Sensitivity to corners in flow patterns

Flow patterns are two-dimensional orientation structures that arise from the projection of certain kinds of surface coverings (such as fur) onto images. Detecting orientation changes within them is an important task, since the changes often correspond to significant events such as corners, occluding edges, or surface creases. We model such patterns as random-dot Moiré patterns, and examine sensitivity to change in orientation within them. We show that the amount of structure available from which orientation and curvature can be estimated is critical, and introduce a path-length parameter to model it. For short path lengths many discontinuities are smoothed over, which has further implications for computational modeling of orientation selectivity.     

Texture fields and texture flows: sensitivity to differences

There are two large classes of textures, those with an overall orientation structure (texture flows) and those without (texture fields). We investigate human sensitivity to detecting a patch of texture field within a texture flow psychophysically by using random not Moiré patterns. The resultant sensitivity, as a function of patch-size and path-length, is then related to a computational model of orientation selection, which reveals a connection between texture structure and the estimation of curvature. Finally, the connection back to curvature is confirmed by demonstrating a similarity between the patch sensitivity data and previous data on sensitivity to corners in flow patterns.     

A model for the perception of curves in dot figures: The role of local salience of “virtual lines”

In many models of visual information processing the notion of a virtual line or dipole is introduced in order to represent the configurational information, notably length and relative orientation, between identical figure elements in figures with discrete elements. Virtual lines have proven to be very useful in predicting perceptual phenomena (Julesz et al. 1973; Stevens 1978). In the present study, virtual lines are utilized in a model which aims to predict the perception of (dotted) curves in dot figures. Clearly many possible curves, formed by adjacent virtual lines, can be constructed within a set of dots. It is proposed that already at the local level of the virtual lines each line has a perceptual salience which results from the function induced by the global dot figure. It is this local line salience or connectivity that directs further processing and determines the curves to be seen in a dot figure. The model presented is an information processing model with a clear modular design. It entails three successive levels of representation. First image functions are derived through a convolution of the input with gaussian distribution functions. Next, a discrete internal representation is extracted from the image function consisting of two primitives; blobs, representing the dots, and virtual lines, representing pairwise relations between blobs. The attributes of the blobs are their positions in the image plane, while those of the virtual lines are length, relative orientation and connectivity. At the third level, the discrete internal representation is used to predict the perceived curves. It is shown that the model has advantages over other approaches, e.g. autocorrelation and network models.     

Stress Distribution in the Canine Left Ventricle during Diastole and Systole

A model is proposed for stress analysis of the left ventricular wall (LV wall) based on the realistic assumption that the myocardium is essentially composed of fiber elements which carry only axial tension and vary in orientation through the wall. Stress analysis based on such a model requires an extensive study of muscle fiber orientation and curvature through the myocardium. Accordingly, the principal curvatures were studied at a local site near the equator in ten dog hearts rapidly fixed in situ at end diastole and end systole; the fiber orientation for these hearts had already been established in a previous study. The principal radii of curvature were (a) measured by fitting templates to the endocardial and epicardial wall surfaces in the circumferential and longitudinal directions and (b) computed from measured lengths of semiaxes of ellipsoids of revolution representing the LV wall (“ellipsoid” data). The wall was regarded as a tethered set of nested shells, each having a unique fiber orientation. Results indicate the following. (a) Fiber curvature, k, is maximum at midwall at end systole; this peak shifts towards endocardium at end diastole. (b) The pressure or radial stress through the wall decreases more rapidly near the endocardium than near the epicardium at end diastole and at end systole when a constant tension is assumed for each fiber through the wall. (c) At end diastole the curve for the circumferential stress vs. wall thickness is convex with a maximum at midwall. In the longitudinal direction the stress distribution curve is concave with a minimum at midwall. Similar distributions are obtained at end systole when a constant tension is assumed for each fiber through the wall. (d) The curvature and stress distributions obtained by direct measurements at a selected local site agree well with those computed from “ellipsoid” data.     

Orientation variance as a quantifier of structure in texture

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.     

Data-Driven Method to Estimate Nonlinear Chemical Equivalence

There is great need to express the impacts of chemicals found in the environment in terms of effects from alternative chemicals of interest. Methods currently employed in fields such as life-cycle assessment, risk assessment, mixtures toxicology, and pharmacology rely mostly on heuristic arguments to justify the use of linear relationships in the construction of “equivalency factors,” which aim to model these concentration-concentration correlations. However, the use of linear models, even at low concentrations, oversimplifies the nonlinear nature of the concentration-response curve, therefore introducing error into calculations involving these factors. We address this problem by reporting a method to determine a concentration-concentration relationship between two chemicals based on the full extent of experimentally derived concentration-response curves. Although this method can be easily generalized, we develop and illustrate it from the perspective of toxicology, in which we provide equations relating the sigmoid and non-monotone, or “biphasic,” responses typical of the field. The resulting concentration-concentration relationships are manifestly nonlinear for nearly any chemical level, even at the very low concentrations common to environmental measurements. We demonstrate the method using real-world examples of toxicological data which may exhibit sigmoid and biphasic mortality curves. Finally, we use our models to calculate equivalency factors, and show that traditional results are recovered only when the concentration-response curves are “parallel,” which has been noted before, but we make formal here by providing mathematical conditions on the validity of this approach.     

ROC curve estimation when covariates affect the verification process

A receiver operating characteristic (ROC) curve is commonly used to measure the accuracy of a medical test. It is a plot of the true positive fraction (sensitivity) against the false positive fraction (1-specificity) for increasingly stringent positivity criterion. Bias can occur in estimation of an ROC curve if only some of the tested patients are selected for disease verification and if analysis is restricted only to the verified cases. This bias is known as verification bias. In this paper, we address the problem of correcting for verification bias in estimation of an ROC curve when the verification process and efficacy of the diagnostic test depend on covariates. Our method applies the EM algorithm to ordinal regression models to derive ML estimates for ROC curves as a function of covariates, adjusted for covariates affecting the likelihood of being verified. Asymptotic variance estimates are obtained using the observed information matrix of the observed data. These estimates are derived under the missing-at-random assumption, which means that selection for disease verification depends only on the observed data, i.e., the test result and the observed covariates. We also address the issues of model selection and model checking. Finally, we illustrate the proposed method on data from a two-phase study of dementia disorders, where selection for verification depends on the screening test result and age.     

Gamma oscillations in primate primary visual cortex are severely attenuated by small stimulus discontinuities

Gamma oscillations (30 to 80 Hz) have been hypothesized to play an important role in feature binding, based on the observation that continuous long bars induce stronger gamma in the visual cortex than bars with a small gap. Recently, many studies have shown that natural images, which have discontinuities in several low-level features, do not induce strong gamma oscillations, questioning their role in feature binding. However, the effect of different discontinuities on gamma has not been well studied. To address this, we recorded spikes and local field potential from 2 monkeys while they were shown gratings with discontinuities in 4 attributes: space, orientation, phase, or contrast. We found that while these discontinuities only had a modest effect on spiking activity, gamma power drastically reduced in all cases, suggesting that gamma could be a resonant phenomenon. An excitatory–inhibitory population model with stimulus-tuned recurrent inputs showed such resonant properties. Therefore, gamma could be a signature of excitation–inhibition balance, which gets disrupted due to discontinuities.

Gamma oscillations (30-80 Hz) in visual cortex have been hypothesized to play an important role in feature binding, but this role has recently been questioned. This study shows that visual stimulus-induced gamma oscillations are highly attenuated with even small discontinuities in the stimulus. This "resonant" behaviour can be explained by a simple excitatory-inhibitory model in which discontinuities lead to a small reduction in lateral inputs.     

Effect of red light on the phototropic sensitivity of corn coleoptiles

The effect of red light in alteration of the phototropic sensitivity of corn coleoptiles (Zea mays L., cultivar Burpee Barbecue Hybrid) is investigated. Phototropic dosage-response curves for etiolated coleoptiles are compared with those for coleoptiles receiving 1 hour of continuous red light immediately prior to phototropic induction. In the former case, only curvature comparable to the first positive curvature of oat coleoptiles is obtained. There is no evidence for first negative curvature and only minimal second positive curvature. The reciprocity law proved valid for all curvatures obtained. With red light, the sensitivity of the first positive curvature was decreased over ten-fold and there was clear appearance of second positive curvature for which the reciprocity law was not valid. Once again there was no evidence for negative curvature. Time course studies indicated that within 1 hour of the beginning of red light treatment at 25°, reactions leading to the decrease in phototropic sensitivity of the first positive component had gone to completion whether the red light was continuous or consisted of a single 1 second exposure followed by a 1 hour dark period. An action spectrum for the red-induced change in phototropic sensitivity showed a marked peak near 660 mμ with a small broad shoulder between 610 and 630 mμ, characteristic of phytochrome-mediated responses. The effect of red light could be fully reversed by low dosages of far-red light, but longer doses of far red were less effective. Large dosages of far-red light alone induced the same alteration in phototropic sensitivity as did red light.     

Age-Related Changes in Expectation-Based Modulation of Motion Detectability

Expecting motion in some particular direction biases sensitivity to that direction, which speeds detection of motion. However, the neural processes underlying this effect remain underexplored, especially in the context of normal aging. To address this, we examined younger and older adults'' performance in a motion detection task. In separate conditions, the probability was either 50% or 100% that a field of dots would move coherently in the direction a participant expected (either vertically or horizontally). Expectation and aging effects were assessed via response times (RT) to detect motion and electroencephalography (EEG). In both age groups, RTs were fastest when motion was similar to the expected direction of motion. RT tuning curves exhibited a characteristic U-shape such that detection time increased with an increasing deviation from the participant''s expected direction. Strikingly, EEG results showed an analogous, hyperbolic curve for N1 amplitude, reflecting neural biasing. Though the form of behavioral and EEG curves did not vary with age, older adults displayed a clear decline in the speed of detection and a corresponding reduction in EEG N1 amplitude when horizontal (but not vertical) motion was expected. Our results suggest that expectation-based detection ability varies with age and, for older adults, also with axis of motion.     

Orientation-Specificity of Adaptation: Isotropic Adaptation Is Purely Monocular

Numerous studies have found that prolonged exposure to grating stimuli reduces sensitivity to subsequently presented gratings, most evidently when the orientations of the adapting and test patterns are similar. The rate of sensitivity loss varies with angular difference indicating both the presence and bandwidths of psychophysical ‘orientation channels’. Here we study the orientation dependency of contrast adaptation measured both monoptically and dichoptically. Earlier psychophysical reports show that orientation bandwidths are broader at lower spatial frequencies, and we confirm this with a simple von Mises model using 0.25 vs. 2 c.p.d. gratings. When a single isotropic (orientation invariant) parameter is added to this model, however, we find no evidence for any difference in bandwidth with spatial frequency. Consistent with cross-orientation masking effects, we find isotropic adaptation to be strongly low spatial frequency-biased. Surprisingly, unlike masking, we find that the effects of interocular adaptation are purely orientation-tuned, with no evidence of isotropic threshold elevation. This dissociation points to isotropic (or ‘cross-orientation’) adaptation being an earlier and more magnocellular-like process than that which supports orientation-tuned adaptation and suggests that isotropic masking and adaptation are likely mediated by separate mechanisms.     

Responses of central auditory neurons to frequency-modulated stimuli and temporal characteristics of inhibitory interaction

Responses to frequency-modulated stimuli of 118 inferior collicular neurons were compared with quantitative characteristics of the frequency — threshold curves and lateral inhibitory zones during time-varying two-tone stimulation in anesthetized albino rats. In one third of neurons high sensitivity to the direction of frequency modulation does not correspond to their spatial characteristics (the shape, width, and arrangement of the lateral inhibitory zones relative to the frequency — threshold curve). The specificity of response of these neurons to a particular direction of frequency modulation is evidently based on differences in the temporal course of inhibition evoked by high-frequency and low-frequency tones.I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 7, No. 6, pp. 603–607, November–December, 1975.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Severely Reduced Gravitropism in Dark-Grown Hypocotyls of a Starch-Deficient Mutant of Nicotiana sylvestris

Gravitropism in dark-grown hypocotyls of the wild type was compared with a starch-deficient Nicotiana sylvestris mutant (NS 458) to test the effects of starch deficiency on gravity sensing. In a time course of curvature measured using infrared video, the response of the mutant was greatly reduced compared to the wild type; 72 hours after reorientation, curvature was about 10° for NS 458 and about 70° for wild type. In dishes maintained in a vertical orientation, wild-type hypocotyls were predominantly vertical, whereas NS 458 hypocotyls were severely disoriented with about 5 times more orientational variability than wild type. Since the growth rates were equal for both genotypes and phototropic curvature was only slightly inhibited in NS 458, the mutation probably affects gravity perception rather than differential growth. Our data suggest that starch deficiency reduces gravitropic sensitivity more in dark-grown hypocotyls than in dark- or light-grown roots in this mutant and support the hypothesis that amyloplasts function as statoliths in shoots as well as roots.     

Hermitian splines for modeling biological soft tissue systems that exhibit nonlinear force-elongation curves

Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.     

Generic properties of edges and “corners” on smooth greyvalue surfaces

The edge line on a smooth greyvalue surface, defined as locus of maximal slope, is a curve embedded in the negatively curved part of the greyvalue surface. For an open and dense set of greyvalue functions the edge line has transverse double points as its only singular points, meets the parabolic curve tangentially at isolated points, and intersects the zero crossings of the Laplacean of the greyvalue function transversely. Defining a greyvalue corner as a curvature extremum of the edge line one can show that, again for an open and dense set of greyvalue functions, these corners are isolated points in the image corresponding to ordinary curvature extrema of the edge. Detecting such corners in greyvalue images requires differential operators containing partial derivatives of order five, which raises some doubts about the existence of numerically robust algorithms for detecting these features in digital images.     

Model of total skin electron treatment using the 'six-dual-field' technique

During implementation of the total skin electron treatment, using six-dual-field technique, at radiotherapy department a large number of measurements are needed. To assess depth dose curve required by clinicians and dose uniformity over a whole treatment plane, combinations of different irradiation parameters are used (electron energy, beam angle, scatterers). Measurements for each combination must be performed. One possible way to reduce number of measurements is to model the treatment using the Monte Carlo simulation of electron transport. We made a simplified multiple-source Monte Carlo model of electron beam and tested it by comparing calculations and experimental results. Calculated data differs less than 5 percent from measurements in the treatment plane. During the treatment patient can be approximated using cylinders with different diameters and orientations. We tried to model the depth dose variations in the total skin electron treatment not just around the body cross-section (simplified to cylinders of different diameters), but also along the body to account for the variations in body curvature longitudinally. This effect comes down to the problem of modeling distribution in different cylinders, but varying the longitudinal orientation of those cylinders. We compared Monte Carlo calculations and film measurements of depth dose curves for two orientations of the cylindrical phantom, which were the simplest for experimental arrangement. Comparison of the results proved accuracy of the model and we used it to calculate depth dose curves for a number of other cylinder orientations.     

大优角蚱卵块外型的数学模型研究及其生态学意义

【目的】探究大优角蚱Eucriotettix grandis独特的卵块形态的生态学意义。【方法】在大量野外调查大优角蚱卵块生态学特征的基础上, 通过对卵块图片的三维数据点进行截面线抽取, 获得卵块截面曲线的拟合方程, 并用线条拟合法建立相应的数学模型。依据拟合曲线的曲率图和二阶导数值图对数据拟合曲线的几何特性进行分析。【结果】大优角蚱多以完整卵块的形式产卵, 卵块为约六边形的橘子瓣状结构, 且卵块顶部有一明显的半球形凹槽, 底部则中间略隆起。利用线条拟合理论, 构造出既能够有效满足拟合优度, 又能够满足光滑度的核函数, 通过对函数取值得到模型曲线非常近似拟合于真值曲线。【结论】凹槽很可能是便于存水, 保持卵块的湿润, 利于卵的存活和孵化; 棱角有利于缓解卵块的远距离滚动和破散, 紧密结合的卵块结构利于卵的保温保湿。