bragg grating using a derivative spectroscopy technique. A quasi-linear relationship between the output of the sensing scheme and the curvature experienced by the long period grating is demonstrated, with a sensitivity of 5.05 m and with an average curvature resolution of 2.9 × 10-2 m-1. In addition, the feasibility of multiplexing an in-line series of long period gratings with this interrogation scheme is demonstrated with two pairs of fibre Bragg gratings and long period gratings. With this arrangement the cross-talk error between channels was less than ± 2.4 × 10-3 m-1.

Operational Rules for a Mixed Operator of the Erdélyi-Kober Type

2000 Mathematics Subject Classification: 26A33 (main), 44A40, 44A35, 33E30, 45J05, 45D05

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Calculating the derivative of piecewise functions

Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions.

Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

MSC 2010: 26A33, 34D05, 37C25

Novel double-sided linear generator for the wave energy conversion

The direct drive point absorber is a robust and efficient system for wave energy harvesting, where the linear generator represents the most complex part of the system. Therefore, its design and optimization are crucial tasks. The tubular shape of a linear generator’s magnetic circuit offers better permanent magnet flux encapsulation and reduction in radial forces on the translator due to its symmetry. A double stator topology can improve the power density of the linear tubular machine. Common designs employ a set of aligned stators on each side of a translator with radially magnetized permanent magnets. Such designs require doubling the amount of permanent magnet material and lead to an increase in the cogging force. The design presented in this thesis utilizes a translator with buried axially magnetized magnets and axially shifted positioning of the two stators such that no additional magnetic material, compared to single side machine, is required. In addition to the conservation of magnetic material, a significant improvement in the cogging force occurs in the two phase topology, while the double sided three phase system produces more power at the cost of a small increase in the cogging force. The analytical and the FEM models of the generator are described and their results compared to the experimental results. In general, the experimental results compare favourably with theoretical predictions. However, the experimentally observed permanent magnet flux leakage in the double sided machine is larger than predicted theoretically, which can be justified by the limitations in the prototype fabrication and resulting deviations from the theoretical analysis.

Recovery of palladium from a spent automobile catalyst leaching solution by a thiodiglycolamide derivative

In the sequence of previous research on the development of novel liquid-liquid amidetype compounds to efficiently and selectively extract platinum-group metals (PGMs) from concentrated hydrochloric acid media, a specific thiodiglycolamide derivative – N,N’-dimethyl-N,N’-dicyclohexylthiodiglycolamide (DMDCHTDGA) – has been applied for the recovery of palladium(II) from a spent automobile catalyst leaching solution, containing palladium(II) and rhodium(III) as PGMs. The results obtained are rather promising, since the DMDCHTDGA behavior towards the two PGMs is similar to that observed for hydrochloric acid aqueous media studied before, simulating the real leaching phases. Within eleven metal elements co-existing in solution, the majority in high fold-excesses, only aluminum(III) and cerium(III) interfere in the palladium(II) liquid-liquid extraction process, requiring further optimization.

New bodipy dyads for two-photons fluorescence imaging in cells

Fluorescent probes are essential tools for studying biological systems. The last decade has witnessed particular interest in the development of two-photon excitable probes, due to their advantageous features in tissue imaging compared to the corresponding one-photon probes [1]. Recently, we have designed and synthetized an aminonaphthalimide–BODIPY derivative as energy transfer cassettes and were found to show very fast and efficient BODIPY fluorescence sensitization [2]. This was observed upon one- and two-photon excitation, which extends the application range of the investigated bichromophoric dyads in terms of accessible excitation wavelengths. In order to increase the two-photon absorption of the system aminonaphthalimide fluorophore was replace with a Prodan analog (BODIPY dyad 1), which presents found a variety of applications as probes and labels in biology [3]. The two-photon absorption cross-section  of the dyads is significantly incremented by the presence of the 6-acetyl-2-naphthylamine donor group. The emission maximum of a BODIPY fluorophore can significantly be red-shifted in comparison to their precursors by conjugation with aromatic aldehydes. [4] We use a synthetic strategy to obtain BODIPY dyad 2 that incorporates an imidazole ring. This molecule can be used in biological media as a near-neutral pH indicator based on one- and two-photon excitable BODIPY acceptor.

Effect of investigation intensity and treatment differences on prostate cancer survivor's physical symptoms, psychological well-being and health-related quality of life: a two country cross-sectional study.

Aim: To investigate effects on men's health and well-being of higher prostate cancer (PCa) investigation and treatment levels in similar populations. Participants: PCa survivors in Ireland where the Republic of Ireland (RoI) has a 50% higher PCa incidence than Northern Ireland (NI). Method: A cross-sectional postal questionnaire was sent to PCa survivors 2–18 years post-treatment, seeking information about current physical effects of treatment, health-related quality of life (HRQoL; EORTC QLQ-C30; EQ-5D-5L) and psychological well-being (21 question version of the Depression, Anxiety and Stress Scale, DASS-21). Outcomes in RoI and NI survivors were compared, stratifying into ‘late disease’ (stage III/IV and any Gleason grade (GG) at diagnosis) and ‘early disease’ (stage I/II and GG 2–7). Responses were weighted by age, jurisdiction and time since diagnosis. Between-country differences were investigated using multivariate logistic and linear regression. Results: 3348 men responded (RoI n=2567; NI n=781; reflecting population sizes, response rate 54%). RoI responders were younger; less often had comorbidities (45% vs 38%); were more likely to present asymptomatically (66%; 41%) or with early disease (56%; 35%); and less often currently used androgen deprivation therapy (ADT; 2%; 28%). Current prevalence of incontinence (16%) and impotence (56% early disease, 67% late disease) did not differ between RoI and NI. In early disease, only current bowel problems (RoI 12%; NI 21%) differed significantly in multivariate analysis. In late disease, NI men reported significantly higher levels of gynaecomastia (23% vs 9%) and hot flashes(41% vs 19%), but when ADT users were analysed separately, differences disappeared. For HRQoL, in multivariate analysis, only pain (early disease: RoI 11.1, NI 19.4) and financial difficulties (late disease: RoI 10.4, NI 7.9) differed significantly between countries. There were no significant between-country differences in DASS-21 or index ED-5D-5L score. Conclusions: Treatment side effects were commonly reported and increased PCa detection in RoI has left more men with these side effects. We recommended that men be offered a PSA test only after informed discussion.

The Applicability Of Ordered Mesoporous Sba-15 And Its Hydrophobic Glutaraldehyde-bridge Derivative To Improve Ibuprofen-loading In Releasing System.

The mesoporous SBA-15 silica with uniform hexagonal pore, narrow pore size distribution and tuneable pore diameter was organofunctionalized with glutaraldehyde-bridged silylating agent. The precursor and its derivative silicas were ibuprofen-loaded for controlled delivery in simulated biological fluids. The synthesized silicas were characterized by elemental analysis, infrared spectroscopy, (13)C and (29)Si solid state NMR spectroscopy, nitrogen adsorption, X-ray diffractometry, thermogravimetry and scanning electron microscopy. Surface functionalization with amine containing bridged hydrophobic structure resulted in significantly decreased surface area from 802.4 to 63.0 m(2) g(-1) and pore diameter 8.0-6.0 nm, which ultimately increased the drug-loading capacity from 18.0% up to 28.3% and a very slow release rate of ibuprofen over the period of 72.5h. The in vitro drug release demonstrated that SBA-15 presented the fastest release from 25% to 27% and SBA-15GA gave near 10% of drug release in all fluids during 72.5 h. The Korsmeyer-Peppas model better fits the release data with the Fickian diffusion mechanism and zero order kinetics for synthesized mesoporous silicas. Both pore sizes and hydrophobicity influenced the rate of the release process, indicating that the chemically modified silica can be suggested to design formulation of slow and constant release over a defined period, to avoid repeated administration.

Long-term Postoperative Atrophy Of Contralateral Hippocampus And Cognitive Function In Unilateral Refractory Mtle With Unilateral Hippocampal Sclerosis.

This study aimed to evaluate long-term atrophy in contralateral hippocampal volume after surgery for unilateral MTLE, as well as the cognitive outcome for patients submitted to either selective transsylvian amygdalohippocampectomy (SelAH) or anterior temporal lobe resection (ATL). We performed a longitudinal study of 47 patients with MRI signs of unilateral hippocampal sclerosis (23 patients with right-sided hippocampal sclerosis) who underwent surgical treatment for MTLE. They underwent preoperative/postoperative high-resolution MRI as well as neuropsychological assessment for memory and estimated IQ. To investigate possible changes in the contralateral hippocampus of patients, we included 28 controls who underwent two MRIs at long-term intervals. The volumetry using preoperative MRI showed significant hippocampal atrophy ipsilateral to the side of surgery when compared with controls (p<0.0001) but no differences in contralateral hippocampal volumes. The mean postoperative follow-up was 8.7 years (± 2.5 SD; median=8.0). Our patients were classified as Engel I (80%), Engel II (18.2%), and Engel III (1.8%). We observed a small but significant reduction in the contralateral hippocampus of patients but no volume changes in controls. Most of the patients presented small declines in both estimated IQ and memory, which were more pronounced in patients with left TLE and in those with persistent seizures. Different surgical approaches did not impose differences in seizure control or in cognitive outcome. We observed small declines in cognitive scores with most of these patients, which were worse in patients with left-sided resection and in those who continued to suffer from postoperative seizures. We also demonstrated that manual volumetry can reveal a reduction in volume in the contralateral hippocampus, although this change was mild and could not be detected by visual analysis. These new findings suggest that dynamic processes continue to act after the removal of the hippocampus, and further studies with larger groups may help in understanding the underlying mechanisms.

[why Does The Prevalence Of Cytopathological Results Of Cervical Cancer Screening Can Vary Significantly Between Two Regions Of Brazil?].

To analyze the prevalence of cervical cytopathological results for the screening of cervical cancer with regard to women's age and time since the last examination in Maceió and Rio de Janeiro, Brazil, among those assisted by the Brazilian Unified Health System. Cervical cytopathological results available in the Information System of Cervical Cancer Screening for the year 2011 were analyzed, corresponding to 206,550 for Rio de Janeiro and 45,243 for Maceió. In Rio de Janeiro, examination at one and two year intervals predominated, while in Maceió examination at one and three year intervals had a higher predominance. Women who underwent cervical smear screening in Maceió were older than those in Rio de Janeiro. The prevalence of invasive squamous cell carcinoma was similar for the two cities, but all the other results presented a higher prevalence in Rio de Janeiro: ASCUS (PR=5.32; 95%CI 4.66-6.07); ASCH (PR=4.27; 95%CI 3.15-5.78); atypical glandular cells (PR=10.02; 95%CI 5.66-17.76); low-grade squamous intraepithelial lesions (PR=6.10; 95%CI 5.27-7.07); high-grade squamous intraepithelial lesions (PR=8.90; 95%CI 6.50-12.18) and adenocarcinoma (PR=3.00; 95%CI 1.21-7.44). The rate of unsatisfactory cervical samples was two times higher in Maceió and that of rejected samples for analysis was five times higher in Maceió when compared to Rio de Janeiro. The prevalence rates of altered cervical cytopathological results was significantly higher in Rio de Janeiro than in Maceió. There is no objective information that may justify this difference. One hypothesis is that there may be a difference in the diagnostic performance of the cervical cancer screening, which could be related to the quality of the Pap smear. Thus, these findings suggest that it would be necessary to perform this evaluation at national level, with emphasis on the performance of cervical cancer screening in order to improve the effectiveness of cervical cancer control.