Quantitative results on continuity of the spectral factorization mapping

The spectral factorization mapping $F\to F^+$ puts a positive definite integrable matrix function $F$ having an integrable logarithm of the determinant in correspondence with an outer analytic matrix function $F^+$ such that $F = F^+(F^+)^*$ almost everywhere. The main question addressed here is to what extent $\|F^+ - G^+\|_{H_2}$ is controlled by $\|F-G\|_{L_1}$ and $\|\log \det F - \log\det G\|_{L_1}$.Comment: 22 page

Low-frequency oscillatory correlates of auditory predictive processing in cortical-subcortical networks: a MEG-study

Emerging evidence supports the role of neural oscillations as a mechanism for predictive information processing across large-scale networks. However, the oscillatory signatures underlying auditory mismatch detection and information flow between brain regions remain unclear. To address this issue, we examined the contribution of oscillatory activity at theta/alpha-bands (4–8/8–13 Hz) and assessed directed connectivity in magnetoencephalographic data while 17 human participants were presented with sound sequences containing predictable repetitions and order manipulations that elicited prediction-error responses. We characterized the spectro-temporal properties of neural generators using a minimum-norm approach and assessed directed connectivity using Granger Causality analysis. Mismatching sequences elicited increased theta power and phase-locking in auditory, hippocampal and prefrontal cortices, suggesting that theta-band oscillations underlie prediction-error generation in cortical-subcortical networks. Furthermore, enhanced feedforward theta/alpha-band connectivity was observed in auditory-prefrontal networks during mismatching sequences, while increased feedback connectivity in the alpha-band was observed between hippocampus and auditory regions during predictable sounds. Our findings highlight the involvement of hippocampal theta/alpha-band oscillations towards auditory prediction-error generation and suggest a spectral dissociation between inter-areal feedforward vs. feedback signalling, thus providing novel insights into the oscillatory mechanisms underlying auditory predictive processing

Brain Functional and Structural Networks Underpinning Musical Creativity

Musical improvisation is one of the most complex forms of creative behavior, which offers a realistic task paradigm for the investigation of real-time creativity. Despite previous studies on the topics of musical improvisation, brain activations, and creativity, the main questions about the neural mechanisms for musical improvisation in efforts to unlocking the mystery of human creativity remain unanswered. What are the brain regions that are activated during the improvised performances of music? How do these brain areas coordinate activity among themselves and others during such performances? Whether and how does the brain connectivity structure encapsulate such creative skills? In attempts to contribute to answering these questions, this dissertation examines the brain activity dynamics during musical improvisation, explores white matter fiber architecture in advanced jazz improvisers using functional and structural magnetic resonance imaging (MRI) techniques. A group of advanced jazz musicians underwent functional and structural magnetic resonance brain imaging. While the functional MRI (fMRI) of their brains were collected, these expert improvisers performed vocalization and imagery improvisation and pre-learned melody tasks. The activation and connectivity analysis of the fMRI data showed that musical improvisation is characterized by higher brain activity with less functional connectivity compared to pre-learned melody in the brain network consisting of the dorsolateral prefrontal cortex (dlPFC), supplementary motor area (SMA), lateral premotor cortex (lPMC), Cerebellum (Cb) and Broca’s Area (BCA). SMA received a dominant causal information flow from dlPFC during improvisation and prelearned melody tasks. The deterministic fiber tractography analysis also revealed that the underlying white matter structure and fiber pathways in advanced jazz improvisers were enhanced in advanced jazz improvisers compared to the control group of nonmusicians, specifically the dlPFC - SMA network. These results point to the notion that an expert\u27s performance under real-time constraints is an internally directed behavior controlled primarily by a specific brain network, that has enhanced task-supportive structural connectivity. Overall, these findings suggest that a creative act of an expert is functionally controlled by a specific cortical network as in any internally directed attention and is encapsulated by the long-timescale brain structural network changes in support of the related cognitive underpinnings

Wavelet correlations to reveal multiscale coupling in geophysical systems

The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth System. However, these models are based on simplifications of our understanding of nature, thus are unavoidably imperfect. Conversely, observation-based data of climatic and environmental variables are becoming increasingly accessible over large scales due to the progress of space-borne sensing technologies and data-assimilation techniques. Albeit uncertain, these data enable the possibility to start unraveling complex multivariable, multiscale relationships if the appropriate statistical methods are applied. Here, we investigate the potential of the wavelet cross-correlation method as a tool for identifying multiscale interactions, feedback and regime shifts in geophysical systems. The ability of wavelet cross-correlation to resolve the fast and slow components of coupled systems is tested on synthetic data of known directionality, and then applied to observations to study one of the most critical interactions between land and atmosphere: the coupling between soil moisture and near-ground air temperature. Results show that our method is not only able to capture the dynamics of the soil moisture-temperature coupling over a wide range of temporal scales (from days to several months) and climatic regimes (from wet to dry), but also to consistently identify the magnitude and directionality of the coupling. Consequently, wavelet cross-correlations are presented as a promising tool for the study of multiscale interactions, with the potential of being extended to the analysis of causal relationships in the Earth system.Comment: Submitted to Journal of Geophysical Research - Atmospher