Impaired judgments of sadness but not happiness following bilateral amygdala damage

Although the amygdala's role in processing facial expressions of fear has been well established, its role in the processing of other emotions is unclear. In particular, evidence for the amygdala's involvement in processing expressions of happiness and sadness remains controversial. To clarify this issue, we constructed a series of morphed stimuli whose emotional expression varied gradually from very faint to more pronounced. Five morphs each of sadness and happiness, as well as neutral faces, were shown to 27 subjects with unilateral amygdala damage and 5 with complete bilateral amygdala damage, whose data were compared to those from 12 brain-damaged and 26 normal controls. Subjects were asked to rate the intensity and to label the stimuli. Subjects with unilateral amygdala damage performed very comparably to controls. By contrast, subjects with bilateral amygdala damage showed a specific impairment in rating sad faces, but performed normally in rating happy faces. Furthermore, subjects with right unilateral amygdala damage performed somewhat worse than subjects with left unilateral amygdala damage. The findings suggest that the amygdala's role in processing of emotional facial expressions encompasses multiple negatively valenced emotions, including fear and sadness

Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context

Dominance attributions following damage to the ventromedial prefrontal cortex

Damage to the human ventromedial prefrontal cortex (VM) can result in dramatic and maladaptive changes in social behavior despite preservation of most other cognitive abilities. One important aspect of social cognition is the ability to detect social dominance, a process of attributing from particular social signals another person's relative standing in the social world. To test the role of the VM in making attributions of social dominance, we designed two experiments: one requiring dominance judgments from static pictures of faces, the second requiring dominance judgments from film clips. We tested three demographically matched groups of subjects: subjects with focal lesions in the VM (n=15), brain-damaged comparison subjects with lesions excluding the VM (n=11), and a reference group of normal individuals with no history of neurological disease (n=32). Contrary to our expectation, we found that subjects with VM lesions gave dominance judgments on both tasks that did not differ significantly from those given by the other groups. Despite their grossly normal performance, however, subjects with VM lesions showed more subtle impairments specifically when judging static faces: They were less discriminative in their dominance judgments, and did not appear to make normal use of gender and age of the faces in forming their judgments. The findings suggest that, in the laboratory tasks we used, damage to the VM does not necessarily impair judgments of social dominance, although it appears to result in alterations in strategy that might translate into behavioral impairments in real life

Impaired recognition of social emotions following amygdala damage

Lesion, functional imaging, and single-unit studies in human and nonhuman animals have demonstrated a role for the amygdala in processing stimuli with emotional and social significance. We investigated the recognition of a wide variety of facial expressions, including basic emotions (e.g., happiness, anger) and social emotions (e.g., guilt, admiration, flirtatiousness). Prior findings with a standardized set of stimuli indicated that recognition of social emotions can be signaled by the eye region of the face and is disproportionately impaired in autism (Baron-Cohen, Wheelwright, & Jolliffe, 1997). To test the hypothesis that the recognition of social emotions depends on the amygdala, we administered the same stimuli to 30 subjects with unilateral amygdala damage (16 left, 14 right), 2 with bilateral amygdala damage, 47 brain-damaged controls, and 19 normal controls. Compared with controls, subjects with unilateral or bilateral amygdala damage were impaired when recognizing social emotions; moreover, they were more impaired in recognition of social emotions than in recognition of basic emotions, and, like previously described patients with autism, they were impaired also when asked to recognize social emotions from the eye region of the face alone. The findings suggest that the human amygdala is relatively specialized to process stimuli with complex social significance. The results also provide further support for the idea that some of the impairments in social cognition seen in patients with autism may result from dysfunction of the amygdala

Supply Function Equilibria: Step Functions and Continuous Representations

In most wholesale electricity markets generators must submit step-function offers of supply to a uniform price auction, and the market is cleared at the price of the most expensive offer needed to meet realised demand. Such markets can most elegantly be modelled as the pure-strategy, Nash Equilibrium of continuous supply functions, in which each supplier has a unique profit maximising choice of supply function given the choices of other suppliers. Critics argue that the discreteness and discontinuity of the required steps can rule out pure-strategy equilibria and may result in price instability. This paper argues that if prices must be selected from a finite set the resulting step function converges to the continuous supply function as the number of steps increases, reconciling the apparently very disparate approaches to modelling electricity markets.Auctions; Supply Function Equilibria; Convergence of Step-Functions; Electricity Markets