Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

Rotating stripes and the impulse response of the eye: I. Uniform illumination

A rotating striped pattern produces an unexpected visual effect: a band of relatively high contrast is seen obliquely across the striped pattern, moving steadily around with the pattern and lagging behind the perpendicular to the stripes. Photographs of the moving pattern display similar effects. An analysis of the effect (based on a simple linear model) shows that the perceived contrast observed at any instant across the pattern represents the temporal modulation transfer function of the eye and the asymmetrical shape of the lines is a display of the phase transfer function. The analysis establishes and uses an analogy with the amplitude distribution in a Fraunhofer diffraction pattern. The temporal impulse response of the eye is related to the perceived contrast in the same way that the aperture function is to the amplitude distribution in the diffraction pattern. The binocularly perceived contrast distribution is considered as the interference or phasor addition of the two monocularly perceived effects, and the clinical potential of this approach is illustrated. In addition, since the band itself is not an object with a physical boundary, but a perceptual consequence of blurring and spatial averaging, the effect provides a means for investigating the perceived location of moving objects in general.     

Methods for the identification of evoked response components in the frequency and combined time/frequency domains

Two prominent frequency components designated f1 and f2 have been identified in the visual evoked response to the transient presentation of sinusoidal luminance gratings in the range of 0.5–8 c/deg. The components occur at temporal frequencies below the alpha band, with the f1 frequency roughly half that of the f2 frequency. The f1 component is largest at low spatial frequencies with f2 becoming progressively dominant as spatial frequency is increased.The frequency and amplitude of f1 and f2 change substantially over the time course of the response. This has been studied by calculating the temporal frequency spectrum of the transient evoked potential over successive short-time epochs running through the response. Using this technique, the response is shown to consist of narrow- and frequency peaks or ‘formants’ emerging at different times after stimulus onset. These formants occur at frequencies other than those of the spontaneous EEG and undergo changes in frequency and amplitude over the time course of the response.Two spectrum analysis techniques were employed: the Discrete Fourier Transform and Linear Predictive Coding. Frequency components were successfully identified in single-trial responses using the LPC technique.     

Double‐wavelet transform for multisubject task‐induced functional magnetic resonance imaging data

The goal of this article is to model multisubject task‐induced functional magnetic resonance imaging (fMRI) response among predefined regions of interest (ROIs) of the human brain. Conventional approaches to fMRI analysis only take into account temporal correlations, but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio‐temporal covariance matrix. Other spatio‐temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not always feasible. To address these limitations, we propose a double‐wavelet approach for modeling the spatio‐temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio‐temporal model. The main advantages of the wavelet approach are that it is scalable and that it deals with nonstationarity in brain signals. Simulation studies showed that our method could reduce false‐positive and false‐negative rates by taking into account spatial and temporal correlations simultaneously. We also applied our method to fMRI data to study activation in prespecified ROIs in the prefontal cortex. Data analysis showed that the result using the double‐wavelet approach was more consistent than the conventional approach when sample size decreased.     

Maximizing contrast resolution in the outer retina of mammals

The outer retina removes the first-order correlation, the background light level, and thus more efficiently transmits contrast. This removal is accomplished by negative feedback from horizontal cell to photoreceptors. However, the optimal feedback gain to maximize the contrast sensitivity and spatial resolution is not known. The objective of this study was to determine, from the known structure of the outer retina, the synaptic gains that optimize the response to spatial and temporal contrast within natural images. We modeled the outer retina as a continuous 2D extension of the discrete 1D model of Yagi et al. (Proc Int Joint Conf Neural Netw 1: 787–789, 1989). We determined the spatio-temporal impulse response of the model using small-signal analysis, assuming that the stimulus did not perturb the resting state of the feedback system. In order to maximize the efficiency of the feedback system, we derived the relationships between time constants, space constants, and synaptic gains that give the fastest temporal adaptation and the highest spatial resolution of the photoreceptor input to bipolar cells. We found that feedback which directly modulated photoreceptor calcium channel activation, as opposed to changing photoreceptor voltage, provides faster adaptation to light onset and higher spatial resolution. The optimal solution suggests that the feedback gain from horizontal cells to photoreceptors should be ∼0.5. The model can be extended to retinas that have two or more horizontal cell networks with different space constants. The theoretical predictions closely match experimental observations of outer retinal function.     

Analysis of prehistoric biological variation under a model of isolation by geographic and temporal distance

Biological distances calculated between archeologically recovered human skeletal collections are often used to assess the effects of temporal and spatial distance on subpopulation divergence. Although there are many previous empirical studies that examine skeletal material arrayed across time and/or space, the theoretical expectations for temporally or spatially related variation in biological characteristics have not been formally developed. In this paper I present the infinite island model, the unidimensional stepping-stone model, and the migration matrix method in forms that allow prediction of the genetic distance between groups separated by a given spatial and temporal lag. These models demonstrate that, if there is isolation by geographic distance, then the correlation between genetic and spatial distance (controlling for temporal distance) should be positive and the correlation between genetic and temporal distance (controlling for spatial distance) should be negative. I use observations of nonmetric traits in a sample of prehistoric crania from west-central Illinois to demonstrate the expected relationships among biological, temporal, and spatial distance. The results indicate that, once the effects of temporal trend are removed, biological and spatial distance are positively correlated and biological and temporal distance negatively correlated within this sample.     

Quasi-elastic light scattering from migrating chemotactic bands of Escherichia coli.

We report the observation of migrating chemotactic bands of Escherichia coli in a buffer solution. The temporal development of the bacterial density profile is observed by the scattered light intensity as the band migrates through a stationary laser beam. We have made a preliminary analysis of the observed band profile with help of the Keller-Segel theory. The model accounts for only some aspects of the observed time evolution of the density profile. The microscopic motility characteristics of the E. coli in the band are simultaneously studied by photon correlation. The measured correlation functions are analyzed to obtain the spatial dependence of the half-width within the band. A simple analytical model is proposed to account for the contribution of the twiddle motion to the correlation function. By analyzing the correlation function as a superposition of straight-line and twiddle motions, we obtain a satisfactory agreement between the theory and the measured angular dependence of the line shape. As a consequence we are able to extract a parameter beta, which measures the average fraction of twiddling bacteria in the center of the band at a given time.     

Development of spatiotemporal receptive fields of simple cells: I. Model formulation

A model for the development of spatiotemporal receptive fields of simple cells in the visual cortex is proposed. The model is based on the 1990 hypothesis of Saul and Humphrey that the convergence of four types of input onto a cortical cell, viz. non-lagged ON and OFF inputs and lagged ON and OFF inputs, underlies the spatial and temporal structure of the receptive fields. It therefore explains both orientation and direction selectivity of simple cells. The response properties of the four types of input are described by the product of linear spatial and temporal response functions. Extending the 1994 model of one of the authors (K.D. Miller), we describe the development of spatiotemporal receptive fields as a Hebbian learning process taking into account not only spatial but also temporal correlations between the different inputs. We derive the correlation functions that drive the development both for the period before and after eye-opening and demonstrate how the joint development of orientation and direction selectivity can be understood in the framework of correlation-based learning. Our investigation is split into two parts that are presented in two papers. In the first, the model for the response properties and for the development of direction-selective receptive fields is presented. In the second paper we present simulation results that are compared with experimental data, and also provide a first analysis of our model. Received: 18 June 1997 / Accepted: 16 September 1997     

Task-Oriented Modular Decomposition of Biological Networks: Trigger Mechanism in Blood Coagulation

Analysis of complex time-dependent biological networks is an important challenge in the current postgenomic era. We propose a middle-out approach for decomposition and analysis of complex time-dependent biological networks based on: 1), creation of a detailed mechanism-driven mathematical model of the network; 2), network response decomposition into several physiologically relevant subtasks; and 3), subsequent decomposition of the model, with the help of task-oriented necessity and sensitivity analysis into several modules that each control a single specific subtask, which is followed by further simplification employing temporal hierarchy reduction. The technique is tested and illustrated by studying blood coagulation. Five subtasks (threshold, triggering, control by blood flow velocity, spatial propagation, and localization), together with responsible modules, can be identified for the coagulation network. We show that the task of coagulation triggering is completely regulated by a two-step pathway containing a single positive feedback of factor V activation by thrombin. These theoretical predictions are experimentally confirmed by studies of fibrin generation in normal, factor V-, and factor VIII-deficient plasmas. The function of the factor V-dependent feedback is to minimize temporal and parametrical intervals of fibrin clot instability. We speculate that this pathway serves to lessen possibility of fibrin clot disruption by flow and subsequent thromboembolism.     

Modelling habitat and planning surveillance using Landsat imagery: a case study using Imported Red Fire ants

This paper presents a Bayesian mixture model approach for detecting areas of habitat that are suitable for S. invicta infestation, aiding the ongoing surveillance for early detection of these exotic pests. We show that Landsat imagery is an affordable and valuable tool to assist in determining an informed surveillance strategy. In this paper, we use Landsat band 3 (visible red), Landsat band 6 (mid infrared) and a soil brightness index, in various combinations, to assess the probability that the area associated with each pixel is habitable terrain, either in a multivariate analysis, or as a univariate spatial temporal model. The multivariate analysis allows researchers to create meaningful clusters that reflect the sometimes complex combinations of conditions of conditions that form suitable habitat, rather then relying on single derived indices.     

昆虫种群动态时空回归预测方法及应用研究

根据昆虫种群内个体空间相互作用的特点,提出分析昆虫种群时空相关的三维相关图方法及种群动态预测的时空混合回归模型,对马尾松毛虫幼虫密切分布的预测采用了时空自回归加空趋势面的形式,预测的马尾松毛虫幼虫的平均密度和实测的平均密度在时空变化的趋势上是完全一致的,而且预测结果给出了马尾松毛虫的幼虫密度分布的图形形式,给防治决策提供了方便。     

Spatial patterning in Polysphondylium: monoclonal antibodies specific for whorl prepatterns

In this report we describe three monoclonal antibodies which detect prepatterning events preceding the appearance of visible tips in Polysphondylium pallidum whorls. A spatial and temporal analysis of the antigens against which these antibodies are directed reveals that the radial distribution of arms within whorls has its origins in an initial global amplification of tip-specific antigens over the surface of very early whorl masses. This two-dimensional distribution becomes restricted with time to a single dimension, a smooth distribution of antigen in a band about the equator of the whorl mass. This equatorial distribution breaks up into patches which eventually become visible tips. These results reveal that a spatial pattern can arise from a smooth prepattern, and grow through a series of intermediates characteristic of the symmetry breaking model first described by A. Turing (1952).     

A model for traveling bands of chemotactic bacteria.

A theoretical model is used to study band formation by chemotactic populations of Escherichia coli. The model includes the bacterial response to attractant gradients, the chemotactic sensitivity of the bacteria to the concentration of the attractant, and population growth. For certain values of the parameters in the model, traveling bands of bacteria form and propagate with or without growth. Under specific growth conditions the band profile is maintained and the band propagates at constant speed. These predictions are in general agreement with the experiment results of J. Adler and earlier theoretical work by L. Segel and his collaborators. However, our theory differs in several important respects from the latter efforts. Suggestions are made for further experiments to test the proposed model and to clarify the nature of the processes which lead to band formation.     

Temporal and spatial scales in epidemiological concepts.

Traditional concepts in epidemiology are reviewed from ecological, cultural, and logical perspectives. In zoological epidemiology (including the study of human and livestock diseases caused by pathogens), temporal and spatial scales are typically not used in definitions, by hypotheses, and theories concerning epidemic and endemic diseases. The same is true for botanical and theoretical epidemiology, although these two subdisciplines use a different definition of an epidemic than does zoological epidemiology. If hypotheses are to be tested and implemented, more precise concepts that include general temporal and spatial scales are needed. Criteria proposed here for identifying temporal and spatial scales are based on the need for consistency of observation and ecological validity. Consistency of observation depends upon the relative life cycles of the hosts and pathogens and upon the environmental effects that lead to stable or unstable population structures. Pathogens are classified as absent, sporadic, or persistent (endemic). Epidemics can occur in the latter two cases but require a separate evaluation. A definition of an epidemic based on temporal and spatial scales and statistics is proposed for use by all subdisciplines. An epidemic occurs when an indicator variable reaches a statistically unusually high value due to transmission of a pathogen in an ecologically proper space-time unit. Threshold theorems in botanical and theoretical epidemiology are also discussed. These proposals do not directly affect modeling, but changes to hypotheses may influence model analyses.     

Spatio‐temporal variation in European starling reproductive success at multiple small spatial scales

Understanding population dynamics requires spatio‐temporal variation in demography to be measured across appropriate spatial and temporal scales. However, the most appropriate spatial scale(s) may not be obvious, few datasets cover sufficient time periods, and key demographic rates are often incompletely measured. Consequently, it is often assumed that demography will be spatially homogeneous within populations that lack obvious subdivision. Here, we quantify small‐scale spatial and temporal variation in a key demographic rate, reproductive success (RS), within an apparently contiguous population of European starlings. We used hierarchical cluster analysis to define spatial clusters of nest sites at multiple small spatial scales and long‐term data to test the hypothesis that small‐scale spatio‐temporal variation in RS occurred. RS was measured as the number of chicks alive ca. 12 days posthatch either per first brood or per nest site per breeding season (thereby incorporating multiple breeding attempts). First brood RS varied substantially among spatial clusters and years. Furthermore, the pattern of spatial variation was stable across years; some nest clusters consistently produced more chicks than others. Total seasonal RS also varied substantially among spatial clusters and years. However, the magnitude of variation was much larger and the pattern of spatial variation was no longer temporally consistent. Furthermore, the estimated magnitude of spatial variation in RS was greater at smaller spatial scales. We thereby demonstrate substantial spatial, temporal, and spatio‐temporal variation in RS occurring at very small spatial scales. We show that the estimated magnitude of this variation depended on spatial scale and that spatio‐temporal variation would not have been detected if season‐long RS had not been measured. Such small‐scale spatio‐temporal variation should be incorporated into empirical and theoretical treatments of population dynamics.     

Spatio-temporal modeling of localized brain activity

Functional neuroimaging, including positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), plays an important role in identifying specific brain regions associated with experimental stimuli or psychiatric disorders such as schizophrenia. PET and fMRI produce massive data sets that contain both temporal correlations from repeated scans and complex spatial correlations. Several methods exist for handling temporal correlations, some of which rely on transforming the response data to induce either a known or an independence covariance structure. Despite the presence of spatial correlations between the volume elements (voxels) comprising a brain scan, conventional methods perform voxel-by-voxel analyses of measured brain activity. We propose a two-stage spatio-temporal model for the estimation and testing of localized activity. Our second-stage model specifies a spatial auto-regression, capturing correlations within neural processing clusters defined by a data-driven cluster analysis. We use maximum likelihood methods to estimate parameters from our spatial autoregressive model. Our model protects against type-I errors, enables the detection of both localized and regional activations (including volume of interest effects), provides information on functional connectivity in the brain, and establishes a framework to produce spatially smoothed maps of distributed brain activity for each individual. We illustrate the application of our model using PET data from a study of working memory in individuals with schizophrenia.     

Bet‐hedging as a complex interaction among developmental instability,environmental heterogeneity,dispersal, and life‐history strategy

One potential evolutionary response to environmental heterogeneity is the production of randomly variable offspring through developmental instability, a type of bet‐hedging. I used an individual‐based, genetically explicit model to examine the evolution of developmental instability. The model considered both temporal and spatial heterogeneity alone and in combination, the effect of migration pattern (stepping stone vs. island), and life‐history strategy. I confirmed that temporal heterogeneity alone requires a threshold amount of variation to select for a substantial amount of developmental instability. For spatial heterogeneity only, the response to selection on developmental instability depended on the life‐history strategy and the form and pattern of dispersal with the greatest response for island migration when selection occurred before dispersal. Both spatial and temporal variation alone select for similar amounts of instability, but in combination resulted in substantially more instability than either alone. Local adaptation traded off against bet‐hedging, but not in a simple linear fashion. I found higher‐order interactions between life‐history patterns, dispersal rates, dispersal patterns, and environmental heterogeneity that are not explainable by simple intuition. We need additional modeling efforts to understand these interactions and empirical tests that explicitly account for all of these factors.     

A model of the human visual system in its response to certain classes of moving stimuli

The purpose of this study is to construct a functional model of the human visual system in its response to certain classes of moving stimuli.Experimental data are presented describing the interdependence of the input variables, temporal frequency, spatial period, etc., for two constant response states, viz. threshold motion response and threshold flicker response. On the basis of these data, two basic units are isolated, a vertical (V) unit and a horizontal (H) unit. The H-unit is identified with the Reichardt multiplier (Reichardt and Varju, 1959), and the V-unit with the de Lange filter (de Lange, 1954).A definition of the general motion response of the H-units is obtained, and this is then reduced to an expression which may be applied directly to the observed motion response data. By this method, Thorson's simplification of the Reichardt scheme (Thorson, 1966) is adopted for the H-unit and total and relative (population) weighting factors, associated with the H-unit output, are defined.In order to reconcile the theoretical square-wave threshold motion response with the experimental data, Thorson's simplification is modified with the introduction of a low-pass filter on the output. The amended scheme is shown to predict a (temporal) frequency-dependent phase-sensitivity. This prediction is tested experimentally, and its validity indicated.     

Oscillations of electric spatial patterns emerging from the homogeneous state in characean cells

Electric spatial patterns of bands formed along the cell wall of the characean internode were studied using a multi-electrode measuring system. The electric potential near the surface of the cell was measured by arranging about 25 electrodes along the cell at approximately 1.6 mm intervals. Since the time required for one scan over the cell length is only 1 s, the temporal change in the spatial pattern of surface electric potential can be readily observed. Oscillations were sometimes found as the electric pattern started to appear after the cell was illuminated. Fourier analysis shows that a single spatial mode arises gradually and then becomes stabilized in an oscillatory manner. A simple electric circuit model comprising three variables, i.e., a membrane potential, an electric current across the membrane and an electromotive force, can simulate well the oscillatory rise of bands. These results imply that the electric spatial pattern observed in characean internodes is a self-organized structure emerging far from equilibrium, known as a dissipative structure. Biophysical mechanisms of band formation are discussed.