The influence of mood on visual perception of neutral material

In the study we investigated how current mood affects spontaneous perceptual processes of neutral stimuli of low‑arousal, unrelated to any specific task. Two separate but similar procedures were carried out: one using functional magnetic resonance imaging (fMRI), the other using electroencephalography based source localization. In both experiments, sessions of passive viewing of neutral pictures were preceded by either a negative or positive mood induction. In response to neutral stimuli, we observed higher activation of visual areas after positive mood induction and lower activations in medial prefrontal and right frontotemporal regions after negative mood induction. We conclude that in relatively safe laboratory conditions, after being exposed to negative emotional content, automatic processes of affective control are recruited by the prefrontal cortex. This results in attenuation of processing of incoming stimuli, as the stimuli do not carry salient information with respect to bottom‑up or top‑down processes. The observed effects may therefore represent an implicit mechanism of perceptual modulation

Topics in high-dimensional geometry and optimal transport

The first two chapters of this thesis are devoted to a question of Vitali Milman about the existence of well-complemented almost Euclidean subspaces of spaces uniformly isomorphic to $\ell_2^n$. First, we show that there exist constants $\alpha,\epsilon>0$ such that for every positive integer $n$ there is a continuous odd function $\psi : S^m\to S^n$, with $m\geq \alpha n$, such that the $\epsilon$-expansion of the image of $\psi$ does not contain a great circle. We also show how this result is connected to the aforementioned conjecture, more precisely that it allows to build a counterexample to a variation of the question. We then, in the second chapter, present an example of a normed space $X$ of arbitrarily high dimension that is strongly 2-Euclidean but contains no 2-dimensional subspace that is strongly $(1+\epsilon)$-Euclidean and strongly $(1+\epsilon)$-complemented, where $\epsilon>0$ is an absolute constant. This is a counterexample to the ``strong'' Milman problem. The second part of this thesis involves topics related to optimal transport theory. The third chapter focuses on cost induced transforms. In particular, a family of order reversing isomorphisms $\mathcal{A}_t$, which are related to the polarity transform $\mathcal{A}$, is discussed. We prove that $\mathcal{A}_t$ is the unique, up to linear terms, order reversing isomorphism on its image class. In the last chapter, we give a new proof of the Rockafellar-R\"uschendorf theorem about the existence of a potential for a given $c$-cyclically monotone set with a real-valued cost function. We then generalize the theorem to non-traditional cost functions, i.e. those which may also take the value $+\infty$, and prove that a necessary and sufficient condition for the existence of a potential is that of $c$-path boundedness. Finally, we apply our theorem to show that for a continuous cost function and a compact, $c$-cyclically monotone set which is ``bounded away from infinity'' one gets a potential.UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the Cambridge Centre for Analysis (CCA)

Religious fundamentalism modulates neural responses to error-related words : the role of motivation toward closure

Examining the relationship between brain activity and religious fundamentalism, this study explores whether fundamentalist religious beliefs increase responses to error-related words among participants intolerant to uncertainty (i.e., high in the need for closure) in comparison to those who have a high degree of toleration for uncertainty (i.e., those who are low in the need for closure). We examine a negative-going event-related brain potentials occurring 400 ms after stimulus onset (the N400) due to its well-understood association with the reactions to emotional conflict. Religious fundamentalism and tolerance of uncertainty were measured on self-report measures, and electroencephalographic neural reactivity was recorded as participants were performing an emotional Stroop task. In this task, participants read neutral words and words related to uncertainty, errors, and pondering, while being asked to name the color of the ink with which the word is written. The results confirm that among people who are intolerant of uncertainty (i.e., those high in the need for closure), religious fundamentalism is associated with an increased N400 on error-related words compared with people who tolerate uncertainty well (i.e., those low in the need for closure)

Towards a constructionist approach to emotions : verification of the three-dimensional model of affect with EEG-independent component analysis

The locationist model of affect, which assumes separate brain structures devoted to particular discrete emotions, is currently being questioned as it has not received enough convincing experimental support. An alternative, constructionist approach suggests that our emotional states emerge from the interaction between brain functional networks, which are related to more general, continuous affective categories. In the study, we tested whether the three-dimensional model of affect based on valence, arousal, and dominance (VAD) can reflect brain activity in a more coherent way than the traditional locationist approach. Independent components of brain activity were derived from spontaneous EEG recordings and localized using the DIPFIT method. The correspondence between the spectral power of the revealed brain sources and a mood self-report quantified on the VAD space was analysed. Activation of four (out of nine) clusters of independent brain sources could be successfully explained by the specific combination of three VAD dimensions. The results support the constructionist theory of emotions

Effective connectivity during visual processing is affected by emotional state

The limitations of our cognitive resources necessitate the selection of relevant information from the incoming visual stream. This selection and prioritizing of stimuli allows the organism to adapt to the current conditions. However, the characteristics of this process vary with time and depend on numerous external and internal factors. The present study was aimed at determining how the emotional state affects effective connectivity between visual, attentional and control brain areas during the perception of affective visual stimuli. The Directed Transfer Function was applied on a 32-electrode EEG recording to quantify the direction and intensity of the information flow during two sessions: positive and negative. These data were correlated with a self-report of the emotional state. We demonstrated that the current mood, as measured by self-report, is a factor which affects the patterns of effective cortical connectivity. An increase in prefrontal top-down control over the visual and attentional areas was revealed in a state of tension. It was accompanied by increased outflow within and from the areas recognized as the ventral attentional network. By contrast, a positive emotional state was associated with heightened flow from the parietal to the occipital area. The functional significance of the revealed effects is discussed

The dynamics of pain reappraisal : the joint contribution of cognitive change and mental load

This study was designed to investigate the neural mechanism of cognitive modulation of pain via a reappraisal strategy with high temporal resolution. The EEG signal was recorded from 29 participants who were instructed to down-regulate, up-regulate, or maintain their pain experience. The L2 minimum norm source reconstruction method was used to localize areas in which a significant effect of the instruction was present. Down-regulating pain by reappraisal exerted a robust effect on pain processing from as early as ~100 ms that diminished the activity of limbic brain regions: the anterior cingulate cortex, right orbitofrontal cortex, left anterior temporal region, and left insula. However, compared with the no-regulation condition, the neural activity was similarly attenuated in the up- and down-regulation conditions. We suggest that this effect could be ascribed to the cognitive load that was associated with the execution of a cognitively demanding reappraisal task that could have produced a general attenuation of pain-related areas regardless of the aim of the reappraisal task (i.e., up- or down-regulation attempts). These findings indicate that reappraisal effects reflect the joint influence of both reappraisal-specific (cognitive change) and unspecific (cognitive demand) factors, thus pointing to the importance of cautiously selected control conditions that allow the modulating impact of both processes to be distinguished

Stability of polydisc slicing

We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and Pelczy\'nski (2000). Intriguingly, compared to the real case, there is an additional asymptotic maximiser. In addition to Fourier-analytic bounds, we crucially rely on a self-improving feature of polydisc slicing, established via probabilistic arguments