The combined effects of delay and probability in discounting

Human discounting studies have frequently observed hyperbolic discounting of rewards that are delayed or probabilistic. However, no studies have systematically combined delay and probability in a single discounting procedure. Indifference points of hypothetical money rewards that are both delayed and probabilistic were determined. Probabilities were converted into comparable delays according to the h/k constant of proportionality determined by , and discounting rates were calculated. These data provided a very good fit to the hyperbolic model of discounting, suggesting that delay and probability can be combined into a single metric in studies of discounting. The inclusion of a magnitude condition found the Magnitude Effect commonly found in studies of temporal discounting. A temporal resolution of uncertainty condition found no effect. The present paper offers a novel statistical method, within an established framework, for the analysis of data from studies of discounting that combine delay and probability.     

On the scaling interpretation of exponents in hyperboloid models of delay and probability discounting

Previously, we (McKerchar et al., 2009) showed that two-parameter hyperboloid models ( [Green and Myerson, 2004] and [Rachlin, 2006]) provide significantly better fits to delay discounting data than simple, one-parameter hyperbolic and exponential models. Here, we extend this effort by comparing fits of the two-parameter hyperboloid models to data from a larger sample of participants (N = 171) who discounted probabilistic as well as delayed rewards. In particular, we examined the effects of amount on the exponents in the two hyperboloid models of delay and probability discounting in order to evaluate key theoretical predictions of the standard psychophysical scaling interpretation of these exponents. Both the Rachlin model and the Green and Myerson model provided very good fits to delay and probability discounting of both small and large amounts at both the group and individual levels (all R²s > .97 at the group level; all median R²s > .92 at the individual level). For delay discounting, the exponent in both models did not vary as a function of delayed amount, consistent with the psychophysical scaling interpretation. For probability discounting, however, the exponent in both models increased as the probabilistic amount increased—a finding inconsistent with the scaling interpretation.     

Monkeys Are More Patient in a Foraging Task than in a Standard Intertemporal Choice Task

Studies of animal impulsivity generally find steep subjective devaluation, or discounting, of delayed rewards – often on the order of a 50% reduction in value in a few seconds. Because such steep discounting is highly disfavored in evolutionary models of time preference, we hypothesize that discounting tasks provide a poor measure of animals’ true time preferences. One prediction of this hypothesis is that estimates of time preferences based on these tasks will lack external validity, i.e. fail to predict time preferences in other contexts. We examined choices made by four rhesus monkeys in a computerized patch-leaving foraging task interleaved with a standard intertemporal choice task. Monkeys were significantly more patient in the foraging task than in the intertemporal choice task. Patch-leaving behavior was well fit by parameter-free optimal foraging equations but poorly fit by the hyperbolic discount parameter obtained from the intertemporal choice task. Day-to-day variation in time preferences across the two tasks was uncorrelated with each other. These data are consistent with the conjecture that seemingly impulsive behavior in animals is an artifact of their difficulty understanding the structure of intertemporal choice tasks, and support the idea that animals are more efficient rate maximizers in the multi-second range than intertemporal choice tasks would suggest.     

Repeated injection (continuous labelling) experiments in mouse epidermis

Theoretical labelling index curves for epidermis have been generated under conditions of repeated tritiated thymidine injection. These curves take into account different injection intervals, circadian fluctuations in labelling and two different models for epidermal proliferation; one based on a homogeneous basal layer with “random” loss initially (later, loss was restricted to late G₁), and the other based on a programmed sequential aging of proliferative cells in a compartment derived from a minority class of stem cells. These curves have been compared with previously published experimental results and with results from some new experiments. Both models fit the data to some extent provided a mean value of T_c of about 140 h is assumed. However, the sequential aging model provides a slightly better overall fit. A further conclusion is that it is impossible to make any accurate statements on the epidermal growth fraction from repeated labelling data.     

Hyperbolic Discounting: Value and Time Processes of Substance Abusers and Non-Clinical Individuals in Intertemporal Choice

The single parameter hyperbolic model has been frequently used to describe value discounting as a function of time and to differentiate substance abusers and non-clinical participants with the model''s parameter k. However, k says little about the mechanisms underlying the observed differences. The present study evaluates several alternative models with the purpose of identifying whether group differences stem from differences in subjective valuation, and/or time perceptions. Using three two-parameter models, plus secondary data analyses of 14 studies with 471 indifference point curves, results demonstrated that adding a valuation, or a time perception function led to better model fits. However, the gain in fit due to the flexibility granted by a second parameter did not always lead to a better understanding of the data patterns and corresponding psychological processes. The k parameter consistently indexed group and context (magnitude) differences; it is thus a mixed measure of person and task level effects. This was similar for a parameter meant to index payoff devaluation. A time perception parameter, on the other hand, fluctuated with contexts in a non-predicted fashion and the interpretation of its values was inconsistent with prior findings that supported enlarged perceived delays for substance abusers compared to controls. Overall, the results provide mixed support for hyperbolic models of intertemporal choice in terms of the psychological meaning afforded by their parameters.     

Effect of delay and social distance on the perceived value of social interaction

Temporal discounting is a process by which the perceived value of an outcome decreases as delay increases. Social discounting is a process by which the perceived value of an outcome decreases as the social distance between the decision-maker and recipient increases. Both temporal and social discounting are well established for monetary outcomes. However, little is known regarding the effect of delay-to-occurrence or increased social distance on the perceived value of social interactions. The current study demonstrates that the decrease in perceived value for delayed social interactions is well described by the same hyperbola-like function used for monetary outcomes and that the rate of discounting decreases (indicating increased preference for larger, more delayed outcomes) as social distance increases. Conceptualizing the current discounting procedure as entailing both potential gains and losses, suggest that under certain circumstances, higher discount rates may not reflect increased preference.     

Motor response vigour and visual fixation patterns reflect subjective valuation during intertemporal choice

Value-based decision-making is of central interest in cognitive neuroscience and psychology, as well as in the context of neuropsychiatric disorders characterised by decision-making impairments. Studies examining (neuro-)computational mechanisms underlying choice behaviour typically focus on participants’ decisions. However, there is increasing evidence that option valuation might also be reflected in motor response vigour and eye movements, implicit measures of subjective utility. To examine motor response vigour and visual fixation correlates of option valuation in intertemporal choice, we set up a task where the participants selected an option by pressing a grip force transducer, simultaneously tracking fixation shifts between options. As outlined in our preregistration (https://osf.io/k6jct), we used hierarchical Bayesian parameter estimation to model the choices assuming hyperbolic discounting, compared variants of the softmax and drift diffusion model, and assessed the relationship between response vigour and the estimated model parameters. The behavioural data were best explained by a drift diffusion model specifying a non-linear scaling of the drift rate by the subjective value differences. Replicating previous findings, we found a magnitude effect for temporal discounting, such that higher rewards were discounted less. This magnitude effect was further reflected in motor response vigour, such that stronger forces were exerted in the high vs. the low magnitude condition. Bayesian hierarchical linear regression further revealed higher grip forces, faster response times and a lower number of fixation shifts for trials with higher subjective value differences. An exploratory analysis revealed that subjective value sums across options showed an even more pronounced association with trial-wise grip force amplitudes. Our data suggest that subjective utility or implicit valuation is reflected in motor response vigour and visual fixation patterns during intertemporal choice. Taking into account response vigour might thus provide deeper insight into decision-making, reward valuation and maladaptive changes in these processes, e.g. in the context of neuropsychiatric disorders.     

Cricket mate selection as a spatial discounting phenomenon without learning

Many animals prefer small local benefits to large but temporally or spatially distant benefits, and this preference is termed “temporal discounting” or “spatial discounting.” Although temporal discounting has been studied in many taxa, only a limited number of papers have primarily focused on spatial discounting. Here, a mate-choice experiment was conducted using female house crickets (Acheta domesticus) tasked with selecting between a non-attractive local male and an attractive distant male; training procedures were not performed. The results showed that females that had never heard the calling songs of males exhibited spatial discounting behavior. This finding may be key to determining the fundamental differences between temporal and spatial discounting.     

Estimating the subjective value of future rewards: comparison of adjusting-amount and adjusting-delay procedures

The present study examined whether equivalent discounting of delayed rewards is observed with different experimental procedures. If the underlying decision-making process is the same, then similar patterns of results should be observed regardless of procedure, and similar estimates of the subjective value of future rewards (i.e., indifference points) should be obtained. Two experiments compared discounting on three types of procedure: adjusting-delay (AD), adjusting-immediate-amount (AIA), and adjusting-delayed-amount (ADA). For the two procedures for which discounting functions can be established (i.e., AD and AIA), a hyperboloid provided good fits to the data at both the group and individual levels, and individuals' discounting on one procedure tended to be correlated with their discounting on the other. Notably, the AIA procedure produced the more consistent estimates of the degree of discounting, and in particular, discounting on the AIA procedure was unaffected by the order in which choices were presented. Regardless of which of the three procedures was used, however, similar patterns of results were obtained: Participants systematically discounted the value of delayed rewards, and robust magnitude effects were observed. Although each procedure may have its own advantages and disadvantages, use of all three types of procedure in the present study provided converging evidence for common decision-making processes underlying the discounting of delayed rewards.     

Identification of structures for ion channel kinetic models

Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium currents and human left ventricular fast transient outward potassium currents. Successful models identified with this approach have certain characteristics in common, suggesting that aspects of the model topology are determined by the experimental data. Incorporating these channel models into cell and tissue simulations to assess model performance within protocols that were not used for training provided validation and further narrowing of the number of acceptable models. The success of this approach suggests a channel model creation pipeline may be feasible where the structure of the model is not specified a priori.     

Modeling the microbial growth and temperature profile in a fixed-bed bioreactor

Aiming to scale up and apply control and optimization strategies, currently is required the development of accurate plant models to forecast the process nonlinear dynamics. In this work, a mathematical model to predict the growth of the Kluyveromyces marxianus and temperature profile in a fixed-bed bioreactor for solid-state fermentation using sugarcane bagasse as substrate was built up. A parameter estimation technique was performed to fit the mathematical model to the experimental data. The estimated parameters and the model fitness were evaluated with statistical analyses. The results have shown the estimated parameters significance, with 95 % confidence intervals, and the good quality of process model to reproduce the experimental data.     

Temporal-Difference Reinforcement Learning with Distributed Representations

Temporal-difference (TD) algorithms have been proposed as models of reinforcement learning (RL). We examine two issues of distributed representation in these TD algorithms: distributed representations of belief and distributed discounting factors. Distributed representation of belief allows the believed state of the world to distribute across sets of equivalent states. Distributed exponential discounting factors produce hyperbolic discounting in the behavior of the agent itself. We examine these issues in the context of a TD RL model in which state-belief is distributed over a set of exponentially-discounting “micro-Agents”, each of which has a separate discounting factor (γ). Each µAgent maintains an independent hypothesis about the state of the world, and a separate value-estimate of taking actions within that hypothesized state. The overall agent thus instantiates a flexible representation of an evolving world-state. As with other TD models, the value-error (δ) signal within the model matches dopamine signals recorded from animals in standard conditioning reward-paradigms. The distributed representation of belief provides an explanation for the decrease in dopamine at the conditioned stimulus seen in overtrained animals, for the differences between trace and delay conditioning, and for transient bursts of dopamine seen at movement initiation. Because each µAgent also includes its own exponential discounting factor, the overall agent shows hyperbolic discounting, consistent with behavioral experiments.     

Enhanced adsorption of congo red from aqueous solutions by chitosan hydrogel beads impregnated with cetyl trimethyl ammonium bromide

The adsorption of congo red (CR) onto chitosan (CS) beads impregnated by a cationic surfactant (CTAB, cetyl trimethyl ammonium bromide) was investigated. Chitosan beads impregnated at a ratio of 1/20 of CTAB to CS (0.05% of CTAB and 1% of CS) increased the CR adsorption capacity by 2.2 times from 162.3 mg/g (0% CTAB) to 352.5 mg/g (0.05% CTAB). The CR adsorption decreased with an increase in pH of the CR solution from 4.0 to 9.0. The Sips isotherm model showed a good fit with the equilibrium experimental data and the values of the heterogeneity factor (n) indicated heterogeneous adsorption of CR onto CS/CTAB beads, as well as CS beads. The kinetic data showed better fit to the pseudo second-order rate model than to the pseudo first-order rate model. The impregnation of CS beads by cationic surfactants showed the highest adsorption capacities of CR compared to any other adsorbents and would be a good method to increase adsorption efficiency for the removal of anionic dyes in a wastewater treatment process.     

Toward an adequate mathematical model of mental space: Conscious/unconscious dynamics on m-adic trees

We try to perform geometrization of cognitive science and psychology by representing information states of cognitive systems by points of mental space given by a hierarchic m-adic tree. Associations are represented by balls and ideas by collections of balls. We consider dynamics of ideas based on lifting of dynamics of mental points. We apply our dynamical model for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1–3, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of associations and ideas.     

Impulsiveness without discounting: the ecological rationality hypothesis

Observed animal impulsiveness challenges ideas from foraging theory about the fitness value of food rewards, and may play a role in important behavioural phenomena such as cooperation and addiction. Behavioural ecologists usually invoke temporal discounting to explain the evolution of animal impulsiveness. According to the discounting hypothesis, delay reduces the fitness value of the delayed food. We develop an alternative model for the evolution of impulsiveness that does not require discounting. We show that impulsive or short-sighted rules can maximize long-term rates of food intake. The advantages of impulsive rules come from two sources. First, naturally occurring choices have a foreground-background structure that reduces the long-term cost of impulsiveness. Second, impulsive rules have a discrimination advantage because they tend to compare smaller quantities. Discounting contributes little to this result. Although we find that impulsive rules are optimal in a simple foreground-background choice situation in the absence of discounting, in contrast we do not find comparable impulsiveness in binary choice situations even when there is strong discounting.     

Fitting the Incidence Data from the City of Campinas,Brazil, Based on Dengue Transmission Modellings Considering Time-Dependent Entomological Parameters

Four time-dependent dengue transmission models are considered in order to fit the incidence data from the City of Campinas, Brazil, recorded from October 1^st 1995 to September 30^th 2012. The entomological parameters are allowed to depend on temperature and precipitation, while the carrying capacity and the hatching of eggs depend only on precipitation. The whole period of incidence of dengue is split into four periods, due to the fact that the model is formulated considering the circulation of only one serotype. Dengue transmission parameters from human to mosquito and mosquito to human are fitted for each one of the periods. The time varying partial and overall effective reproduction numbers are obtained to explain the incidence of dengue provided by the models.     

Continuous fixed-bed column study and adsorption modeling: Removal of cadmium (II) and lead (II) ions in aqueous solution by dead calcareous skeletons

The sorption of Cd(II) and Pb(II) ions was conducted in a continuous fixed-bed column by using dead calcareous skeletons (CS). The column performances were evaluated by varying the adsorbent bed height, influent flow rate and metals initial concentration. The breakthrough curve for the bed height indicated that a longer bed column prolonged the life span of the column with a maximum capacity of 26.447 and 38.460 mg/g for the Cd(II) and Pb(II) column, respectively. The increased flow rate and initial concentration caused the column exhaustion time to occur earlier. The experimental column data were also expressed in column adsorption models, namely, the Thomas, Yoon–Nelson and Adam–Bohart models. The Thomas model fitted well with the Cd(II) data with the correlated curve (r² > 0.9). The Yoon–Nelson model was selected to predict the 50% breakthrough time achieved by the column system and provided the estimated breakthrough time for the columns that were not exhausted during the operation. The Adam–Bohart model was applicable for the initial part of adsorption with the saturation concentration data at the equilibrium. The saturation index of aragonite and calcite depicted that dissolution of calcium occurred in the aqueous solution. The experimental and theoretical data were correlated with a significant relationship trend (p < 0.01), which showed that the trend of experimental data fit well with the modeling trend. The trends of both the experimental and theoretical data were strongly and significantly correlated due to involving the column parameters and the components of CS.     

A C. elegans homolog of the Cockayne syndrome complementation group A gene

Cockayne syndrome (CS) is a debilitating and complex disorder that results from inherited mutations in the CS complementation genes A and B, CSA and CSB. The links between the molecular functions of the CS genes and the complex pathophysiology of CS are as of yet poorly understood and are the subject of intense debate. While mouse models reflect the complexity of CS, studies on simpler genetic models might shed new light on the consequences of CS mutations. Here we describe a functional homolog of the human CSA gene in Caenorhabditis elegans. Similar to its human counterpart, mutations in the nematode csa-1 gene lead to developmental growth defects as a consequence of DNA lesions.     

Chemical modification of chitosan by tetraethylenepentamine and adsorption study for anionic dye removal

To utilize the contribution of introduced amino groups to the adsorption of an anionic dye (eosin Y), a batch adsorption system was applied to study the adsorption of eosin Y from aqueous solution by tetraethylenepentamine (TEPA) modified chitosan (TEPA–CS). Experiments were carried out as a function of particle size, initial pH, agitation rate, adsorbent dosage, agitation period, temperature and initial concentration of eosin Y. The Langmuir and Freundlich models were used to fit the adsorption isotherms. From the values of correlation coefficients (R²), it was observed that the experimental data fit very well to the Langmuir model, giving a maximum sorption capacity of 292.4 mg/g at 298 K. Kinetic studies showed that the kinetic data were well described by the pseudo-second-order kinetic model. The thermodynamic study revealed negative value of enthalpy change (ΔH°) and free energy change (ΔG°), indicating spontaneous and endothermic nature of the adsorption of eosin Y on to TEPA–CS.