Representing contrast detection as an eigenvalue problem.

Contrast detection can be formulated as an eigenvalue problem. One of the simplest resulting models has only two parameters. The model is space variant and employs the Hermite functions as eigenfunctions. Computing the response to a sinusoidal acuity grating yields the observer's contrast response. The model itself, however, is developed within an abstract mathematical framework which is general enough to include Fourier analysis as a special case. Consequently, the methods of Fourier analysis are generalized to those of eigenfunction expansion and the spectral theory of linear operators.     

Detection of simple radially symmetric targets: further evidence for the matched filter processing scheme in human pattern detection

The detection of small radially symmetric targets was studied using a subthreshold summation paradigm. Small disc and disc-like patterns with diameters up to 0.6^∘ were used for superposition on Bessel functions of zero order, subthreshold contrast and various spatial frequencies. Contrast interrelation functions prove linear over the whole range of contrasts used for the Bessel functions while their slopes show systematic variation with spatial frequency. An extrapolation of sensitivity from the slopes reveals that sensitivity can be predicted by a simple model assuming detection to be mediated by a transfer function made up as a cascade of an even bandpass function and the disc pattern spectrum, as has been found previously using one dimensional luminance distributions. Problems concerning the formation of pattern-specific radial symmetric filters are discussed. Received: 31 January 2000 / Accepted in revised form: 16 June 2000     

Distinct modulated pupil function system for real-time imaging of living cells

Optical microscopy is one of the most contributive tools for cell biology in the past decades. Many microscopic techniques with various functions have been developed to date, i.e., phase contrast microscopy, differential interference contrast (DIC) microscopy, confocal microscopy, two photon microscopy, superresolution microscopy, etc. However, person who is in charge of an experiment has to select one of the several microscopic techniques to achieve an experimental goal, which makes the biological assay time-consuming and expensive. To solve this problem, we have developed a microscopic system with various functions in one instrument based on the optical Fourier transformation with a lens system for detection while focusing on applicability and user-friendliness for biology. The present instrument can arbitrarily modulate the pupil function with a micro mirror array on the Fourier plane of the optical pathway for detection. We named the present instrument DiMPS (Distinct optical Modulated Pupil function System). The DiMPS is compatible with conventional fluorescent probes and illumination equipment, and gives us a Fourier-filtered image, a pseudo-relief image, and a deep focus depth. Furthermore, DiMPS achieved a resolution enhancement (pseudo-superresolution) of 110 nm through the subtraction of two images whose pupil functions are independently modulated. In maximum, the spatial and temporal resolution was improved to 120 nm and 2 ms, respectively. Since the DiMPS is based on relay optics, it can be easily combined with another microscopic instrument such as confocal microscope, and provides a method for multi-color pseudo-superresolution. Thus, the DiMPS shows great promise as a flexible optical microscopy technique in biological research fields.     

The motion of the left ventricle. I

The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.     

Colour Vision Impairment in Young Alcohol Consumers

Alcohol consumption among young adults is widely accepted in modern society and may be the starting point for abusive use of alcohol at later stages of life. Chronic alcohol exposure can lead to visual function impairment. In the present study, we investigated the spatial luminance contrast sensitivity, colour arrangement ability, and colour discrimination thresholds on young adults that weekly consume alcoholic beverages without clinical concerns. Twenty-four young adults were evaluated by an ophthalmologist and performed three psychophysical tests to evaluate their vision functions. We estimated the spatial luminance contrast sensitivity function at 11 spatial frequencies ranging from 0.1 to 30 cycles/degree. No difference in contrast sensitivity was observed comparing alcohol consumers and control subjects. For the evaluation of colour vision, we used the Farnsworth-Munsell 100 hue test (FM 100 test) to test subject’s ability to perform a colour arrangement task and the Mollon-Reffin test (MR test) to measure subject’s colour discrimination thresholds. Alcohol consumers made more mistakes than controls in the FM100 test, and their mistakes were diffusely distributed in the FM colour space without any colour axis preference. Alcohol consumers also performed worse than controls in the MR test and had higher colour discrimination thresholds compared to controls around three different reference points of a perceptually homogeneous colour space, the CIE 1976 chromaticity diagram. There was no colour axis preference in the threshold elevation observed among alcoholic subjects. Young adult weekly alcohol consumers showed subclinical colour vision losses with preservation of spatial luminance contrast sensitivity. Adolescence and young adult age are periods of important neurological development and alcohol exposure during this period of life might be responsible for deficits in visual functions, especially colour vision that is very sensitive to neurotoxicants.     

Method for measuring sensitivity to periodic spectral energy modulations in human

The distribution of spectral energy of a visual stimulus can be subject to Fourier analysis. In this perspective, we have built a device which produces periodic variations in energy (square waves) over the visible spectrum (400-700 nm), and where the amplitude, phase and frequency of the stimuli can be independently controlled. From the non-modulated spectrum, supplying a white spot, for a given frequency and phase, there is a minimal amplitude modulation (contrast threshold) for which the spot becomes chromatic. As an illustrative example we present here a curve of optimal sensitivity values (inverse of contrast) as a function of frequency (from 0.5 to 3.6 cycles/300 nm) for a normal subject.     

Spatial integration characteristics in motion detection and direction identification

Spatial integration characteristics were assessed with drifting gratings for both detection and direction-identification contrast thresholds. Thresholds were measured while stimulus width, length or both were varied. It was found that: (1) the shape of the size/sensitivity functions changes with spatial, but not with temporal, frequency; (2) direction-identification thresholds diverge from the detection thresholds below 1 cycle but can be reliably measured for stimulus widths as small as 0.1275 cycles; (3) the integration characteristics are slightly anisotropic for the identification but not for the detection process, and (4) the two-dimensional spatial integration cannot be directly predicted from its one-dimensional characteristics. Width/sensitivity detection functions are well fitted by predictions of Wilson and Bergen's four-channel model. Predictions from a temporal covariance model provide a poor fit to the identification data. It is argued that classes of detection and direction-identification models must involve identical nonlinearities prior to their respective thresholds. It is concluded that the hypothesis according to which both performances are determined by the same spatial integration stage cannot be rejected.     

Reflections on Plant and Soil Nematode Ecology: Past,Present and Future

The purpose of this review is to highlight key developments in nematode ecology from its beginnings to where it stands today as a discipline within nematology. Emerging areas of research appear to be driven by crop production constraints, environmental health concerns, and advances in technology. In contrast to past ecological studies which mainly focused on management of plant-parasitic nematodes, current studies reflect differential sensitivity of nematode faunae. These differences, identified in both aquatic and terrestrial environments include response to stressors, environmental conditions, and management practices. Methodological advances will continue to influence the role nematodes have in addressing the nature of interactions between organisms, and of organisms with their environments. In particular, the C. elegans genetic model, nematode faunal analysis and nematode metagenetic analysis can be used by ecologists generally and not restricted to nematologists.     

Application of global sensitivity analysis to determine goals for design of experiments: an example study on antibody-producing cell cultures

Global sensitivity analysis (GSA) can be used to quantify the importance of model parameters and their interactions with respect to model output. In this study, the Sobol' method for GSA is applied to a dynamic model of monoclonal antibody-producing mammalian cell cultures in order to identify the parameters that need to be accurately determined experimentally. Our results show that most parameters have low sensitivity indices and exhibit strong interactions with one another. These parameters can be set at their nominal values and unnecessary experimentation can therefore be avoided. In contrast, certain parameters are identified as sensitive, necessitating their estimation given sufficiently rich experimental data. Moreover, parameter sensitivity varies during culture time in a biologically meaningful manner. In conclusion, GSA can serve as an excellent precursor to optimal experiment design.     

A Suprasystem of Probability Distributions

A set of differential equations is described whose solutions represent a general system of probability distribution functions. Previously reported systems of such distribution functions are special cases of this general system. The differential equations can be used to represent distribution functions and generate their related statistics in cases for which no simple formula for the distribution is known. The generality of this suprasystem of distribution functions and its potential utility are discussed.     

Anharmonic analysis of arterial blood pressure and flow pulses

Fourier analysis is usually employed for the computation of blood flow in arteries. Although the orthogonality of Fourier eigenfunctions guarantees the accurate mathematical modeling of the blood pressure and flow waveforms, the physics behind this objective function is frequently missing. We propose a new method to account for the blood pressure and flow, single-cycle (systole-diastole) waveforms. It is based on the one dimensional hydrodynamic mass and momentum conservation equations for viscous flow. The similarity of the linear problem, under discussion, with related transmission line theory in electromagnetic wave propagation, permits expansion in anharmonic, non-separable eigenfunctions. In some cases one term in the expansion is adequate to fit the main peak of the observed waveforms. Analytical formulas are derived for the dependence of the pressure and flow main peaks on whole blood viscosity and distance from the heart, which interpret observations related to hypertension.     

Phase-Lifetime Spectroscopy of Photocycle Processes: Kinetic Analysis of Amplitude Dispersion Curves

Phase-lifetime spectroscopy has been recently used to obtain kinetic information on biological photocycles. A simple, general method is presented for deriving the amplitude response function for light-driven processes. These amplitude response functions may be used to analyze the experimental data obtained when driving the photosystem with a mechanically chopped, actinic light source. This analysis allows a comparison of kinetic parameters obtained from modulation methods with those obtained by flash techniques. Typically the experimental data consist of the signal amplitude measured at several chopping frequencies of the actinic light. These amplitude dispersion curves will be dependent on the harmonic sensitivity of the phase-sensitive detector used to measure the signal. This harmonic sensitivity is taken into account by performing a Fourier decomposition on the amplitude response function of the system and weighting each harmonic in a fashion appropriate for the specific amplifier under consideration. The resulting response function obtained for two commonly used amplifiers is derived. In addition to simple photocycles, the analysis of photocycle-coupled processes is also considered. This second relaxation process, which is coupled to a photocycle process, could represent the chemiosmotic coupling of a light-driven ion pump to a second ion transport protein. Conditions are established in which the kinetics of the second process can be resolved from the photocycle process.     

Two-dimensional Fourier representation used in the bioelectric forward problem.

The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.     

Variation,selection and evolution of function-valued traits

We describe an emerging framework for understanding variation, selection and evolution of phenotypic traits that are mathematical functions. We use one specific empirical example – thermal performance curves (TPCs) for growth rates of caterpillars – to demonstrate how models for function-valued traits are natural extensions of more familiar, multivariate models for correlated, quantitative traits. We emphasize three main points. First, because function-valued traits are continuous functions, there are important constraints on their patterns of variation that are not captured by multivariate models. Phenotypic and genetic variation in function-valued traits can be quantified in terms of variance-covariance functions and their associated eigenfunctions: we illustrate how these are estimated as well as their biological interpretations for TPCs. Second, selection on a function-valued trait is itself a function, defined in terms of selection gradient functions. For TPCs, the selection gradient describes how the relationship between an organism's performance and its fitness varies as a function of its temperature. We show how the form of the selection gradient function for TPCs relates to the frequency distribution of environmental states (caterpillar temperatures) during selection. Third, we can predict evolutionary responses of function-valued traits in terms of the genetic variance-covariance and the selection gradient functions. We illustrate how non-linear evolutionary responses of TPCs may occur even when the mean phenotype and the selection gradient are themselves linear functions of temperature. Finally, we discuss some of the methodological and empirical challenges for future studies of the evolution of function-valued traits.     

不同运动速度下人眼的阈上调制特性

本文报道了在光栅的三种恒定运动速度(0°/S,10°/S,30°/S)下,阈值对比敏感度函数CSF(V)和阈上对比度比配函数CMF(V,C)的测试数据.计算机拟合结果表明,在各个不同的恒定运动速度下,人眼的阈上对比度比配函数CMF(V,C)和阈值对比敏感度函数CSF(V),可以由静止目标的阈值对比敏感函数CSF近似地预测出来.本文给出了预测方法的数学描述及有关经验公式.     

对比度检测学习提高猫的视觉对比敏感度

对人的心理学研究结果显示,对比度检测学习可提高学习者对视觉刺激的对比敏感度,但其潜在的神经机制尚不清楚。该研究用二选一（two-alternative forced choice）方法训练3只猫（Felis catus）通过单眼进行对比度检测学习,发现每只猫对视觉刺激的对比敏感度随着训练而显著提高。该学习效果虽然对训练眼有明显的特异性,但部分学习效果可以传递给非训练眼,提示对比度检测学习可能会引起双眼信息汇聚前后的视觉中枢的神经可塑性。另外,猫视觉对比敏感度的提高主要发生在训练刺激的空间频率附近,表明对比度检测学习具有一定的空间频率选择性。该研究结果显示,猫对视觉刺激的对比度检测学习表现出与人类相似的特性,因此可以作为模式动物来研究人类学习诱导的视觉对比敏感度升高的神经机制。     

Recasting nonlinear differential equations as S-systems: a canonical nonlinear form

An enormous variety of nonlinear differential equations and functions have been recast exactly in the canonical form called an S-system. This is a system of nonlinear ordinary differential equations, each with the same structure: the change in a variable is equal to a difference of products of power-law functions. We review the development of S-systems, prove that the minimum for the range of equations that can be recast as S-systems consists of all equations composed of elementary functions and nested elementary functions of elementary functions, give a detailed example of the recasting process, and discuss the theoretical and practical implications. Among the latter is the ability to solve numerically nonlinear ordinary differential equations in their S-system form significantly faster than in their original form through utilization of a specially designed algorithm.     

Visual analysis in unspecialized receptive fields as an orthogonal series expansion

It was postulated on the basis of results obtained by investigating retinal receptive fields of cats that experimental data reflecting the pattern of sensitivity of the receptive field coincide with certain orthogonal polynomials. These special functions have certain properties which can be regarded as spatial characteristics of the receptive fields whose differential sensitivity they describe. Within the framework of the suggested hypothesis visual analysis in the retina from the mathematical point of view can be regarded as a process of expansion of the curve of spatial distribution of brightness within the receptive fields in an orthogonal series. Physiologically speaking the retinal receptive fields can be interpreted as filters distinguishing an elementary orthogonal harmonic from the signal. This method of analysis results in maximal economy of the coding of visual information in the retina. The concepts put forward provide a fresh explanation of a number of physiological facts and they provide precise quantitative evaluations of the response of the receptive field to an arbitrary stimulus.     

Structure-function relationships of integral membrane proteins: membrane transporters vs channels

Escherichia coli lactose permease, a paradigm for membrane transport proteins, and Streptomyces lividans KcsA, a paradigm for K+ channels, are compared on the level of structure, dynamics, and function. The homotetrameric channel, which allows the downhill movement of K+ with an electrochemical gradient, is relatively rigid and inflexible, as observed by Fourier transform infrared spectroscopy. Lactose permease catalyzes transduction of free energy stored in an electrochemical H+ gradient into work in the form of a concentration gradient. In marked contrast to KcsA, the permease exhibits a high degree of H/D exchange, in addition to enhanced sensitivity to lateral lipid packing pressure, thereby indicating that this symport protein is extremely flexible and conformationally active. Finally, the differences between lactose permease and KcsA are discussed in the context of their specific functions with particular emphasis on differences between coupling in symport proteins and gating in channels.