Electroencephalographic topography measures of experienced utility

Economic theory distinguishes two concepts of utility: decision utility, objectively quantifiable by choices, and experienced utility, referring to the satisfaction by an obtainment. To date, experienced utility is typically measured with subjective ratings. This study intended to quantify experienced utility by global levels of neuronal activity. Neuronal activity was measured by means of electroencephalographic (EEG) responses to gain and omission of graded monetary rewards at the level of the EEG topography in human subjects. A novel analysis approach allowed approximating psychophysiological value functions for the experienced utility of monetary rewards. In addition, we identified the time windows of the event-related potentials (ERP) and the respective intracortical sources, in which variations in neuronal activity were significantly related to the value or valence of outcomes. Results indicate that value functions of experienced utility and regret disproportionally increase with monetary value, and thus contradict the compressing value functions of decision utility. The temporal pattern of outcome evaluation suggests an initial (∼250 ms) coarse evaluation regarding the valence, concurrent with a finer-grained evaluation of the value of gained rewards, whereas the evaluation of the value of omitted rewards emerges later. We hypothesize that this temporal double dissociation is explained by reward prediction errors. Finally, a late, yet unreported, reward-sensitive ERP topography (∼500 ms) was identified. The sources of these topographical covariations are estimated in the ventromedial prefrontal cortex, the medial frontal gyrus, the anterior and posterior cingulate cortex and the hippocampus/amygdala. The results provide important new evidence regarding “how,” “when,” and “where” the brain evaluates outcomes with different hedonic impact.

Executive functions in 5- to 8-year olds: Developmental changes and relationship to academic achievement

Pronounced improvements in executive functions (EF) during preschool years have been documented in cross-sectional studies. However, longitudinal evidence on EF development during the transition to school and predictive associations between early EF and later school achievement are still scarce. This study examined developmental changes in EF across three time-points, the predictive value of EF for mathematical, reading and spelling skills and explored children's specific academic attainment as a function of early EF. Participants were 323 children following regular education; 160 children were enrolled in prekindergarten (younger cohort: 69 months) and 163 children in kindergarten (older cohort: 78.4 months) at the first assessment. Various tasks of EF were administered three times with an interval of one year each. Mathematical, reading and spelling skills were measured at the last assessment. Individual background characteristics such as vocabulary, non-verbal intelligence and socioeconomic status were included as control variables. In both cohorts, changes in EF were substantial; improvements in EF, however, were larger in preschoolers than school-aged children. EF assessed in preschool accounted for substantial variability in mathematical, reading and spelling achievement two years later, with low EF being especially associated with significant academic disadvantages in early school years. Given that EF continue to develop from preschool into primary school years and that starting with low EF is associated with lower school achievement, EF may be considered as a marker or risk for academic disabilities.

Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis

The responses of carbon dioxide (CO2) and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%). The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence) lies within the range of (68 to 117) × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and subjective choice to determine AGWP of CO2 and GWP is the time horizon.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.