257,416 research outputs found
A^1-homotopy groups, excision, and solvable quotients
We study some properties of A^1-homotopy groups: geometric interpretations of
connectivity, excision results, and a re-interpretation of quotients by free
actions of connected solvable groups in terms of covering spaces in the sense
of A^1-homotopy theory. These concepts and results are well-suited to the study
of certain quotients via geometric invariant theory.
As a case study in the geometry of solvable group quotients, we investigate
A^1-homotopy groups of smooth toric varieties. We give simple combinatorial
conditions (in terms of fans) guaranteeing vanishing of low degree A^1-homotopy
groups of smooth (proper) toric varieties. Finally, in certain cases, we can
actually compute the "next" non-vanishing A^1-homotopy group (beyond
\pi_1^{A^1}) of a smooth toric variety. From this point of view, A^1-homotopy
theory, even with its exquisite sensitivity to algebro-geometric structure, is
almost "as tractable" (in low degrees) as ordinary homotopy for large classes
of interesting varieties.Comment: 48 pages, To appear Adv. Math, typographical and grammatical update
Hierarchical modularity in human brain functional networks
The idea that complex systems have a hierarchical modular organization
originates in the early 1960s and has recently attracted fresh support from
quantitative studies of large scale, real-life networks. Here we investigate
the hierarchical modular (or "modules-within-modules") decomposition of human
brain functional networks, measured using functional magnetic resonance imaging
(fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a
customized template to extract networks with more than 1800 regional nodes, and
we applied a fast algorithm to identify nested modular structure at several
hierarchical levels. We used mutual information, 0 < I < 1, to estimate the
similarity of community structure of networks in different subjects, and to
identify the individual network that is most representative of the group.
Results show that human brain functional networks have a hierarchical modular
organization with a fair degree of similarity between subjects, I=0.63. The
largest 5 modules at the highest level of the hierarchy were medial occipital,
lateral occipital, central, parieto-frontal and fronto-temporal systems;
occipital modules demonstrated less sub-modular organization than modules
comprising regions of multimodal association cortex. Connector nodes and hubs,
with a key role in inter-modular connectivity, were also concentrated in
association cortical areas. We conclude that methods are available for
hierarchical modular decomposition of large numbers of high resolution brain
functional networks using computationally expedient algorithms. This could
enable future investigations of Simon's original hypothesis that hierarchy or
near-decomposability of physical symbol systems is a critical design feature
for their fast adaptivity to changing environmental conditions
Frontal brain asymmetries as effective parameters to assess the quality of audiovisual stimuli perception in adult and young cochlear implant users
How is music perceived by cochlear implant (CI) users? This question arises as "the next step" given the impressive performance obtained by these patients in language perception. Furthermore, how can music perception be evaluated beyond self-report rating, in order to obtain measurable data? To address this question, estimation of the frontal electroencephalographic (EEG) alpha activity imbalance, acquired through a 19-channel EEG cap, appears to be a suitable instrument to measure the approach/withdrawal (AW index) reaction to external stimuli. Specifically, a greater value of AW indicates an increased propensity to stimulus approach, and vice versa a lower one a tendency to withdraw from the stimulus. Additionally, due to prelingually and postlingually deafened pathology acquisition, children and adults, respectively, would probably differ in music perception. The aim of the present study was to investigate children and adult CI users, in unilateral (UCI) and bilateral (BCI) implantation conditions, during three experimental situations of music exposure (normal, distorted and mute). Additionally, a study of functional connectivity patterns within cerebral networks was performed to investigate functioning patterns in different experimental populations. As a general result, congruency among patterns between BCI patients and control (CTRL) subjects was seen, characterised by lowest values for the distorted condition (vs. normal and mute conditions) in the AW index and in the connectivity analysis. Additionally, the normal and distorted conditions were significantly different in CI and CTRL adults, and in CTRL children, but not in CI children. These results suggest a higher capacity of discrimination and approach motivation towards normal music in CTRL and BCI subjects, but not for UCI patients. Therefore, for perception of music CTRL and BCI participants appear more similar than UCI subjects, as estimated by measurable and not self-reported parameters
State-dependent changes of connectivity patterns and functional brain network topology in Autism Spectrum Disorder
Anatomical and functional brain studies have converged to the hypothesis that
Autism Spectrum Disorders (ASD) are associated with atypical connectivity.
Using a modified resting-state paradigm to drive subjects' attention, we
provide evidence of a very marked interaction between ASD brain functional
connectivity and cognitive state. We show that functional connectivity changes
in opposite ways in ASD and typicals as attention shifts from external world
towards one's body generated information. Furthermore, ASD subject alter more
markedly than typicals their connectivity across cognitive states. Using
differences in brain connectivity across conditions, we classified ASD subjects
at a performance around 80% while classification based on the connectivity
patterns in any given cognitive state were close to chance. Connectivity
between the Anterior Insula and dorsal-anterior Cingulate Cortex showed the
highest classification accuracy and its strength increased with ASD severity.
These results pave the path for diagnosis of mental pathologies based on
functional brain networks obtained from a library of mental states
Developmental time windows for axon growth influence neuronal network topology
Early brain connectivity development consists of multiple stages: birth of
neurons, their migration and the subsequent growth of axons and dendrites. Each
stage occurs within a certain period of time depending on types of neurons and
cortical layers. Forming synapses between neurons either by growing axons
starting at similar times for all neurons (much-overlapped time windows) or at
different time points (less-overlapped) may affect the topological and spatial
properties of neuronal networks. Here, we explore the extreme cases of axon
formation especially concerning short-distance connectivity during early
development, either starting at the same time for all neurons (parallel, i.e.
maximally-overlapped time windows) or occurring for each neuron separately one
neuron after another (serial, i.e. no overlaps in time windows). For both
cases, the number of potential and established synapses remained comparable.
Topological and spatial properties, however, differed: neurons that started
axon growth early on in serial growth achieved higher out-degrees, higher local
efficiency, and longer axon lengths while neurons demonstrated more homogeneous
connectivity patterns for parallel growth. Second, connection probability
decreased more rapidly with distance between neurons for parallel growth than
for serial growth. Third, bidirectional connections were more numerous for
parallel growth. Finally, we tested our predictions with C. elegans data.
Together, this indicates that time windows for axon growth influence the
topological and spatial properties of neuronal networks opening the possibility
to a posteriori estimate developmental mechanisms based on network properties
of a developed network.Comment: Biol Cybern. 2015 Jan 30. [Epub ahead of print
Multiscale Topological Properties Of Functional Brain Networks During Motor Imagery After Stroke
In recent years, network analyses have been used to evaluate brain
reorganization following stroke. However, many studies have often focused on
single topological scales, leading to an incomplete model of how focal brain
lesions affect multiple network properties simultaneously and how changes on
smaller scales influence those on larger scales. In an EEG-based experiment on
the performance of hand motor imagery (MI) in 20 patients with unilateral
stroke, we observed that the anatomic lesion affects the functional brain
network on multiple levels. In the beta (13-30 Hz) frequency band, the MI of
the affected hand (Ahand) elicited a significantly lower smallworldness and
local efficiency (Eloc) versus the unaffected hand (Uhand). Notably, the
abnormal reduction in Eloc significantly depended on the increase in
interhemispheric connectivity, which was in turn determined primarily by the
rise in regional connectivity in the parieto-occipital sites of the affected
hemisphere. Further, in contrast to the Uhand MI, in which significantly high
connectivity was observed for the contralateral sensorimotor regions of the
unaffected hemisphere, the regions that increased in connection during the
Ahand MI lay in the frontal and parietal regions of the contralaterally
affected hemisphere. Finally, the overall sensorimotor function of our
patients, as measured by Fugl-Meyer Assessment (FMA) index, was significantly
predicted by the connectivity of their affected hemisphere. These results
increase our understanding of stroke-induced alterations in functional brain
networks.Comment: Neuroimage, accepted manuscript (unedited version) available online
19-June-201
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