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 $v=(v_{ij})$ that half commute in the sense that $abc=cba$ for any $a,b,c \in \{v_{ij}\}$. 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 $G \subset U_n$ a half-commutative orthogonal Hopf algebra $\mathcal A_*(G)$. It is shown that any half-commutative orthogonal Hopf algebra arises in this way. The fusion rules of $\mathcal A_*(G)$ are expressed in term of those of $G$.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 time–frequency 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 “split"

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 “split” 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 100–150 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 “resting state”: subjects in the scanner are instructed to “lie still and think of nothing in particular,” 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, ∼40% 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 = ∼700), multimodal (MRI, MEG, and behavioral), cross-sectional, population-based adult lifespan (18–87 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 (∼100 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 “Bang, you're dead!,” 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 × 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 − 87%TV = 12%TV; i.e., 12%TV/99%TV = 11.9%EV, for the REST–TASK 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