975 research outputs found
The quantum group of a preregular multilinear form
We describe the universal quantum group preserving a preregular multilinear
form, by means of an explicit finite presentation of the corresponding Hopf
algebra.Comment: 17 pages - Ref. 11 correcte
Half-commutative orthogonal Hopf algebras
A half-commutative orthogonal Hopf algebra is a Hopf *-algebra generated by
the self-adjoint coefficients of an orthogonal matrix corepresentation
that half commute in the sense that for any . The first non-trivial such Hopf algebras were discovered by Banica
and Speicher. We propose a general procedure, based on a crossed product
construction, that associates to a self-transpose compact subgroup a half-commutative orthogonal Hopf algebra . It is shown
that any half-commutative orthogonal Hopf algebra arises in this way. The
fusion rules of are expressed in term of those of .Comment: 11 page
The phase of ongoing EEG oscillations predicts visual perception
Oscillations are ubiquitous in electrical recordings of brain activity. While the amplitude of ongoing oscillatory activity is known to
correlate with various aspects of perception, the influence of oscillatory phase on perception remains unknown. In particular, since phase varies on a much faster timescale than the more sluggish amplitude fluctuations, phase effects could reveal the fine-grained neural mechanisms underlying perception. We presented brief flashes of light at the individual luminance threshold while EEG was recorded.
Although the stimulus on each trial was identical, subjects detected approximately half of the flashes (hits) and entirely missed the other
half (misses). Phase distributions across trials were compared between hits and misses. We found that shortly before stimulus onset, each of the two distributions exhibited significant phase concentration, but at different phase angles. This effect was strongest in the theta and alpha frequency bands. In this timeâfrequency range, oscillatory phase accounted for at least 16% of variability in detection performance and allowed the prediction of performance on the single-trial level. This finding indicates that the visual detection threshold fluctuates over time along with the phase of ongoing EEG activity. The results support the notion that ongoing oscillations shape our perception, possibly by providing a temporal reference frame for neural codes that rely on precise spike timing
Attentional selection of noncontiguous locations: The spotlight is only transiently âsplit"
It is still a matter of debate whether observers can attend simultaneously to more than one location. Using essentially the same paradigm as was used previously by N. P. Bichot, K. R. Cave, and H. Pashler (1999), we demonstrate that their finding of an attentional âsplitâ between separate target locations only reflects the early phase of attentional selection. Our subjects were asked to compare the shapes (circle or square) of 2 oddly colored targets within an array of 8 stimuli. After a varying stimulus onset asynchrony (SOA), 8 letters were flashed at the previous stimulus locations, followed by a mask. For a given SOA, the performance of subjects at reporting letters in each location was taken to reflect the distribution of spatial attention. In particular, by considering the proportion of trials in which none or both of the target letters were reported, we were able to infer the respective amount of attention allocated to each target without knowing, on a trial-by-trial basis which location (if any) was receiving the most attentional resources. Our results show that for SOAs under 100â150 ms, attention can be equally split between the two targets, a conclusion compatible with previous reports. However, with longer SOAs, this attentional division can no longer be sustained and attention ultimately settles at the location of one single stimulus
Brain Age: A State-Of-Mind? On the Stability of Functional Connectivity across Behavioral States
The study of functional connectivity (FC) has become a major branch of functional MRI (fMRI) research. Biswal et al. (1995)'s seminal discovery, that voxels in the sensorimotor cortex exhibited highly correlated activity at rest, seeded the field; however, it took at least 10 more years for it to gain widespread interest (Cordes et al., 2000; Greicius et al., 2003; Fox et al., 2005; Smith et al., 2009). There is currently much research into using FC as a biomarker for clinical diagnosis (Greicius, 2008; Linden, 2012) and, more generally, to gain insight into individual differences in brain function (Smith et al., 2013). Most studies investigate FC in the so-called âresting stateâ: subjects in the scanner are instructed to âlie still and think of nothing in particular,â with eyes closed, or open and fixating (Patriat et al., 2013); however, FC can also be computed from task fMRI data, usually after regressing out stimulus-evoked activity (Fair et al., 2007).
Cole et al. (2014) showed that, on average across subjects, a reliable intrinsic network structure is preserved through all tasks and rest. Additionally, âŒ40% of the connections show mild but significant changes that are task- (equivalently, state-) dependent. The variability of FC in individual subjects is now well recognized; functional network structure actually moves through several states within the span of a single resting-state run (Hutchison et al., 2013; Allen et al., 2014). While some authors have used the dynamic nature of individual network structure to their advantage, e.g., Damaraju et al. (2014), there is growing concern that this variability could impede our ability to use FC as a stable, trait-like measure of individual subjects. A recent study in The Journal of Neuroscience (Geerligs et al., 2015) reinforces this concern.
Geerligs et al. (2015)'s study is among the first published outputs of the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) cohort study, a large-scale (N = âŒ700), multimodal (MRI, MEG, and behavioral), cross-sectional, population-based adult lifespan (18â87 years old) investigation of the neural underpinnings of successful cognitive aging (Shafto et al., 2014; Taylor et al., 2015). Geerligs et al. (2015) used state-of-the-art imaging and preprocessing techniques, notably with respect to motion correction, which has been a thorny issue in the functional connectivity literature (Power et al., 2012; Satterthwaite et al., 2012; Van Dijk et al., 2012; Tyszka et al., 2014), and is especially problematic in aging studies (older people tend to move more, as confirmed in this study). Geerligs et al. (2015)'s study boasts a final sample size of 587 subjects (âŒ100 per decade of life), all of whom completed three different tasks in the scanner: an 8 min, 40 s eyes-closed resting-state run (REST state), an 8 min, 40 s sensorimotor task (detection of brief auditory tones and/or visual checkerboard flashes; TASK state), and an 8 min, 13 s movie-watching run (the movie being a shortened version of Alfred Hitchcock's television episode âBang, you're dead!,â as described in Hasson et al. (2010); MOVIE state).
Whole-brain FC was assessed among 748 nodes from a published functional parcellation (Craddock et al., 2012) (Fig. 1e), in each of the three states (REST, TASK, MOVIE), yielding a 748 Ă 748 FC matrix for each subject and each state (Fig. 1a). First, the authors performed the same analysis as Cole et al. (2014): they averaged FC matrices across subjects, then quantified the similarity of the average FC matrices for each pair of states using the Pearson correlation coefficient r (Fig. 1b). As in Cole et al. (2014), they found a high similarity between the REST and TASK FC matrices [variance explained r^2 = 87% of total variance (TV)]. Crucially, Geerligs et al. (2015) also quantified the reliability of the average FC matrix in each state using a (conservative) split-half procedure: the explainable variance (EV) was high (99%TV), because of the large number of subjects. The variance attributable to state effects was thus 99%TV â 87%TV = 12%TV; i.e., 12%TV/99%TV = 11.9%EV, for the RESTâTASK comparison
AGN feedback using AMR cosmological simulations
Feedback processes are thought to solve some of the long-standing issues of
the numerical modelling of galaxy formation: over-cooling, low angular
momentum, massive blue galaxies, extra-galactic enrichment, etc. The accretion
of gas onto super-massive black holes in the centre of massive galaxies can
release tremendous amounts of energy to the surrounding medium. We show, with
cosmological Adaptive Mesh Refinement simulations, how the growth of black
holes is regulated by the feedback from Active Galactic Nuclei using a new dual
jet/heating mechanism. We discuss how this large amount of feedback is able to
modify the cold baryon content of galaxies, and perturb the properties of the
hot plasma in their vicinity.Comment: 4 pages, 2 figures, contribution to the Astronomical Society of the
Pacific Conference Series for the Cefal\`u meeting "Advances in computational
astrophysics: methods, tools and outcomes
The cosmic evolution of massive black holes in the Horizon-AGN simulation
We analyse the demographics of black holes (BHs) in the large-volume
cosmological hydrodynamical simulation Horizon-AGN. This simulation
statistically models how much gas is accreted onto BHs, traces the energy
deposited into their environment and, consequently, the back-reaction of the
ambient medium on BH growth. The synthetic BHs reproduce a variety of
observational constraints such as the redshift evolution of the BH mass density
and the mass function. Strong self-regulation via AGN feedback, weak supernova
feedback, and unresolved internal processes result in a tight BH-galaxy mass
correlation. Starting at z~2, tidal stripping creates a small population of BHs
over-massive with respect to the halo. The fraction of galaxies hosting a
central BH or an AGN increases with stellar mass. The AGN fraction agrees
better with multi-wavelength studies, than single-wavelength ones, unless
obscuration is taken into account. The most massive halos present BH
multiplicity, with additional BHs gained by ongoing or past mergers. In some
cases, both a central and an off-centre AGN shine concurrently, producing a
dual AGN. This dual AGN population dwindles with decreasing redshift, as found
in observations. Specific accretion rate and Eddington ratio distributions are
in good agreement with observational estimates. The BH population is dominated
in turn by fast, slow, and very slow accretors, with transitions occurring at
z=3 and z=2 respectively.Comment: Accepted for publication in MNRA
Alien Registration- Dubois, J. Julien (Sanford, York County)
https://digitalmaine.com/alien_docs/2690/thumbnail.jp
Towards simulating star formation in turbulent high-z galaxies with mechanical supernova feedback
Feedback from supernovae is essential to understanding the self-regulation of
star formation in galaxies. However, the efficacy of the process in a
cosmological context remains unclear due to excessive radiative losses during
the shock propagation. To better understand the impact of SN explosions on the
evolution of galaxies, we perform a suite of high-resolution (12 pc), zoom-in
cosmological simulations of a Milky Way-like galaxy at z=3 with adaptive mesh
refinement. We find that SN explosions can efficiently regulate star formation,
leading to the stellar mass and metallicity consistent with the observed
mass-metallicity relation and stellar mass-halo mass relation at z~3. This is
achieved by making three important changes to the classical feedback scheme: i)
the different phases of SN blast waves are modelled directly by injecting
radial momentum expected at each stage, ii) the realistic time delay of SNe,
commencing at as early as 3 Myr, is required to disperse very dense gas before
a runaway collapse sets in at the galaxy centre via mergers of gas clumps, and
iii) a non-uniform density distribution of the ISM is taken into account below
the computational grid scale for the cell in which SN explodes. The last
condition is motivated by the fact that our simulations still do not resolve
the detailed structure of a turbulent ISM in which the fast outflows can
propagate along low-density channels. The simulated galaxy with the SN feedback
model shows strong outflows, which carry approximately ten times larger mass
than star formation rate, as well as smoothly rising circular velocity. Other
feedback models that do not meet the three conditions form too many stars,
producing a peaked rotation curve. Our results suggest that understanding the
structure of the turbulent ISM may be crucial to assess the role of SN and
other feedback processes in galaxy formation theory.Comment: 22 pages, 18 figures, Accepted for publication in MNRA
Black hole evolution: II. Spinning black holes in a supernova-driven turbulent interstellar medium
Supermassive black holes (BH) accrete gas from their surroundings and
coalesce with companions during galaxy mergers, and both processes change the
BH mass and spin. By means of high-resolution hydrodynamical simulations of
galaxies, either idealised or embedded within the cosmic web, we explore the
effects of interstellar gas dynamics and external perturbations on BH spin
evolution. All these physical quantities were evolved on-the-fly in a
self-consistent manner. We use a `maximal' model to describe the turbulence
induced by stellar feedback to highlight its impact on the angular momentum of
the gas accreted by the BH. Periods of intense star formation are followed by
phases where stellar feedback drives large-scale outflows and hot bubbles. We
find that BH accretion is synchronised with star formation, as only when gas is
cold and dense do both processes take place. During such periods, gas motion is
dominated by consistent rotation. On the other hand, when stellar feedback
becomes substantial, turbulent motion randomises gas angular momentum. However
BH accretion is strongly suppressed in that case, as cold and dense gas is
lacking. In our cosmological simulation, at very early times (z>6), the
galactic disc has not yet settled and no preferred direction exists for the
angular momentum of the accreted gas, so the BH spin remains low. As the gas
settles into a disc (6>z>3), the BH spin then rapidly reaches its maximal
value. At lower redshifts (z<3), even when galaxy mergers flip the direction of
the angular momentum of the accreted gas, causing it to counter-rotate, the BH
spin magnitude only decreases modestly and temporarily. Should this be a
typical evolution scenario for BH, it potentially has dramatic consequences
regarding their origin and assembly, as accretion on maximally spinning BH
embedded in thin Shakura-Sunyaev disc is significantly reduced.Comment: 16 pages, 13 figures, MNRAS accepte
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