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Introduction Smokers discount delayed rewards steeper than non-smokers or ex-smokers, possibly due to neuropharmacological effects of tobacco on brain circuitry, or lower abstinence rates in smokers with steep discounting. To delineate both theories from each other, we tested if temporal discounting, choice inconsistency, and related brain activity in treatment-seeking smokers (1) are higher compared to non-smokers, (2) decrease after smoking cessation, and (3) predict relapse. Methods At T1, 44 dependent smokers, 29 non-smokers, and 30 occasional smokers underwent fMRI while performing an intertemporal choice task. Smokers were measured before and 21 days after cessation if abstinent from nicotine. In total, 27 smokers, 28 non-smokers, and 29 occasional smokers were scanned again at T2. Discounting rate k and inconsistency var(k) were estimated with Bayesian analysis. Results First, k and var(k) in smokers in treatment were not higher than in non-smokers or occasional smokers. Second, neither k nor var(k) changed after smoking cessation. Third, k did not predict relapse, but high var(k) was associated with relapse during treatment and over 6 months. Brain activity in valuation and decision networks did not significantly differ between groups and conditions. Conclusion Our data from treatment-seeking smokers do not support the pharmacological hypothesis of pronounced reversible changes in discounting behavior and brain activity, possibly due to limited power. Behavioral data rather suggest that differences between current and ex-smokers might be due to selection. The association of choice consistency and treatment outcome possibly links consistent intertemporal decisions to remaining abstinent.

Background This study investigated whether patterns of impulsive decision-making (i) differ between individuals with DSM-5 substance use disorders (SUD) or non-substance-related addictive disorders (ND) and healthy controls, and (ii) predict the increase of SUD and ND severity after one year. Methods In a prospective-longitudinal community study, 338 individuals (19–27 years, 59% female) were included in one of three groups: SUD (n = 100), ND (n = 118), or healthy controls (n = 120). Group differences in four impulsive decision-making facets were analyzed with the Bayesian priors: delay discounting (mean = 0.37, variance = 0.02), probability discounting for gains and for losses (each − 0.16, 0.02), and loss aversion (− 0.44, 0.02). SUD and ND severity were assessed at baseline and after 1 year (n = 312, 92%). Predictive associations between decision-making and SUD/ND severity changes were analyzed with the Bayesian prior: mean = 0.25, variance = 0.016. Results Compared with controls, the SUD group displayed steeper delay discounting and lower probability discounting for losses; the ND group displayed lower probability discounting for losses (posterior probabilities > 98%). SUD symptom increase after 1 year was predicted by steeper delay discounting and lower loss aversion; ND symptom increase by lower probability discounting for losses and lower loss aversion (posterior probabilities > 98%). There was low evidence for predictive relations between decision-making and the quantity-frequency of addictive behaviours. Discussion Impulsive decision-making characterizes SUD and ND and predicts the course of SUD and ND symptoms but not the engagement in addictive behaviours. Strength of evidence differed between different facets of impulsive decision-making and was mostly weaker than a priori expected.

Recently, cross-sectional relationships between psycho-social resilience factors (RFs) and resilience, operationalized as an outcome of low reactivity of mental health to stressor exposure (low ‘stressor reactivity’) during the first wave of the COVID-19 pandemic, were reported. Extending these findings, we here examine prospective relationships and weekly dynamics between the same RFs and stressor reactivity in a longitudinal sample during the aftermath of the first wave in several European countries. Over five weeks of app-based assessments, participants weekly reported stressor exposure, mental health problems, RFs, and demographic data, in one of six different languages. As (partly) preregistered, hypotheses were tested cross-sectionally at baseline (N=558) and longitudinally (N=200), using mixed effects models and mediation analyses. RFs at baseline, including positive appraisal style, optimism, self-efficacy, perceived good stress recovery, and perceived social support, were negatively associated with stressor reactivity (SR) scores, not only cross-sectionally (baseline SR scores) but also prospectively (average SR scores across subsequent weeks). In both analyses, positive appraisal style mediated the effects of perceived social support on SR. In the analyses of weekly RF-SR dynamics, RFs positive appraisal (of stressors generally and specifically of the Corona crisis) and general self-efficacy were negatively associated with SR in a contemporaneous, but not lagged fashion. We identify psychological RFs which prospectively predict resilience and co-fluctuate with weekly stressor reactivity within individuals. The prospective results endorse that the previously reported RF-SR associations do not exclusively reflect mood-congruency or other temporal bias effects. We further confirm an important role for positive appraisal in resilience.

Background: Serotonin has been implicated in impulsive behaviours such as temporal discounting. While animal studies and theoretical approaches suggest that reduced tonic serotonin levels increase temporal discounting rates and vice versa, evidence from human studies is scarce and inconclusive. Furthermore, an important modulator of serotonin signalling, a genetic variation in the promoter region of the serotonin transporter gene ( 5-HTTLPR), has not been investigated for temporal discounting so far. Objective: First, the purpose of this study was to test for a significant association between 5-HTTLPR and temporal discounting. Second, we wished to investigate the effect of high/low tonic serotonin levels on intertemporal choice and blood oxygen-level-dependent response, controlling for 5-HTTLPR. Methods: We tested the association of 5-HTTLPR with temporal discounting rates using an intertemporal choice task in 611 individuals. We then manipulated tonic serotonin levels with acute tryptophan interventions (depletion, loading, balanced) in a subsample of 45 short (S)-allele and 45 long (L)/L-allele carriers in a randomised double-blind crossover design using functional magnetic resonance imaging and an intertemporal choice task. Results: Overall, we did not find any effect of serotonin and 5-HTTLPR on temporal discounting rates or the brain networks associated with valuation and cognitive control. Conclusion: Our findings indicate that serotonin may not be directly involved in choices including delays on longer timescales such as days, weeks or months. We speculate that serotonin plays a stronger role in dynamic intertemporal choice tasks where the delays are on a timescale of seconds and hence are therefore directly experienced during the experiment.

In a previous study (Neukam, Kroemer et al. 2018), we found for the5-HTTLPRgenotype higher risk-seeking for losses in S/S vs. L/L carrier, which could not be explained by acutely changed central serotonin levels. This finding alternatively may be the result of reduced top-down control from the frontal cortex due to altered signal pathways involving the amygdala and ventral striatum. The serotonergic system is known to be involved in neurodevelopment and neuroplasticity. Therefore, the aim of this study was to investigate whether structural differences in white matter can explain the differences in risk-seeking behaviour that we observed in our previous study and whether5-HTTLPRgroups differ in their white matter microstructure. These differences can be detected using diffusion-weighted imaging (DWI). We assumed lower structural connectivity in S/S compared to L/L carrier, and a negative relationship between risk-seeking for losses and connectivity. We used DWI to compute diffusion parameters for the frontostriatal and uncinate tract in 175 individuals (39 S/S, 80 S/L, 56 L/L). Results showed no significant relationship between diffusion parameters and risk-seeking for losses. Furthermore, we did not find significant differences in diffusion parameters of the S/S vs. L/L group. There were only group differences in the frontostriatal tract showing stronger structural connectivity in the S/L group, which is also reflected in the whole brain approach. Therefore, the data do not support our hypothesis that the association between5- HTTLPRand risk-seeking for losses is related to differences in white matter pathways implicated in decision-making.

Perceptual decisions entail the accumulation of evidence until a decision criterion is reached. The amount of noise in this process is inversely related to the behavioral performance of the decision-maker. Hence, reducing the amount of perceived noise could improve performance in perceptual decisions. In this study, we investigated whether providing monetary reward for correct responses in a perceptual decision-making task would enhance performance based on prior research linking noise reduction to the administration of reward. To this end, thirty-one healthy young adults carried out an incentivized dot tracking task (iDT) during recording of functional magnetic resonance imaging (fMRI). Behavioral responses were fitted to a Bayesian version of the drift-diffusion model that, among other parameters, also includes an estimate of sensory noise. Fifty percent of the trials were incentivized to compare rewarded with unrewarded trials regarding behavior, brain responses and estimates of model parameters. In order to establish a link between the noise parameter and fMRI activity, we correlated percent signal change (PSC) values from nucleus accumbens and caudate nucleus with noise levels in rewarded and unrewarded trials respectively. Although reward did not affect behavioral performance and model parameters, the fMRI analyses showed notable differences in nucleus accumbens, caudate nucleus and rostral anterior cingulate cortex in rewarded relative to unrewarded trials. Furthermore, higher PSC within nucleus accumbens was significantly associated with lower sensory noise levels, which was specific to rewarded trials. This work is consistent with previous findings on reward modulation of brain responses and marks a first step towards elucidating the effects of reward-induced noise suppression during perceptual decision-making.

Background: Neurodevelopmental and alcohol-induced changes in decision-making have been proposed to critically influence impulsive behaviour in adolescents. Objective: This study tested the influence of acute alcohol administration on impulsive choice in adolescents. Methods: Fifty-four males aged 18–19 years were tested in a single-blind placebo-controlled cross-over design. During alcohol administration (infusion resulting in an arterial blood alcohol concentration of 80 mg%) and placebo condition (saline infusion), participants performed a task battery providing estimates of delay discounting, probability discounting for gains, for losses and loss aversion, and also rated subjectively experienced alcohol effects. Additionally, baseline alcohol consumption (Alcohol Use Disorders Identification Test, blood phosphatidylethanol levels), motives (Drinking Motive Questionnaire, Alcohol Expectancy Questionnaire and Obsessive Compulsive Drinking Scale), family history and self-report measures of impulsivity (Barratt Impulsiveness Scale, Substance Use Risk Profile Scale) were provided. Results: No overall effects of treatment on choice behaviour were found. However, individual differences were observed. In the alcohol condition, more impulsive choice tendencies for delay discounting were associated with higher subjectively experienced alcohol effects. Further, higher risk aversion for probabilistic gains and higher loss aversion during alcohol condition were related to higher levels of real-life alcohol consumption and a family history of alcohol problems, respectively. Finally, the time to make a decision was substantially shortened for choices involving negative prospects. Conclusions: Contrary to common beliefs, acute alcohol intoxication did not generally incite impulsive decision-making. It rather appears that alcohol-induced behavioural changes in adolescents vary considerably depending on prior experiences and subjective effects of alcohol.

Background Patients with anorexia nervosa forgo eating despite emaciation and severe health consequences. Such dysfunctional decision-making might be explained by an excessive level of self-control, alterations in homeostatic and hedonic regulation, or an interplay between these processes. We aimed to understand value-based decision-making in anorexia nervosa and its association with the gut hormone ghrelin. Besides its homeostatic function, ghrelin has been implicated in the hedonic regulation of appetite and reward via the modulation of phasic dopamine signalling. Methods In a cross-sectional design, we studied acutely underweight (n = 94) and recovered (n = 37) patients with anorexia nervosa of the restrictive subtype, as well as healthy control participants (n = 119). We assessed plasma concentrations of desacyl ghrelin and parameters of delay discounting, probability discounting for gains and losses, and loss aversion. Results Recovered patients displayed higher risk aversion for gains, but we observed no group differences for the remaining decision-making parameters. Desacyl ghrelin was higher in acutely underweight and recovered participants with anorexia nervosa relative to healthy controls. Moreover, we found a significant group × desacyl ghrelin interaction in delay discounting, indicating that in contrast to healthy controls, acutely underweight patients with anorexia nervosa who had high desacyl ghrelin concentrations preferably chose the delayed reward option. Limitations We probed decision-making using monetary rewards, but patients with anorexia nervosa may react differently to disorder-relevant stimuli. Furthermore, in contrast to acyl ghrelin, the functions of desacyl ghrelin are unclear. Therefore, the interpretation of the results is preliminary. Conclusion The propensity for risk aversion as found in recovered patients with anorexia nervosa could help them successfully complete therapy, or it could reflect sequelae of the disorder. Conversely, ghrelin findings might be related to a mechanism contributing to disease maintenance; that is, in acutely underweight anorexia nervosa, a hungry state may facilitate the ability to forgo an immediate reward to achieve a (dysfunctional) long-term goal.

Value-based decision making (VBDM) is a principle that states that humans and other species adapt their behavior according to the dynamic subjective values of the chosen or unchosen options. The neural bases of this process have been extensively investigated using task-based fMRI and lesion studies. However, the growing field of resting-state functional connectivity (RSFC) may shed light on the organization and function of brain connections across different decision-making domains. With this aim, we used independent component analysis to study the brain network dynamics in a large cohort of young males (N = 145) and the relationship of these dynamics with VBDM. Participants completed a battery of behavioral tests that evaluated delay aversion, risk seeking for losses, risk aversion for gains, and loss aversion, followed by an RSFC scan session. We identified a set of large-scale brain networks and conducted our analysis only on the default mode network (DMN) and networks comprising cognitive control, appetitive-driven, and reward-processing regions. Higher risk seeking for losses was associated with increased connectivity between medial temporal regions, frontal regions, and the DMN. Higher risk seeking for losses was also associated with increased coupling between the left frontoparietal network and occipital cortices. These associations illustrate the participation of brain regions involved in prospective thinking, affective decision making, and visual processing in participants who are greater risk-seekers, and they demonstrate the sensitivity of RSFC to detect brain connectivity differences associated with distinct VBDM parameters.

Reinforcement learning involves a balance between model-free (MF) and model-based (MB) systems. Recent studies suggest that individuals with either pharmacologically enhanced levels of dopamine (DA) or higher baseline levels of DA exhibit more MB control. However, it remains unknown whether such pharmacological effects depend on baseline DA.Here, we investigated whether effects of L-DOPA on the balance of MB/MF control depend on ventral striatal baseline DA. Sixty participants had two functional magnetic resonance imaging (fMRI) scans while performing a two-stage sequential decision-making task under 150 mg L-DOPA or placebo (counterbalanced), followed by a 4-hour 18F-DOPA positron emission tomography (PET) scan (on a separate occasion).We found an interaction between baseline DA levels and L-DOPA induced changes in MB control. Individuals with higher baseline DA levels showed a greater L-DOPA induced enhancement in MB control. Surprisingly, we found a corresponding drug-by-baseline DA interaction on MF, but not MB learning signals in the ventromedial prefrontal cortex. We did not find a significant interaction between baseline DA levels and L-DOPA effects on MF control or MB/MF balance.In sum, our findings point to a baseline dependency of L-DOPA effects on differential aspects of MB and MF control. Individual differences in DA washout may be an important moderator of L-DOPA effects. Overall, our findings complement the general notion where higher DA levels is related to a greater reliance on MB control. Although the relationship between phasic DA firing and MF learning is conventionally assumed in the animal literature, the relationship between DA and MF control is not as straightforward and requires further clarification.

We previously reported that L-DOPA effects on reward-based decision-making in a randomized, placebo-controlled, double-blind, crossover study were consistent with an inverted U-shaped function whereby both low and high extremes of dopamine signaling are associated with high-impulsive choice. To test this hypothesis, we performed [18F]DOPA positron emission tomography in 60 of the 87 participants in that study, and measured the effective distribution volume ratio (EDVR) of [18F]DOPA influx rate to [18F]dopamine washout rate, an index of presynaptic dopaminergic function. Participants with higher baseline EDVR self-reported lower impulsivity, and discounted rewards as a function of delay more strongly after receiving L-DOPA, whereas the opposite was detected for those with lower baseline EDVR. Our findings support a relationship of striatal dopaminergic activity to trait impulsivity, and the view that there is a non-linear, possibly inverted U-shaped relationship of striatal dopaminergic function with delay discounting. Individuals with optimal dopamine signaling would become more impulsive when receiving dopamine-enhancing drugs, whereas those with suboptimal dopaminergic signaling would benefit and exhibit less impulsive choice. Consideration of differences in endogenous dopamine signaling and possibly also other neurotransmitter activity may be crucial to advance understanding of the neurobiochemical mechanisms of impulsive decision-making and related mental disorders.

Serotonin has been implicated in impulsive behaviours such as temporal discounting. While animal studies and theoretical approaches suggest that reduced tonic serotonin levels increase temporal discounting rates and vice versa, evidence from human studies is scarce and inconclusive. Furthermore, an important modulator of serotonin signalling, a genetic variation in the promoter region of the serotonin transporter gene (First, the purpose of this study was to test for a significant association betweenWe tested the association ofOverall, we did not find any effect of serotonin andOur findings indicate that serotonin may not be directly involved in choices including delays on longer timescales such as days, weeks or months. We speculate that serotonin plays a stronger role in dynamic intertemporal choice tasks where the delays are on a timescale of seconds and hence are therefore directly experienced during the experiment.

Aim Methamphetamine (MA) abuse and dependence are increasing worldwide and are commonly associated with cognitive deficits. Some studies indicate that such impairments can improve if users become abstinent, but overall results remain inconclusive. Hence, we have performed a longitudinal case-control study investigating key surrogates for attention and impulsive decision-making before and after treatment. Methods Thirty patients with MA dependence and 24 non-substance-abusing control participants were recruited. Groups were matched on age, sex and education. All subjects performed a baseline assessment to obtain neurocognitive measures of sustained attention and delay discounting. Patients subsequently participated in an MA-specific relapse prevention program including repeated monitoring of relapse status. After 3 months, participants of both groups were reevaluated for neurocognitive performance. Results At baseline, MA patients showed a significantly higher number of omissions compared to controls, indicative of lower sustained attention. Interestingly, we observed a steep decrease of omissions in MA patients to control-group level post treatment. On the other hand, MA patients discounted delayed rewards significantly stronger than controls, indicating a more impulsive choice behavior both before and after treatment. Limitation The results should be interpreted with care because of the small sample and short follow-up period. Conclusion Our data support earlier findings on partial recovery of cognitive deficits in MA patients. They also strengthen the indication for recently recommended psychotherapeutic interventions and may provide a behavioral monitoring tool to inform treatment progress.

We previously reported that L-DOPA effects on reward-based decision-making in a randomized, placebo-controlled, double-blind, crossover study were consistent with an inverted U-shaped function whereby both low and high extremes of dopamine signaling are associated with high-impulsive choice. To test this hypothesis, we performed [18F]DOPA positron emission tomography in 60 of the 87 participants in that study, and measured the effective distribution volume ratio (EDVR) of [18F]DOPA influx rate to [18F]dopamine washout rate, an index of presynaptic dopaminergic function. Participants with higher baseline EDVR self-reported lower impulsivity, and discounted rewards as a function of delay more strongly after receiving L-DOPA, whereas the opposite was detected for those with lower baseline EDVR. Our findings support a relationship of striatal dopaminergic activity to trait impulsivity, and the view that there is a non-linear, possibly inverted U-shaped relationship of striatal dopaminergic function with delay discounting. Individuals with optimal dopamine signaling would become more impulsive when receiving dopamine-enhancing drugs, whereas those with suboptimal dopaminergic signaling would benefit and exhibit less impulsive choice. Consideration of differences in endogenous dopamine signaling and possibly also other neurotransmitter activity may be crucial to advance understanding of the neurobiochemical mechanisms of impulsive decision-making and related mental disorders.

Dopamine is a key neurotransmitter in action control. However, influential theories of dopamine function make conflicting predictions about the effect of boosting dopamine neurotransmission. Here, we tested if increases in dopamine tone by administration of L-DOPA upregulate reward learning as predicted by reinforcement learning theories, and if increases are specific for deliberative “model-based” control or reflexive “model-free” control. Alternatively, L-DOPA may impair learning as suggested by “value” or “thrift” theories of dopamine. To this end, we employed a two-stage Markov decision-task to investigate the effect of L-DOPA (randomized cross-over) on behavioral control while brain activation was measured using fMRI. L-DOPA led to attenuated model-free control of behavior as indicated by the reduced impact of reward on choice. Increased model-based control was only observed in participants with high working memory capacity. Furthermore, L-DOPA facilitated exploratory behavior, particularly after a stream of wins in the task. Correspondingly, in the brain, L-DOPA decreased the effect of reward at the outcome stage and when the next decision had to be made. Critically, reward-learning rates and prediction error signals were unaffected by L-DOPA, indicating that differences in behavior and brain response to reward were not driven by differences in learning. Taken together, our results suggest that L-DOPA reduces model-free control of behavior by attenuating the transfer of value to action. These findings provide support for the value and thrift accounts of dopamine and call for a refined integration of valuation and action signals in reinforcement learning models.

Serotonin (5-HT) plays a key role in different aspects of value-based decision-making. A recent framework proposed that tonic 5-HT (together with dopamine, DA) codes future average reward expectations, providing a baseline against which possible choice outcomes are compared to guide decision-making. To test whether high 5-HT levels decrease loss aversion, risk-seeking for gains, and risk-seeking for losses. In a first session, 611 participants were genotyped for 5-HTTLPR and performed a mixed gambles (MGA) task and two probability discounting tasks for gains and losses, respectively (PDG/PDL). Afterwards, a subsample of 105 participants (44 with S/S, 6 with S/L, 55 with L/L genotype) completed the pharmacological study using a crossover design with tryptophan depletion (ATD), loading (ATL), and balanced (BAL) conditions. The same decision constructs were assessed. We found increased risk-seeking for losses in S/S compared to L/L individuals at the first visit (p = 0.002). Neither tryptophan depletion nor loading affected decision-making, nor did we observe an interaction between intervention and 5-HTTLPR genotype. Our data do not support the idea that transient changes of tonic 5-HT affect value-based decision-making. We provide evidence for an association of 5-HTTLPR with risk-seeking for losses, independent of acute 5-HT levels. This indicates that the association of 5-HTTLPR and risk-seeking for losses is mediated via other mechanisms, possibly by differences in the structural development of neural circuits of the 5-HT system during early life phases.

Background Impulsive decision making relates to problematic substance use. Specifically, altered delay discounting (DD) has been suggested as a behavioral marker for addiction, while other relevant facets of choice impulsivity such as probability discounting (PD) or loss aversion are clearly understudied. Methods Two studies were performed collecting behavioral data on choice impulsivity with a value-based decision-making battery providing estimates of DD, PD for gains and losses, and loss aversion. Study (1): In a sample of 198 male 18-year-old social drinkers, we analyzed impulsive choice behavior and its association with alcohol consumption and self-report measures of substance use-related personality traits on a cross-sectional level. Additionally, the predictive value of baseline choice behavior for the trajectories of alcohol consumption over a 12-month follow-up period was evaluated. Study (2): Behavioral data on choice impulsivity were collected for 114 detoxified patients with alcohol use disorder (AUD) and 98 control participants. We analyzed group differences at baseline and assessed the predictive value of choice impulsivity for relapse to heavy alcohol use in patients during a follow-up period of 48 weeks. Results Study (1): Only DD was associated with baseline alcohol use, but no measure of choice impulsivity predicted the drinking trajectories over the following 12 months. Study (2): Compared to the control group, AUD patients showed higher DD, lower risk aversion regarding probabilistic gains, lower risk seeking regarding probabilistic losses, and lower loss aversion facing mixed prospects. Further, shallow discounting of probabilistic losses at baseline was predictive for relapse in patients. Conclusions All 4 domains of impulsive decision making were considerably altered in AUD patients though mostly not related to alcohol use in young adult social drinkers. This suggests that these facets of impulsive behavior may develop as consequences of chronic alcohol consumption. Furthermore, discounting of probabilistic losses might prove valuable in identifying patients vulnerable for relapse.

Alcohol-related cues acquire incentive salience through Pavlovian conditioning and then can markedly affect instrumental behavior of alcohol-dependent patients to promote relapse. However, it is unclear whether similar effects occur with alcohol-unrelated cues. We tested 116 early-abstinent alcohol-dependent patients and 91 healthy controls who completed a delay discounting task to assess choice impulsivity, and a Pavlovian-to-instrumental transfer (PIT) paradigm employing both alcohol-unrelated and alcohol-related stimuli. To modify instrumental choice behavior, we tiled the background of the computer screen either with conditioned stimuli (CS) previously generated by pairing abstract pictures with pictures indicating monetary gains or losses, or with pictures displaying alcohol or water beverages. CS paired to money gains and losses affected instrumental choices differently. This PIT effect was significantly more pronounced in patients compared to controls, and the group difference was mainly driven by highly impulsive patients. The PIT effect was particularly strong in trials in which the instrumental stimulus required inhibition of instrumental response behavior and the background CS was associated to monetary gains. Under that condition, patients performed inappropriate approach behavior, contrary to their previously formed behavioral intention. Surprisingly, the effect of alcohol and water pictures as background stimuli resembled that of aversive and appetitive CS, respectively. These findings suggest that positively valenced background CS can provoke dysfunctional instrumental approach behavior in impulsive alcohol-dependent patients. Consequently, in real life they might be easily seduced by environmental cues to engage in actions thwarting their long-term goals. Such behaviors may include, but are not limited to, approaching alcohol., Translational Psychiatry, 7, ISSN:2158-3188

Using simple mathematical models of choice behavior, we present a Bayesian adaptive algorithm to assess measures of impulsive and risky decision making. Practically, these measures are characterized by discounting rates and are used to classify individuals or population groups, to distinguish unhealthy behavior, and to predict developmental courses. However, a constant demand for improved tools to assess these constructs remains unanswered. The algorithm is based on trial-by-trial observations. At each step, a choice is made between immediate (certain) and delayed (risky) options. Then the current parameter estimates are updated by the likelihood of observing the choice, and the next offers are provided from the indifference point, so that they will acquire the most informative data based on the current parameter estimates. The procedure continues for a certain number of trials in order to reach a stable estimation. The algorithm is discussed in detail for the delay discounting case, and results from decision making under risk for gains, losses, and mixed prospects are also provided. Simulated experiments using prescribed parameter values were performed to justify the algorithm in terms of the reproducibility of its parameters for individual assessments, and to test the reliability of the estimation procedure in a group-level analysis. The algorithm was implemented as an experimental battery to measure temporal and probability discounting rates together with loss aversion, and was tested on a healthy participant sample.

Two approximations, derived from continuous expansions of Riemann–Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains fractional derivatives into a classical problem in which only derivatives of integer order are present. Corresponding approximations provide useful numerical tools to compute fractional derivatives of functions. Application of such approximations to fractional differential equations and fractional problems of the calculus of variations are discussed. Illustrative examples show the advantages and disadvantages of each approximation. MSC 2010: 26A33, 33F05, 34A08, 49M99, 65D20.

We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of the approximation method., Submitted 25-Jul-2011; revised 28-Nov-2011; accepted 02-Dec-2011; for publication in Numerical Functional Analysis and Optimization

We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and natural boundary conditions, which provide a generalization of previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and depending on higher-order Caputo derivatives, as well as fractional Lagrange problems, are considered., Comment: Submitted 29-Dec-2010; revised 14-Feb-2011; accepted 16-Feb-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimality conditions become sufficient. Numerical methods to solve the problems are presented, and some computational simulations are discussed in detail., This is a preprint of a paper whose final and definite form will appear at Journal of Industrial and Management Optimization (JIMO). Paper submitted 13-Dec-2012; revised 27-Jan-2013 and 06-Feb-2013; accepted for publication 07-Feb-2013

The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grunwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations., Comment: This is a preprint of a paper whose final and definite form will appear in Central European Journal of Physics. Paper submitted 31-Jan-2013; revised 6-May-2013; accepted for publication 7-May-2013

We review recent results obtained to solve fractional order optimal control problems with free terminal time and a dynamic constraint involving integer and fractional order derivatives. Some particular cases are studied in detail. A numerical scheme is given, based on expansion formulas for the fractional derivative. The efficiency of the method is illustrated through examples., Comment: Submitted 13-Apr-2013; accepted after minor revision 22-May-2013

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann-Liouville fractional derivative. Using the Grunwald-Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points., This work was partially presented 16-May-2012 by Shakoor Pooseh, at FDA'2012, who received a 'Best Oral Presentation Award'. Submitted 26-Aug-2012; revised 25-Jan-2013; accepted 29-Jan-2013; for publication in Computers and Mathematics with Applications

We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional problems of the calculus of variations, is illustrated., Submitted 15-10-2011; revised 24-01-2012; accepted 25-01-2012; for publication in Computers and Mathematics with Applications

We introduce the use of fractional calculus, i.e., the use of integrals and derivatives of non-integer (arbitrary) order, in epidemiology. The proposed approach is illustrated with an outbreak of dengue disease, which is motivated by the first dengue epidemic ever recorded in the Cape Verde islands off the coast of west Africa, in 2009. Numerical simulations show that in some cases the fractional models fit better the reality when compared with the standard differential models. The classical results are obtained as particular cases by considering the order of the derivatives to take an integer value., Comment: This is a preprint of a paper accepted for presentation at ICNAAM 2011, Numerical Optimization and Applications Symposium, whose final and definite form will appear in AIP Conference Proceedings