7,151 research outputs found

    Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries

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    We discuss the possibility of obtaining a non-abelian discrete flavor symmetry from an underlying continuous, possibly gauged, flavor symmetry SU(2) or SU(3) through spontaneous symmetry breaking. We consider all possible cases, where the continuous symmetry is broken by small representations. "Small" representations are these which couple at leading order to the Standard Model fermions transforming as two- or three-dimensional representations of the flavor group. We find that, given this limited representation content, the only non-abelian discrete group which can arise as a residual symmetry is the quaternion group D_2'.Comment: 15 page

    Extremal behavior of stochastic volatility models

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    Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and non-classical stochastic volatility models with respect to their extreme behavior. We show that classical stochastic volatility models driven by Brownian motion can model heavy tails, but obviously they are not able to model volatility jumps. Such phenomena can be modelled by Levy driven volatility processes as, for instance, by Levy driven Ornstein-Uhlenbeck models. They can capture heavy tails and volatility jumps. Also volatility clusters can be found in such models, provided the driving Levy process has regularly varying tails. This results then in a volatility model with similarly heavy tails. As the last class of stochastic volatility models, we investigate a continuous time GARCH(1,1) model. Driven by an arbitrary Levy process it exhibits regularly varying tails, volatility upwards jumps and clusters on high levels

    Human Posterior Parietal Cortex Plans Where to Reach and What to Avoid

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    In this time-resolved functional magnetic resonance imaging (fMRI) study, we aimed to trace the neuronal correlates of covert planning processes that precede visually guided motor behavior. Specifically, we asked whether human posterior parietal cortex has prospective planning activity that can be distinguished from activity related to retrospective visual memory and attention. Although various electrophysiological studies in monkeys have demonstrated such motor planning at the level of parietal neurons, comparatively little support is provided by recent human imaging experiments. Rather, a majority of experiments highlights a role of human posterior parietal cortex in visual working memory and attention. We thus sought to establish a clear separation of visual memory and attention from processes related to the planning of goal-directed motor behaviors. To this end, we compared delayed-response tasks with identical mnemonic and attentional demands but varying degrees of motor planning. Subjects memorized multiple target locations, and in a random subset of trials targets additionally instructed (1) desired goals or (2) undesired goals for upcoming finger reaches. Compared with the memory/attention-only conditions, both latter situations led to a specific increase of preparatory fMRI activity in posterior parietal and dorsal premotor cortex. Thus, posterior parietal cortex has prospective plans for upcoming behaviors while considering both types of targets relevant for action: those to be acquired and those to be avoided

    Space representation for eye movements is more contralateral in monkeys than in humans

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    Contralateral hemispheric representation of sensory inputs (the right visual hemifield in the left hemisphere and vice versa) is a fundamental feature of primate sensorimotor organization, in particular the visuomotor system. However, many higher-order cognitive functions in humans show an asymmetric hemispheric lateralization—e.g., right brain specialization for spatial processing—necessitating a convergence of information from both hemifields. Electrophysiological studies in monkeys and functional imaging in humans have investigated space and action representations at different stages of visuospatial processing, but the transition from contralateral to unified global spatial encoding and the relationship between these encoding schemes and functional lateralization are not fully understood. Moreover, the integration of data across monkeys and humans and elucidation of interspecies homologies is hindered, because divergent findings may reflect actual species differences or arise from discrepancies in techniques and measured signals (electrophysiology vs. imaging). Here, we directly compared spatial cue and memory representations for action planning in monkeys and humans using event-related functional MRI during a working-memory oculomotor task. In monkeys, cue and memory-delay period activity in the frontal, parietal, and temporal regions was strongly contralateral. In putative human functional homologs, the contralaterality was significantly weaker, and the asymmetry between the hemispheres was stronger. These results suggest an inverse relationship between contralaterality and lateralization and elucidate similarities and differences in human and macaque cortical circuits subserving spatial awareness and oculomotor goal-directed actions
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