A spatio-temporal model of ganglion cell receptive field in the cat retina

A spatio-temporal model of ganglion cell receptive fields is proposed on the basis of receptive field characteristics of cat retinal ganglion cells reported in our previous paper. The model consists of the linear and nonlinear mechanisms in the ganglion cell receptive field. The linear mechanism is assumed to be composed of antagonistic center and surround mechanisms. Then, by integrating these mechanisms we construct a spatio-temporal impulse response function of ganglion cell receptive field. Here we assume that spatio-temporal impulse response function may be factored into spatial and temporal terms. By Fouriertransforming the spatio-temporal impulse response function, we can obtain the spatio-temporal transfer function. Contrast sensitivity characteristics of X-and Y-cells in the cat retina may be explained by the transfer function.     

Spatiotemporal inseparability in early visual processing

We examine the implications of significant inseparable behaviour in centre-surround retinal cell types. From the form of a spatiotemporal centre-surround (CS) model which agrees qualitatively with physiological observations, we find that the sustained/transient dichotomy is a poor distinction for X-type/Y-type retinal ganglion cells since both exhibit inseparability. Static centre-surround models and spatiotemporal separable models are not valid for time-varying stimuli. Our results contradict the models for X- and Y-type ganglion cells proposed by Marr and Hildreth (1980) and Marr and Ullman (1981), and raise doubts about the physiological validity of Marr's zerocrossing theory. The CS filter is an attractive precursor to the extraction of 2-d motion information.     

Two spatio-temporal filters in human vision

1. We have studied visual detection of a circular target moving across a spatially and/or temporally modulated background. Illumination, I _t , for threshold detection of the target has been measured as a function of background modulation frequency and changes in I _t associated with background modulation provide a means of determining the frequency response characteristics of visual channels. 2. Temporal frequency responses obtained with temporally modulated, spatially uniform backgrounds have pass-band characteristics and the temporal frequency for peak response increases with increase in mean background illumination. These temporal frequency responses resemble those of the de Lange (1954) filter, but the latter incorporates the incremental thresholds for steady backgrounds. 3. The amplitude of this temporal response saturates at low (40%) background modulation, decreases to zero as the target velocity falls to zero, and is maximum for a circular target of diameter 2°. 4. The spatial characteristics of this temporal filter were measured with a background field consisting of alternate steady and flickering bars. The resulting spatial frequency curve peaks at 1 cycle deg^-1 for all background illuminations and is independent of the background grating orientation. This spatial response differs significantly from the IMG spatial functions observed with a background grating (Barbur and Ruddock, 1980). 5. The spatial and temporal responses reviewed above exhibit similar parametric variations and we therefore associate them with a single spatiotemporal filter, ST2. 6. A second temporal response, with low-pass frequency characteristics, was observed with a background field consisting of two matched gratings, presented in spatial and temporal antiphase. This response has parametric properties similar to those of the IMG spatial response described previously by Barbur and Ruddock (1980), thus we associated the two sets of data with a single spatio-temporal filter, ST1. 7. We show that the ST2 responses can be obtained by combining ST1 responses, and we present a network incorporating the two filters. 8. We review other psychophysical studies which imply the activity of two spatio-temporal filters with properties of the kind revealed in our studies. We argue that filter ST1 has properties equivalent to those of X-type and filter ST2 has properties equivalent to those of Y-type electrophysiological mechanisms.     

Receptive field mechanisms of ganglion cells in the cat retina

On the basis of anatomical and physiological results of the vertebrate retina, a method is proposed for analysing the respective fields of ganglion cells in the cat retina. In the model, we assume the following: (a) Ganglion cells receive their input from bipolar and/or amacrine cells. (b) The nonlinearity of ganglion cell responses is due to the activities of transient type amacrine cells. The method has been proved to be effective. According to the results of this investigation, the receptive field properties of X type and Y type ganglion cells are heterogeneous. Thus, it may be considered that their receptive fields consist of center and surround mechanisms. The receptive field properties of X-cells are almost linear and the X-cells seem to receive most of their input from bipolar cells. On the other hand, the ones of Y-cells are highly nonlinear. Consequently, it is conceivable that the Y-cells receive their input mainly from transient type amacrine cells.     

In Situ Forming Formulation: Development, Evaluation, and Optimization Using 33 Factorial Design

The present investigation concerns with the development and optimization of an in situ forming formulation using 3³ full factorial design experimentation. Metformin, an antidiabetic drug with upper part of gastrointestinal tract as absorption window was used as a model drug. The formulations were designed with an objective to retain in stomach for an extended time period. The effect of three independent factors—concentrations of sodium alginate (X ₁), gellan gum (X ₂), and metformin (X ₃) on in vitro drug release were used to characterize and optimize the formulation. Five dependent variables—release exponent (Y ₁), dissolution efficiency (Y ₂), drug release at 30 min (Y ₃), 210 min (Y ₄), and 480 min (Y ₅) were considered as optimization factors. The data were statistically analyzed using ANOVA, and a p < 0.05 was considered statistically significant. Three dimensional surface response plots were drawn to evaluate the interaction of independent variables on the chosen dependent variables. Of the prepared 27 formulations, the responses exhibited by batch F17 containing medium level sodium alginate (X ₁), low level gellan (X ₂), and medium level metformin (X ₃) were similar to the predicted responses.     

A unified neural model of spatiotemporal processing in X and Y retinal ganglion cells

This work presents unified analyses of spatial and temporal visual information processing in a feed-forward network of neurons that obey membrane, or shunting equations. The feed-forward shunting network possesses properties that make it well suited for processing of static, spatial information. However, it is shown here that those same properties of the shunting network that lead to good spatial processing imply poor temporal processing characteristics. This article presents an extension of the feed-forward shunting network model that solves this problem by means of preprocessing layers. The anatomical interpretation of the resulting model is structurally analogous to recently discovered data on a retinal circuit connecting cones to retinal ganglion cells through pairs of pushpull bipolar cells. Mathematical analysis of the lumped model leads to the hypothesis that X and Y retinal ganglion cells may consist of a single mechanism acting in different parameter ranges. This hypothesis is confirmed in the companion article, wherein the model in conjunction with a nonlinear temporal adaptation mechanism — is used to reproduce experimental data of both X and Y cells by simple changes in morphological and physiological parameters.     

Optimization of polylactic-co-glycolic acid nanoparticles containing itraconazole using 2<Superscript>3</Superscript> factorial design

This study investigated the utility of a 2³ factorial design and optimization process for polylactic-co-glycolic acid (PLGA) nanoparticles containing itraconazole with 5 replicates at the center of the design. Nanoparticles were prepared by solvent displacement technique with PLGAX ₁ (10, 100 mg/mL), benzyl benzoateX ₂ (5, 20 μg/mL), and itraconazoleX ₃ (200, 1800 μg/mL). Particle size (Y ₁), the amount of itraconazole entrapped in the nanoparticles (Y ₂), and encapsulation efficiency (Y ₃) were used as responses. A validated statistical model having significant coefficient figures (P<.001) for the particle size (Y ₁), the amount of itraconazole entrapped in the nanoparticles (Y ₂), and encapsulation efficiency (Y ₃) as function of the PLGA (X ₁), benzyl benzoate (X ₂), and itraconazole (X ₃) were developed: Y₁=373.75+66.54X₁+52.09X₂+105.06X₃−4.73X₁X₂+46.30X₁X₃; Y₂=472.93+73.45X₁+ 169.06X₂+333.03X₃+62.40X₁X₃+141.49X₂X₃; Y₃= 57.36+6.53X₁+15.52X₂−12.59X₃+1.01X₁X₃+ 1.73X₂X₃.X ₁,X ₂, andX ₃ had a significant effect (P<.001) onY ₁,Y ₂, andY ₃. The particle size, the amount of itraconazole entrapped in the nanoparticles, and the encapsulation efficiency of the 4 formulas were in agreement with the predictions obtained from the models (P<.05). An overlay plot for the 3 responses shows the boundary in whichY ₁ shows the boundary in which a number of combinations of concentration of PLGA, benzyl benzoate, and itraconazole will result in a satisfactory process. Using the desirability approach with the same constraints, the solution composition having the highest overall desirability (D=0.769) was 10 mg/mL of PLGA, 16.94 μg/mL of benzyl benzoate, and 1001.01 μg/mL of itraconazole. This approach allowed the selection of the optimum formulation ingredients for PLGA nanoparticles containing itraconazole of 500 μg/mL.     

Response surface methodology for optimization and characterization of limonene-based coenzyme Q10 self-nanoemulsified capsule dosage form

The aim of this study was to systematically obtain a model of factors that would yield an optimized self-nanoemulsified capsule dosage form (SNCDF) of a highly lipophilic model compound, Coenzyme Q10 (CoQ). Independent variables such as amount of R-(+)-limonene (X ₁), surfactant (X ₂), and cosurfactant (X ₃), were optimized using a 3-factor, 3-level Box-Behnken statistical design. The dependent variables selected were cumulative percentage of drug released after 5 minutes (Y ₁) with constraints on drug release in 15 minutes (Y ₂), turbidity (Y ₃), particle size (Y ₄), and zeta potential (Y ₅). A mathematical relationship obtained,Y ₁=78.503+6.058X ₁ +13.738X ₂+5.986X ₃−25.831X ₁ ² +9.12X ₁X₂−26.03X ₁X₃−38.67X ₂ ² +11.02X ₂X₃−15.55X ₃ ³ (r ²=0.97), explained the main and quadratic effects, and the interaction of factors that affected the drug release. Response surface methodology (RSM) predicted the levels of factorsX ₁,X ₂, andX ₃ (0.0344, 0.216, and 0.240, respectively), for a maximized response ofY ₁ with constraints of >90% release onY ₂. The observed and predicted values ofY ₁ were in close agreement. In conclusion, the Box-Behnken experimental design allowed us to obtain SNCDF with rapid (>90%) drug release within 5 minutes with desirable properties of low turbidity and particle size.     

The Mean of the Inverse of a Punctured Normal Distribution and Its Application

The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μ_X and μ_Y respectively. First, estimation of μ_X/μ_Y as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μ_X/μ_Y is given. Finally, an approximate confidence interval for μ_X/μ_Y is provided. A grain yield data set is used to illustrate the results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Four Applications of a Bivariate Pareto Distribution

The following model, of “latent structure” type, is considered: in each subpopulation, X and Y are random variables drawn independently from the same exponential distribution, and the parameter of the exponential distribution varies between subpopulations with a Gamma density. Over the whole population, X and Y are then positively correlated, and jointly have a bivariate PARETO distribution. Four examples show how this distribution is useful in analysing ordered contingency tables in which the two dimensions can be regarded as alternative measures of the same thing: the injuries to the two drivers in a road accident, or the severity of a lesion present in a patient as assessed by two physicians, for instance. Two extensions are considered: (a) allowing X and Y to have Gamma distributions, with each subpopulation having the same shape parameter but different scale parameters; (b) allowing the scale parameter for Y to be correlated with the scale parameter for X, rather than being identical to it. A new bivariate distribution with three shape parameters is derived, expressed in terms of a generalised hypergeometric function.     

On Mohan's Property of the Poisson Distribution

Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to Moran (1952) and Patil & Seshadri (1964), respectively. Morans result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown that if Y, Z are independent, non-negative, integer-valued random variables with X = Y | Z then, under some mild restrictions, the conditional distribution of Y | X is binomial if and only if Y, Z are Poisson random variables. Motivated by Morans result Patil & Seshadri obtained a general characterization. A special case of this characterization suggests that, with conditions similar to those imposed by Moran, Y | X is negative hypergeometric if and only if Y, Z are negative binomials. In this paper we examine the results of Moran and Patil & Seshadri in the case where the conditional distribution of Y | X is truncated at an arbitrary point k – 1 (k = 1, 2, …). In fact we attempt to answer the question as to whether Morans property of the Poisson distribution, and subsequently Patil & Seshadris property of the negative binomial distribution, can be extended, in one form or another, to the case where Y | X is binomial truncated at k – 1 and negative hypergeometric truncated at k – 1 respectively.     

Formulation of Dacarbazine-loaded Cubosomes—Part II: Influence of Process Parameters

The purpose of this study was to investigate the combined influence of three-level, three-factor variables on the formulation of dacarbazine (a water-soluble drug) loaded cubosomes. Box–Behnken design was used to obtain a second-order polynomial equation with interaction terms to predict response values. In this study, the selected and coded variables X ₁, X ₂, and X ₃ representing the amount of monoolein, polymer, and drug as the independent variables, respectively. Fifteen runs of experiments were conducted, and the particle size (Y ₁) and encapsulation efficiency (Y ₂) were evaluated as dependent variables. We performed multiple regression to establish a full-model second-order polynomial equation relating independent and dependent variables. A second-order polynomial regression model was constructed for Y ₁ and confirmed by performing checkpoint analysis. The optimization process and Pareto charts were obtained automatically, and they predicted the levels of independent coded variables X ₁, X ₂, and X ₃ (−1, 0.53485, and −1, respectively) and minimized Y ₁ while maximizing Y ₂. These corresponded to a cubosome formulation made from 100 mg of monoolein, 107 mg of polymer, and 2 mg with average diameter of 104.7 nm and an encapsulation efficiency of 6.9%. The Box–Behnken design proved to be a useful tool to optimize the particle size of these drug-loaded cubosomes. For encapsulation efficiency (Y ₂), further studies are needed to identify appropriate regression model.     

Applying Canonical Analysis to a Kind of Generalized Regression

This paper is concerned with the generalized model E(φ(Y)! X) =φ(X) involving the transformations on both the predictor vector X and the response variable Y. For this purpose, Taylor expansions and canonical analysis are applied. For optimizing the expansions, it is shown by a simulation study that not only prediction error, the combination of model error and noise error, is an important index, but the distribution of the residuals and the t-values of the coefficients also must be considered. Furthermore, the results of penicillin titrition show that the practical situations often need to be considered in selecting an appropriate model for a real-life problem.     

Properties of the sex chromosomes of Lucilia cuprina deduced from radiation studies

From a study of radiation-induced X-chromosome deletions the locus of black body (b) has been localized to the proximal portion of C-band defined euchromatin. Radiation produced mostly X-chromosome deletions rather than point mutations, total X or Y chromosome loss through breakage, or increased frequency of non-disjunction. Aberrant sex ratios obtained indicate that the X chromosome carries vital loci that were deleted with b ⁺ in many cases. The X/O karyotype produces fertile adult females with a characteristic phenotype which is also produced by X deletions. Sex chromosome non-disjunction to give X/O females and X/X/Y males is normally rare but is enhanced by the presence of chromosome rearrangements even when the X and Y are not involved.     

Pleiotropic effects associated with the deletion of heterochromatin surrounding rDNA on the X chromosome of Drosophila

In Drosophila melanogaster X chromosome heterochromatin (Xh) constitutes the proximal 40% of the X chromosome DNA and contains a number of genetic elements with homologous sites on the Y chromosome, one of which is well defined, namely, the bobbed locus, the repetitive structural locus for the 18S and 28S rRNAs. This report presents the localisation of specific repeated DNA sequences within Xh and the employment of this sequence map in constructing new chromosomes to analyse the nature of the heterochromatin surrounding the rDNA region. Repeated sequences were located relative to inversion breakpoints which differentiate Xh cytogenetically. When the rDNA region was manipulated to be in a position in the chromosome so that it was without the Xh which normally surrounds it, the following obser-vations were made, (i) The rDNA region of Xh is intrinsically hetero-chromatic, remaining genetically active and yet possessing major heterochromatic properties even in the absence of the flanking heterochromatin regions, (ii) The size of the deletion removing the portion of Xh normally located distal to the rDNA region affected the dominance relationship between the X and Y nucleolar organizers (activity/endoreduplication assayed in male salivary glands). The X rDNA without any flanking heterochromatin was dominant over Y rDNA while the presence of some Xh allowed both the X and Y rDNA to be utilized, (iii) Enhancement of the position effect variegation on the white locus was demonstrated to occur as a result of the Xh deletions generated. EMS mutagenesis studies argue that the regions of Xh flanking the rDNA region contain no vital loci despite the fact that they strongly effect gene expression in some genotypes. This is consistent with early studies using X-ray mutagenesis (Lindsley et al., 1960). The pleiotropic effects of deleting specific regions of Xh is discussed in relation to the possible influence of heterochromatin on the organisation of the functional interphase nucleus.     

The relationship of environment size and population parameters Oxytrema proxima (say) (Gastropoda: Pleuroceridae)

Summary Environmental size, as measured by cross-sectional area of the inhabited streams, and population density of Oxytrema proxima are related by the power function Y=8.074X ^-0.584, where Y=population density and X=cross-sectional area of the stream. Relationships were also found between maximum size and biomass and cross-sectional area, but maximum size and biomass were more closely related to population density by the equations Y=8.832X ^-0.064 (Y=maximum individual size, X=density) and Y=6.730X ^0.459 (Y=biomass (total live weight), X=density). This is interpreted as evidence that environment size acts directly on density, which in turn produces effects on maximum size, total live weight, and to a lesser extent mean size. The inverse relationship between population size and environment has not been previously reported. It is clear that in this case this distribution and abundance of O. proxima are closely related, and that this can be so when populations disperse extremely poorly as well as extremely well. This must mean that dispersal is secondary in importance to population stability as an influence on distribution and abundance.Part of the Ph.D. dissertation of the senior author. Support from NASA predoctoral fellowship to the senior author, NSF grant GB-5039 to the junior author, and NIH grant ES 00101-01 to K.E.F. Watt is acknowledged.     

Theoretical study on the aromaticity from d-AOs in cationic X 3 + (X = Sc,Y, La) clusters

The stable structures and aromatic characters for three cationic X₃⁺ (X = Sc, Y, and La) and three relevant neutral X₃Cl (X = Sc, Y, La) clusters are investigated at the DFT and post HF level of theory. The calculated results show that the X₃⁺ cations each has two stable structures: the regular trigon (D_3h) and the line (D_￥h {{\hbox{D}}_{\infty {\rm{h}}}} ) with the regular trigon (D_3h) being the ground state, while for three neutral X₃Cl clusters, Sc₃Cl has three stable isomers: the trigon-pyramidal (C_3v), bidentate (C_2v-1), and C_2v-2 structures, Y₃Cl and La₃Cl each has only two stable isomers: the trigon-pyramidal (C_3v) and bidentate (C_2v-1) structures. The ground states for three X₃Cl species are all the bidentate (C_2v-1) isomers. The calculations of the resonance energy (RE) and NICS show that trigonal X₃⁺ isomers exhibit higher degree of aromaticity. The detailed molecular orbital analyzes reveal that the isolated trigonal Sc₃⁺ and Y₃⁺ cations each has one delocalized π-type MO and shows single π-aromaticity, while the isolated trigonal La₃⁺ cation has one delocalized σ-type MO and shows single σ-aromaticity. The single π- or σ-aromaticity for X₃⁺ are attributed to the contributions mainly from the d AOs of the corresponding transition metal X atoms. However, when a singly negatively charged counterion Cl^- is added to Sc₃⁺, Y₃⁺, and La₃⁺ cations respectively, the aromatic type for the two Sc₃⁺, Y₃⁺ units in the corresponding neutral Sc₃Cl, Y₃Cl complexes are changed from π-aromaticity into σ-aromaticity, whereas the σ-aromaticity of the La₃⁺ units in the La₃Cl complex keeps unchanged in this process. Thus three Sc₃⁺, Y₃⁺, La₃⁺ units in the corresponding X₃Cl complexes all have only one σ-type MO and exhibit single σ-aromaticity.     

An example of a regular inbreeding system with cubic ancestral growth that preserves some genetic variability

A specific regular inbreeding system of quadruple half-second cousin mating is considered. A regular inbreeding system can be thought of as a graph which satisfies certain natural homogeneity properties. Random walks X _n and Y _n are introduced on the nodes of the graph; the event {X _n=Y_n} is a renewal event by the homogeneity properties. In Arzberger (1985) it is shown that 1) graphs associated with left cancellative semigroups are regular, and 2) for regular systems, the population becomes genetically uniform if and only if the event {X _n=Y_n} is recurrent. In Arzberger (1986) the system of quadruple half-second cousin mating is associated with a cancellative semigroup, thus the system is regular. In this paper we show that 1) A_n is asymptotically of the form cn ³, where A _n is the number of ancestors n generations into the past, 2) {X _n=Y_n} is not recurrent (this is shown by associating (X _n, Y _n) with a random walk in Z ³, 3) P[X _3n =Y _3n ] is asymptotically of the form cn ^–3/2. Thus, in this example, genetic heterogeneity is maintained, with a cubic rate of growth for A_n, not by an exponential growth rate, as in all previous examples of regular inbreeding systems in which genetic heterogeneity is maintained.     

Chloroplast translocations in Lemna trisulca L. induced by continuous irradiation and by light pulses

The analytical model describing the steady state position of chloroplasts in dependence of fluence rate as well as the chloroplast response to single strong light pulses has been proposed. The model is based on the following assumptions: 1. Irradiation of the cell generates the state X in the cell membrane region, proportional to the local fluence rate. After switching on the light, the value of X increases exponentially with the time constant of about 3 min. The dark decay of X is also exponential with the same time constant. The level of X controls all kinds of chloroplast arrangements. 2. The state X generates two further states: Y ₁ and Y ₂, the first of them representing attraction forces for chloroplasts and the second representing repulsion forces. Empirical equations have been found for both Y states. The fluence rate response curve can be described with the use of functions Y ₁ and Y ₂. 3. The kinetic analysis requires the introduction of two additional functions Z in order to account for delays and time dispersion of the chloroplast movement in response to driving and resistance factors. The computer program for the proposed model was developed and the results of calculations were compared with experimental data (fluence rate response curve and pulse effects) with satisfactory agreement. Initially no attempt was made to ascribe any physical meaning to the postulated states. Some suggestions in this respect are mentioned in the discussion.     

Lysine Requirements of Rats of Various Body Weights

The lysine requirements of rats of various body weights were estimated using the feeding and isotope tests.

The regression equation obtained by the feeding test was Y= 1.03 – 0.58 log X. Where Y is lysine percentage of the diet and X is the mean of initial and final body weights (g) of rats achieving optimal growth gains during the feeding period.

The regression equation obtained by the isotope test was 7=0.90 – 0.49 log X, where Y and X are lysine percentage in the diet and body weights (g) of rats achieving optimal growth gains at the injection time respectively.