Neural representations of social and non-social uncertainty in human decision making

The social landscape is filled with an intricate web of species-specific desired objects and course of actions. Humans are highly social animals and, as they navigate this landscape, they need to produce adapted decision-making behaviour. Traditionally social and non-social neural mechanisms affecting choice have been investigated using different approaches. Recently, in an effort to unite these findings, two main theories have been proposed to explain how the brain might encode social and non-social motivational decision-making: the extended common currency and the social valuation specific schema (Ruff & Fehr 2014). One way to test these theories is to directly compare neural activity related to social and non-social decision outcomes within the same experimental setting. Here we address this issue by focusing on the neural substrates of social and non-social forms of uncertainty. Using functional magnetic resonance imaging (fMRI) we directly compared the neural representations of reward and risk prediction and errors (RePE and RiPE) in social and non- social situations using gambling games. We used a trust betting game to vary uncertainty along a social dimension (trustworthiness), and a card game (Preuschoff et al. 2006) to vary uncertainty along a non-social dimension (pure risk). The trust game was designed to maintain the same structure of the card game. In a first study, we exposed a divide between subcortical and cortical regions when comparing the way these regions process social and non-social forms of uncertainty during outcome anticipation. Activity in subcortical regions reflected social and non-social RePE, while activity in cortical regions correlated with social RePE and non-social RiPE. The second study focused on outcome delivery and integrated the concept of RiPE in non-social settings with that of fairness and monetary utility maximisation in social settings. In particular these results corroborate recent models of anterior insula function (Singer et al. 2009; Seth 2013), and expose a possible neural mechanism that weights fairness and uncertainty but not monetary utility. The third study focused on functionally defined regions of the early visual cortex (V1) showing how activity in these areas, traditionally considered only visual, might reflect motivational prediction errors in addition to known perceptual prediction mechanisms (den Ouden et al 2012). On the whole, while our results do not support unilaterally one or the other theory modeling the underlying neural dynamics of social and non-social forms of decision making, they provide a working framework where both general mechanisms might coexist.

Which way is up? Grounded mental representations of space

Processing language is postulated to involve a mental simulation, or re-enactment of perceptual, motor, and introspective states that were acquired experientially (Barsalou, 1999, 2008). One such aspect that is mentally simulated during processing of certain concepts is spatial location. For example, upon processing the word “moon” the prominent spatial location of the concept (e.g. ‘upward’) is mentally simulated. In six eye-tracking experiments, we investigate how mental simulations of spatial location affect processing. We first address a conflict in previous literature whereby processing is shown to be impacted in both a facilitatory and inhibitory way. Two of our experiments showed that mental simulations of spatial association facilitate saccades launched toward compatible locations; however, a third experiment showed an inhibitory effect on saccades launched towards incompatible locations. We investigated these differences with further experiments, which led us to conclude that the nature of the effect (facilitatory or inhibitory) is dependent on the demands of the task and, in fitting with the theory of Grounded Cognition (Barsalou, 2008), that mental simulations impact processing in a dynamic way. Three further experiments explored the nature of verticality – specifically, whether ‘up’ is perceived as away from gravity, or above our head. Using similar eye-tracking methods, and by manipulating the position of participants, we were able to dissociate these two possible standpoints. The results showed that mental simulations of spatial location facilitated saccades to compatible locations, but only when verticality was dissociated from gravity (i.e. ‘up’ was above the participant’s head). We conclude that this is not due to an ‘embodied’ mental simulation, but rather a result of heavily ingrained visuo-motor association between vertical space and eye movements.

Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.