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PubMed2006

Derivation of the percolation threshold for the network model of Barabási and Albert.

The percolation threshold of the network model by Barabási and Albert [Science 286, 509 (1999)] (BA) has thus far only been "guessed" based on simulations and comparison with other models. Due to the still uncertain influence of correlations, the reference to other models cannot be justified. In this paper, we explicitly derive the well-known values for the BA model. To underline the importance of a null model like that of Barabási and Albert, we close with two basic remarks. First, we establish a connection between the abundance of scale-free networks in nature and the fact that power-law tails in the degree distribution result only from (at least asymptotically) linear preferential attachment: Only in the case of linear preferential attachment does a minimum of topological knowledge about the network suffice for the attachment process. Second, we propose a very simple and realistic extension of the BA model that accounts for clustering. We discuss the influence of clustering on the percolation properties.

Journal Article↗
PubMed2006

Population models for threshold-based control of Tetranychus urticae in small-scale Kenyan tomato fields and for evaluating weather and host plant species effects.

The spatial distribution of motile life stages of the two-spotted spider mite Tetranychus urticae Koch in Kenyan small-scale tomato fields was described by Taylor's power law and an enumerative sampling plan was designed for research purposes. The exponential increase of T. urticae populations during three growing seasons permits the development and use of a simple exponential model for the design of a threshold-based chemical control system. For this purpose, a critical threshold of 440 motile mites per sample unit at the end of the growing season (12 weeks after transplanting) was translated into a proportion of 0.83 infested units in sample 3, i.e. five weeks after transplanting. A sequential binomial sampling plan with respect to the proportion of 0.83, five weeks after transplanting, was designed. The exponential model was extended to account for the influence of weather and host plant species. Model development and parameter estimation were based on three data sets (Kenyan tomato fields, Italian and Californian strawberry fields). The model satisfactorily predicted a positive influence on growth rates by (i) changing the host plant from tomato to strawberry, and (ii) temperature, while a negative effect resulted from (iii) rainfall; both (ii) and (iii) are controlled by temperature-rainfall interactions. In contrast, the estimated parameter values did not satisfactorily describe the expected responses at specific temperature and rainfall values. Nevertheless, the model allowed the rating of host plant species in the field. A fourth data set from Swiss apple orchards was used to test the model, and population build-up on the apple host plant appeared to be higher than on tomatoes but lower than on strawberry.

Animals↗
PubMed2006

Multiple thresholds in a model system of noisy ion channels.

Voltage-activated ion channels vary randomly between open and closed states, influenced by the membrane potential and other factors. Signal transduction is enhanced by noise in a simple ion channel model. The enhancement occurs in a finite range of signals; the range can be extended using populations of channels. The range increases more rapidly in multiple-threshold channel populations than in single-threshold populations. The diversity of ion channels may thus be present as a strategy to reduce the metabolic costs of handling a broad class of electrochemical signals.

Cell Membrane↗
PubMed1988

Adaptive staircase techniques in psychoacoustics: a comparison of human data and a mathematical model.

Data from a simple tone-in-noise simultaneous masking task were used to evaluate each of two common adaptive staircase rules (a "1 up 2 down" rule and a "1 up 3 down" rule) and the parameter estimation by sequential testing (PEST) technique in combination with each of two psychophysical procedures [a two-alternative forced-choice (2AFC) and a three-alternative forced-choice (3AFC) procedure]. These human data were compared to predictions generated by a mathematical model based on Markov theory. The model predicts that threshold estimates obtained with the adaptive techniques should be equal to those derived with equivalent "fixed signal level" techniques. However, the human data indicate that the adaptive techniques tend to yield lower thresholds. The model predicts that the standard error of a threshold estimate obtained from an adaptive technique will decrease and approach zero as the number of trials used to compute the estimate increases. The human data show greater variability than predicted and approach a nonzero value as the number of trials increases. The predictions of the model suggest that the commonly used combination of the 2AFC procedure and the 1 up 2 down rule is the least efficient method of estimating a threshold and that the 3AFC procedure in combination with the 1 up 3 down rule is the most efficient method. The human data are less consistent, but generally show the combination of the 2AFC procedure and the 1 up 2 down rule to be one of the least efficient methods. Possible explanations for the differences between the model's predictions and the human data, as well as suggestions for laboratory practice, are discussed.

Adult↗
PubMedDate not supplied

A new threshold dose-response model including random effects for data from developmental toxicity studies.

Usually, in teratological dose finding studies, there are not only threshold effects but also extra variations that cannot be accounted for by the beta-binomial model alone. The beta-binomial model assumes correlation between fetuses in the same litter. The general random effect threshold (RE) model allows the additional variability that arises due to correlation and between litter variability to be modeled, in combination with threshold in the model. The goal of this research was to investigate a threshold dose-response model with random effects (RE) to model the variability that exists between litters of animals in studies of toxic agents. Data from a developmental toxicity study of a toxic agent were analysed, using the proposed RE threshold dose-response model, which is an extension of logit in form. Also, an approximate likelihood function was used to derive parameter estimates from this model, and tests were performed to determine the significance of the model parameters, in particular, the RE parameter. A simulation study was conducted to assess the performance of the RE threshold model in estimating the model parameters.

Algorithms↗
PubMed1990

Importance of a threshold for error accumulation in cell degenerative processes. I. Modulation of the threshold in a model of free radical-induced cell degeneration.

Antioxidant enzymes (catalase, superoxide dismutase and glutathione peroxidase) have been injected into human fibroblasts exposed to 2 atm O2 in order to test if the threshold of oxidative damage versus antioxidant defenses could be modulated and if the damage remains reversible beyond the threshold. Cell damage was estimated by thymidine incorporation and cell survival curves. The proportion of dividing cells, measured by thymidine incorporation, rapidly decreased after O2 incubation: no cells could divide after 15 h of hyperoxia. However, cells incubated for a short time and injected with a high concentration of any of the three enzymes divided like non-oxygen-incubated cells: the enzymes could protect the cells against their loss of division potential. However, when cells were incubated for a longer period and/or when the injected enzyme concentration was lower, cells were either less or not protected and could no longer divide. These results suggest the presence of a threshold for the oxidative damage which cannot be totally repaired and which impairs the cell division; this threshold can, however, be modulated by supplementation of antioxidant enzymes, glutathione peroxidase being the most efficient.

Catalase↗
PubMed2002

A model for odour thresholds.

Odour detection thresholds, that we have previously obtained, have been analysed by a general equation for selective transport. It is shown that such selective transport can account for some 77% of the total effect. The remainder is due to a specific size effect, that might involve odour-binding proteins, and a specific effect for aldehydes and carboxylic acids. Our analysis raises the question of whether selective transport is physically separable from the specific effects of receptor activation. The model predicts a chemical cut-off in odour detection along any homologous series.

Aldehydes↗
PubMed1999

Energy model for contrast detection: spatiotemporal characteristics of threshold vision.

A model for contrast detection of spatiotemporal stimuli is proposed which consists of a spatiotemporal linear filter, an energy device and a threshold device. Assuming the existence of independent intrinsic noise, the probability of stimulus detection was approximated by a Weibull function of the response energy. With this assumption, the stimulus energy is a constant at fixed detection probability. This energy model for contrast detection satisfactorily accounted for the elliptical threshold contours of line pairs at stimulus separations within the range 2-30 min and at stimulus onset asynchronies within the range 20-140 ms. The threshold contour at a large stimulus onset asynchrony (300 ms) was in the form of a rounded square. This finding was explained by assuming that the probability of seeing the line pair was determined by the joint probability that at least one stimulus had been detected. With the energy model, the temporal and spatial autocorrelation functions of the response to a flashed line were evaluated. The autocorrelation functions thus determined were used to predict the temporal contrast sensitivity function to a flickering line stimulus and the spatial contrast sensitivity function to flashed gratings, which were in agreement with the experimental data. The data obtained were fitted adequately by an impulse response approximated by a spatiotemporal Gabor-like function.

Contrast Sensitivity↗
PubMed1997

A thermal model for human thresholds of microwave-evoked warmth sensations.

Human thresholds for skin sensations of warmth were measured at frequencies from 2.45 to 94 GHz. By solving the one-dimensional bioheat equation, we calculated the temperature increase at the skin surface or at a depth of 175 microm at incident power levels corresponding to the observed thresholds. The thermal analysis suggests that the thresholds correspond to a localized temperature increase of about 0.07 degrees C at and near the surface of the skin. We also found that, even at the highest frequency of irradiation, the depth at which the temperature receptors are located is not a relevant parameter, as long as it is within 0.3 mm of the surface. Over the time range of the simulation, the results of the thermal model are insensitive to blood flow, but sensitive to thermal conduction; and this sensitivity increases strongly with frequency. We conclude with an analysis of the effect of thermal conduction on surface temperature rise, which becomes a dominant factor at microwave frequencies over 10 GHz.

Adult↗
PubMed2006

Reply to comment on "Auditory-nerve first-spike latency and auditory absolute threshold: a computer model".

Krisha [J. Acoust. Soc. Am., in press (2006)] has commented that an explanation based on presynaptic calcium accumulation at the inner hair cell is an incorrect explanation for the success of a model of the auditory periphery [Meddis, R., J. Acoustic. Soc. Am. 119, 406-417 (2006)] in explaining data on first-spike auditory nerve latency. This reply accepts the criticism and accepts the strength of an alternative explanation based on expected latencies in random sequences of low-probability events. This reply also goes on briefly to explore the application of this argument to other phenomena, including the dependence of absolute auditory threshold on the duration of the stimulus. This has wide-ranging implications for the concept of "temporal integration" in psychophysics.

Action Potentials↗
PubMed2000

Molecular mechanisms of radiation carcinogenesis and the linear, non-threshold dose response model of radiation risk estimation.

Recent research in molecular radiation carcinogenesis is reviewed with the specific aim of exploring the implications this research may have on the dose response relationship of radiation-induced cancer at low doses and low dose rates. It is concluded that the linear non-threshold dose response hypothesis may be used in radiation protection planning as a simple, convenient method to optimize procedures and regulations, but should not be mistaken as a stringent scientific conclusion directly derived from the present state of knowledge of the processes involved in radiation carcinogenesis.

DNA Repair↗
PubMed2003

Effect of harmane on the convulsive threshold in epilepsy models in mice.

The study investigated the activity of harmane on maximal electroshock seizures (MES) and seizures induced by pentilentetrazole (PTZ) in mice. Initial studies established convulsive current 50 (CC(50)) values or MES and effective dose 50 (ED(50)) for PTZ to produce seizures. Harmane (2.5, 5.0, or 10 mg/kg intraperitoneally) increased the threshold of seizures in MES dose-dependently. The convulsions produced by PTZ were decreased by the low dose of harmane (2.5 mg/kg), but the high dose of harmane (10 mg/kg) resulted in worse grade V convulsions followed by more lethality compared with PTZ alone. Therefore, harmane seems to be protective against grand mal seizures in the MES model but not against a petit mal seizure model (PTZ) in mice.

Animals↗
PubMed1997

Manual interception of moving targets. I. Performance and movement initiation.

We investigated the capacities of human subjects to intercept moving targets in a two-dimensional (2D) space. Subjects were instructed to intercept moving targets on a computer screen using a cursor controlled by an articulated 2D manipulandum. A target was presented in 1 of 18 combinations of three acceleration types (constant acceleration, constant deceleration, and constant velocity) and six target motion times, from 0.5 to 2.0 s. First, subjects held the cursor in a start zone located at the bottom of the screen along the vertical meridian. After a pseudorandom hold period, the target appeared in the lower left or right corner of the screen and traveled at 45 degrees toward an interception zone located on the vertical meridian 12.5 cm above the start zone. For a trial to be considered successful, the subject's cursor had to enter the interception zone within 100 ms of the target's arrival at the center of the interception zone and stay inside a slightly larger hold zone. Trials in which the cursor arrived more than 100 ms before the target were classified as "early errors," whereas trials in which the cursor arrived more than 100 ms after the target were classified as "late errors." Given the criteria above, the task proved to be difficult for the subjects. Only 41.3% (1080 out of 2614) of the movements were successful, whereas the remaining 58.7% were temporal (i.e., early or late) errors. A large majority of the early errors occurred in trials with decelerating targets, and their percentage tended to increase with longer target motion times. In contrast, late errors occurred in relation to all three target acceleration types, and their percentage tended to decrease with longer target motion times. Three models of movement initiation were investigated. First, the threshold-distance model, originally proposed for optokinetic eye movements to constant-velocity visual stimuli, maintains that response time is composed of two parts, a constant processing time and the time required for the stimulus to travel a threshold distance. This model only partially fit our data. Second, the threshold-tau model, originally proposed as a strategy for movement initiation, assumes that the subject uses the first-order estimate of time-to-contact (tau) to determine when to initiate the interception movement. Similar to the threshold distance model, the threshold-tau model only partially fit the data. Finally, a dual-strategy model was developed which allowed for the adoption of either of the two strategies for movement initiation; namely, a strategy based on the threshold-distance model ("reactive" strategy) and another based on the threshold-tau model ("predictive" strategy). This model provided a good fit to the data. In fact, individual subjects preferred to use one or the other strategy. This preference was allowed to be manifested at long target motion times, whereas shorter target motion times (i.e., 0.5 s and 0.8 s) forced the subjects to use only the reactive strategy.

Adult↗
PubMed2003

Evaluation models and genetic parameters for calving difficulty in beef cattle.

Calving difficulty was analyzed under threshold and linear models considering either a fixed or random herd-year effect. The aim of the study was to compare models for predicting breeding values according to the size of herd-year groups. When simulating data sets with small herds, in order to obtain an unbiased evaluation under a nonrandom and negative association of sire and herd effects, the best model for a practical evaluation was the fixed linear model. Field data included 246,576 records of the largest Charolais herds in France. Models were compared using the correlations of estimated breeding values between the different models. Although the best model from a theoretical point of view was a threshold model with a fixed herd-year effect, a linear model with a fixed herd-year effect was the best choice from a practical point of view for predicting direct effects for calving difficulty in beef cattle and was a sufficient choice for predicting the associated maternal effects for data set with large herds. Correlations between direct estimated breeding values under the reference model and the fixed linear model and the random threshold model were 0.94 and 0.91, respectively. Correlations between the corresponding maternal estimated breeding values were 0.94 and 0.98. Heritabilities of direct effects were 0.27 and 0.14 under fixed threshold and fixed linear models, respectively. The corresponding heritabilities of maternal effects were 0.18 and 0.13, and the genetic correlation between direct and maternal effects were -0.36 and -0.34, respectively.

Animal Husbandry↗
PubMed2006

Sex ratio variation in Iberian pigs.

Within the area of sex allocation, one of the topics that has attracted a lot of attention is the sex ratio problem. Fisher (1930) proposed that equal numbers of males and females have been promoted by natural selection and it has an adaptive significance. But the empirical success of Fisher's theory remains doubtful because a sex ratio of 0.50 is also expected from the chromosomal mechanism of sex determination. Another way of approaching the subject is to consider that Fisher's argument relies on the underlying assumption that offspring inherit their parent's tendency in biased sex ratio and therefore that genetic variance for this trait exists. Here, we analyzed sex ratio data of 56,807 piglets coming from 550 boars and 1893 dams. In addition to classical analysis of heterogeneity we performed analyses fitting linear and threshold animal models in a Bayesian framework using Gibbs sampling techniques. The marginal posterior mean of heritability was 2.63 x 10(-4) under the sire linear model and 9.17 x 10(-4) under the sire threshold model. The probability of the hypothesis p(h(2) = 0) fitting the last model was 0.996. Also, we did not detect any trend in sex ratio related to maternal age. From an evolutionary point of view, the chromosomal sex determination acts as a constraint that precludes control of offspring sex ratio in vertebrates and it should be included in the general theory of sex allocation. From a practical view that means that the sex ratio in domestic species is hardly susceptible to modification by artificial selection.

Animals↗
PubMed2001

Comparison of threshold vs linear and animal vs sire models for predicting direct and maternal genetic effects on calving difficulty in beef cattle.

This study compared the accuracy of several models for obtaining genetic evaluations of calving difficulty. The models were univariate threshold animal (TAM), threshold sire-maternal grandsire (TSM), linear animal (LAM), and linear sire-maternal grandsire (LSM) models and bivariate threshold-linear animal (TLAM), threshold-linear sire-maternal grandsire (TLSM), linear-linear animal (LLAM), and linear-linear sire-maternal grandsire (LLSM) models for calving difficulty and birth weight. Data were obtained from the American Gelbvieh Association and included 84,420 first-parity records of both calving difficulty and birth weight. Calving difficulty scores were distributed as 73.4% in the first category (no assistance), 18.7% in the second, 6.3% in the third, and 1.6% in the fourth. Included in the animal models were fixed sex of calf by age of dam subclasses, random herd-year-season effects, and random animal direct and maternal breeding values. Sire-maternal grandsire models were similar to the animal models, with animal and maternal effects replaced by sire and maternal grandsire effects. Models were compared using a data splitting technique based on the correlation of estimated breeding values from two samples, with one-half of the calving difficulty records discarded randomly in the first sample and the remaining calving difficulty records discarded in the second sample. Reported correlations are averages of 10 replicates. The results obtained using animal models confirmed the slight advantage of TAM over LAM (0.69 vs 0.63) and TLAM over LLAM (0.90 vs 0.86). Bivariate analyses greatly improved the accuracy of genetic prediction of direct effects on calving difficulty relative to univariate analyses. Similar ranking of the models was found for maternal effects, but smaller correlations were obtained for bivariate models. For sire-maternal grandsire models, no differences between sire or maternal grandsire correlations were observed for TLSM compared to LLSM, and small differences were observed between TSM and LSM. The threshold model offered advantages over the linear model in animal models but not in sire-maternal grandsire models. For genetic evaluation of calving difficulty in beef cattle, the threshold-linear animal model seems to be the best choice for predicting both direct and maternal effects.

Animal Husbandry↗
PubMed2003

Application of fluid modeling to determine threshold leak size for liquid foods.

In this study, the mechanism by which a package defect converts to a leaker was examined in an effort to develop a relationship between threshold leak size and loss of package sterility. The threshold leak size is the hole size at which the onset of leakage occurs. The threshold pressure is the pressure required to initiate a leak. Leak initiation was studied in terms of the interaction between three components: liquid attributes of liquid food products, defect size, and pressures required to initiate liquid flow. Liquid surface tension, viscosity, and density values were obtained for 16 liquids. The imposed pressures required to initiate flow through microtubes with interior diameters of 0, 2, 5, 7, 10, 20, and 50 microm were measured with the use of 63 test cells filled with safranin red dye, tryptic soy broth, and distilled water with surface tensions of 18.69, 44.09, and 64.67 mN/m, respectively. Significant differences (P<0.05) between threshold pressures observed for safranin red dye, tryptic soy broth, and distilled water were found. Liquids with low surface tensions, such as safranin red dye, required significantly lower threshold imposed pressures than did liquids with high surface tensions, such as distilled water (P<0.05). An equation to quantify the relationship between liquid surface tension, threshold imposed pressure, and defect size was developed. Threshold pressures observed were not significantly different (P>0.05) from those predicted by the equation. Imposed pressures and vacuums generated within packages during random vibration and sweep resonance tests were measured for brick-style aseptic packages (250 ml), metal cans (76.2 by 114.3 mm [425 ml]), 1-qt gable-top packages (946 ml), 0.5-gal gable-top packages (1.89 liters), and 1-gal milk jugs (4.25 liters). Significant differences between packages were found with respect to observed generated pressures during vibration testing (P<0.05). An equation to calculate threshold size on the basis of liquid surface tension and imposed pressure was established.

Chemical Phenomena↗