This paper characterises the analytical solution to a two period competitive storage model of commodity prices with periodic harvest distributions, extending the analytical results in Chambers and Bailey (1996). We present a sufficient condition is for the general model such that stocks are never depleted in the harvest period. The partial analytical solution for the price function in the harvest period is derived under the assumption of a linear demand function. This solution provides the conditions under which stock-outs in the nonharvest period can become an absorbing state.
Task-based neuroimaging studies face the challenge of developing tasks capable of equivalently probing reading networks across different age groups. Resting-state fMRI, which requires no specific task, circumvents these difficulties. Here, in 25 children (8-14 years) and 25 adults (21-46 years), we examined the extent to which individual differences in reading competence can be related to resting-state functional connectivity (RSFC) of regions implicated in reading. In both age groups, reading standard scores correlated positively with RSFC between the left precentral gyrus and other motor regions, and between Broca's and Wernicke's areas. This suggests that, regardless of age group, stronger coupling among motor regions, as well as between language/speech regions, subserves better reading, presumably reflecting automatized articulation. We also observed divergent RSFC-behavior relationships in children and adults, particularly those anchored in the left fusiform gyrus (FFG) (the visual word form area). In adults, but not children, better reading performance was associated with stronger positive correlations between FFG and phonology-related regions (Broca's area and the left inferior parietal lobule), and with stronger negative relationships between FFG and regions of the "task-negative" default network. These results suggest that both positive RSFC (functional coupling) between reading regions and negative RSFC (functional segregation) between a reading region and default network regions are important for automatized reading, characteristic of adult readers. Together, our task-independent RSFC findings highlight the importance of appreciating developmental changes in the neural correlates of reading competence, and suggest that RSFC may serve to facilitate the identification of reading disorders in different age groups.
Adaptive brain function is characterized by dynamic interactions within and between neuronal circuits, often occurring at the time scale of milliseconds. These complex interactions between adjacent and noncontiguous brain areas depend on a functional architecture that is maintained even in the absence of input. Functional MRI studies carried out during rest (R-fMRI) suggest that this architecture is represented in low-frequency (<0.1 Hz) spontaneous fluctuations in the blood oxygen level-dependent signal that are correlated within spatially distributed networks of brain areas. These networks, collectively referred to as the brain's intrinsic functional architecture, exhibit a remarkable correspondence with patterns of task-evoked coactivation as well as maps of anatomical connectivity. Despite this striking correspondence, there is no direct evidence that this intrinsic architecture forms the scaffold that gives rise to faster processes relevant to information processing and seizure spread. Here, we demonstrate that the spatial distribution and magnitude of temporally correlated low-frequency fluctuations observed with R-fMRI during rest predict the pattern and magnitude of corticocortical evoked potentials elicited within 500 ms after single-pulse electrical stimulation of the cerebral cortex with intracranial electrodes. Across individuals, this relationship was found to be independent of the specific regions and functional systems probed. Our findings bridge the immense divide between the temporal resolutions of these distinct measures of brain function and provide strong support for the idea that the low-frequency signal fluctuations observed with R-fMRI maintain and update the intrinsic architecture underlying the brain's repertoire of functional responses.
Research on the neural correlates of risk-related behaviors and personality traits has provided insight into mechanisms underlying both normal and pathological decision-making. Task-based neuroimaging studies implicate a distributed network of brain regions in risky decision-making. What remains to be understood are the interactions between these regions and their relation to individual differences in personality variables associated with real-world risk-taking.We employed resting state functional magnetic resonance imaging (R-fMRI) and resting state functional connectivity (RSFC) methods to investigate differences in the brain's intrinsic functional architecture associated with beliefs about the consequences of risky behavior. We obtained an individual measure of expected benefit from engaging in risky behavior, indicating a risk seeking or risk-averse personality, for each of 21 participants from whom we also collected a series of R-fMRI scans. The expected benefit scores were entered in statistical models assessing the RSFC of brain regions consistently implicated in both the evaluation of risk and reward, and cognitive control (i.e., orbitofrontal cortex, nucleus accumbens, lateral prefrontal cortex, dorsal anterior cingulate). We specifically focused on significant brain-behavior relationships that were stable across R-fMRI scans collected one year apart. Two stable expected benefit-RSFC relationships were observed: decreased expected benefit (increased risk-aversion) was associated with 1) stronger positive functional connectivity between right inferior frontal gyrus (IFG) and right insula, and 2) weaker negative functional connectivity between left nucleus accumbens and right parieto-occipital cortex.Task-based activation in the IFG and insula has been associated with risk-aversion, while activation in the nucleus accumbens and parietal cortex has been associated with both risk seeking and risk-averse tendencies. Our results suggest that individual differences in attitudes toward risk-taking are reflected in the brain's functional architecture and may have implications for engaging in real-world risky behaviors.
'/%3e%3cpath d='M200 752.362h200v300H200z' style='fill:%23fff;fill-opacity:1;stroke:none' transform='translate(0 -752.362)'/%3e%3cpath d='M400 752.362h200v300H400z' style='fill:%23ff883e;fill-opacity:1;stroke:none' transform='translate(0 -752.362)'/%3e%3c/svg%3e)
'%3e%3cpath fill='%23012169' d='M0 0v30h60V0z'/%3e%3cpath stroke='%23fff' stroke-width='6' d='m0 0 60 30m0-30L0 30'/%3e%3cpath stroke='%23C8102E' stroke-width='4' d='m0 0 60 30m0-30L0 30' clip-path='url(%23b)'/%3e%3cpath stroke='%23fff' stroke-width='10' d='M30 0v30M0 15h60'/%3e%3cpath stroke='%23C8102E' stroke-width='6' d='M30 0v30M0 15h60'/%3e%3c/g%3e%3c/svg%3e)