On representation categories of wreath products in non-integral rank

For an arbitrary commutative ring k and t in k, we construct a 2-functor S_t which sends a tensor category to a new tensor category. By applying it to the representation category of a bialgebra we obtain a family of categories which interpolates the representation categories of the wreath products of the bialgebra. This generalizes the construction of Deligne's category Rep(S_t,k) for representation categories of symmetric groups.Comment: [v3] 41 pages, appendix added; final version [v2] 39 pages, title changed [v1] 32 page

Test of Ideational Praxis (TIP): Preliminary Findings and Interrater and Test–Retest Reliability With Preschoolers

Praxis is the ability of the brain to develop an idea for action and plan, organize, and execute unfamiliar motor actions. It enables purposeful interaction with people and things in the environment. Ideation is central to praxis but has been little researched. This study investigated the reliability of the Test of Ideational Praxis (TIP) and examined ideational praxis in typical preschoolers. TIP performance for 78 preschoolers ages 3, 4, and 5 yr was videotaped and scored by two trained raters. The TIP has strong interrater reliability, supporting earlier findings. Further, we documented test–retest stability over 2 wk. As a group, preschoolers identified 10.6 affordances (ideas) for action on the TIP; no age differences were found. Training is required for accurate scoring of the TIP; following training, clinicians and researchers may find the TIP a useful tool to screen motor ideational abilities in young children

Quivers of monoids with basic algebras

We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term rectangular monoids (in the semigroup theory literature the class is known as $\mathbf{DO}$) to representation theoretic computations for group algebras of maximal subgroups. Hence in good characteristic for the maximal subgroups, this gives an essentially complete computation. Since groups are examples of rectangular monoids, we cannot hope to do better than this. For the subclass of $\mathscr R$-trivial monoids, we also provide a semigroup theoretic description of the projective indecomposables and compute the Cartan matrix.Comment: Minor corrections and improvements to exposition were made. Some theorem statements were simplified. Also we made a language change. Several of our results are more naturally expressed using the language of Karoubi envelopes and irreducible morphisms. There are no substantial changes in actual result

Characteristic-free resolutions of Weyl and Specht modules

We construct explicit resolutions of Weyl modules by divided powers and of co-Specht modules by permutational modules. We also prove a conjecture of Boltje-Hartmann on resolutions of co-Specht modules.Comment: 31 page

Parasympathetic functions in children with sensory processing disorder.

The overall goal of this study was to determine if parasympathetic nervous system (PsNS) activity is a significant biomarker of sensory processing difficulties in children. Several studies have demonstrated that PsNS activity is an important regulator of reactivity in children, and thus, it is of interest to study whether PsNS activity is related to sensory reactivity in children who have a type of condition associated with sensory processing disorders termed sensory modulation dysfunction (SMD). If so, this will have important implications for understanding the mechanisms underlying sensory processing problems of children and for developing intervention strategies to address them. The primary aims of this project were: (1) to evaluate PsNS activity in children with SMD compared to typically developing (TYP) children, and (2) to determine if PsNS activity is a significant predictor of sensory behaviors and adaptive functions among children with SMD. We examine PsNS activity during the Sensory Challenge Protocol; which includes baseline, the administration of eight sequential stimuli in five sensory domains, recovery, and also evaluate response to a prolonged auditory stimulus. As a secondary aim we examined whether subgroups of children with specific physiological and behavioral sensory reactivity profiles can be identified. Results indicate that as a total group the children with severe SMD demonstrated a trend for low baseline PsNS activity, compared to TYP children, suggesting this may be a biomarker for SMD. In addition, children with SMD as a total group demonstrated significantly poorer adaptive behavior in the communication and daily living subdomains and in the overall Adaptive Behavior Composite of the Vineland than TYP children. Using latent class analysis, the subjects were grouped by severity and the severe SMD group had significantly lower PsNS activity at baseline, tones and prolonged auditory. These results provide preliminary evidence that children who demonstrate severe SMD may have physiological activity that is different from children without SMD, and that these physiological and behavioral manifestations of SMD may affect a child\u27s ability to engage in everyday social, communication, and daily living skills

The gluing problem in the fusion systems of the symmetric, alternating and linear groups

Peer reviewedPreprin

A Chandra study of the large-scale shock and cool filaments in Hydra A: Evidence for substantial gas dredge-up by the central outburst

We present the results of a Chandra study of the Hydra A galaxy cluster, where a powerful AGN outburst created a large-scale cocoon shock. We investigated possible azimuthal variations in shock strength and shape, finding indications for a weak shock with a Mach number in the range ~1.2-1.3. We measured the temperature change across the shock front. However, the detection of a temperature rise in the regions immediately inside of the front is complicated by the underlying temperature profile of the cluster atmosphere. We measured the global temperature profile of the cluster up to 700 kpc, which represents the farthest measurement obtained with Chandra for this cluster. A "plateau" in the temperature profile in the range ~70-150 kpc indicates the presence of cool gas, which is likely the result of uplift of material by the AGN outburst. After masking the cool filaments visible in the hardness ratio map, the plateau disappears and the temperature profile recovers a typical shape with a peak around 190 kpc, just inside the shock front. However, it is unlikely that such a temperature feature is produced by the shock as it is consistent with the general shape of the temperature profiles observed for relaxed galaxy clusters. We studied the spectral properties of the cool filaments finding evidence that ~10^11 M_sun of low-entropy material has been dredged up by the rising lobes from the central 30 kpc to the observed current position of 75-150 kpc. The energy required to lift the cool gas is >~2.2 x 10^60 erg, which is comparable to the work required to inflate the cavities and is ~25% of the total energy of the large-scale shock. Our results show that the AGN feedback in Hydra A is acting not only by directly heating the gas, but also by removing a substantial amount of potential fuel for the SMBH.Comment: 11 pages, 9 figures, accepted for publication in ApJ (version with full resolution figures available at http://www.bo.astro.it/~myriam/files/papers/gitti-hydra.pdf

Bridging the gap between low and high mass dwarf galaxies

While the dark matter content within the most massive giant and smallest dwarf galaxies has been probed -- spanning a range of over one million in mass -- an important observational gap remains for galaxies of intermediate mass. This gap covers K band magnitudes of approximately -16 > M_K > -18 (for which dwarf galaxies have B--K ~ 2). On the high mass side of the gap are dwarf elliptical (dE) galaxies, that are dominated by stars in their inner regions. While the low mass side includes dwarf spheroidal (dSph) galaxies that are dark matter-dominated and ultra compact dwarf (UCD) objects that are star-dominated. Evolutionary pathways across the gap have been suggested but remain largely untested because the `gap' galaxies are faint, making dynamical measurements very challenging. With long exposures on the Keck telescope using the ESI instrument we have succeeded in bridging this gap by measuring the dynamical mass for five dwarf galaxies with M_K ~ -17.5 (M_B ~ --15.5). With the exception of our brightest dwarf galaxy, they possess relatively flat velocity dispersion profiles of around 20 km/s. By examining their 2D scaling relations and 3D fundamental manifold, we found that the sizes and velocity dispersions of these gap galaxies reveal continuous trends from dE to dSph galaxies. We conclude that low-luminosity dwarf elliptical galaxies are dominated by stars, not by dark matter, within their half light radii. This finding can be understood if internal feedback processes are operating most efficiently in gap galaxies, gravitationally heating the centrally-located dark matter to larger radii. Whereas external environmental processes, which can strip away stars, have a greater influence on dSph galaxies resulting in their higher dark matter fractions. Abridged.Comment: 20 pages, includes 12 figures, accepted for publication in MNRA

A novel method to allow noninvasive, longitudinal imaging of the murine immune system in vivo

In vivo imaging has revolutionized understanding of the spatiotemporal complexity that subserves the generation of successful effector and regulatory immune responses. Until now, invasive surgery has been required for microscopic access to lymph nodes (LNs), making repeated imaging of the same animal impractical and potentially affecting lymphocyte behavior. To allow longitudinal in vivo imaging, we conceived the novel approach of transplanting LNs into the mouse ear pinna. Transplanted LNs maintain the structural and cellular organization of conventional secondary lymphoid organs. They participate in lymphocyte recirculation and exhibit the capacity to receive and respond to local antigenic challenge. The same LN could be repeatedly imaged through time without the requirement for surgical exposure, and the dynamic behavior of the cells within the transplanted LN could be characterized. Crucially, the use of blood vessels as fiducial markers also allowed precise re-registration of the same regions for longitudinal imaging. Thus, we provide the first demonstration of a method for repeated, noninvasive, in vivo imaging of lymphocyte behavior

On exact categories and applications to triangulated adjoints and model structures

We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures. In particular, the interplay of different exact structures on the category of complexes of quasi-coherent sheaves leads to a streamlined and generalized version of recent results obtained by Estrada, Gillespie, Guil Asensio, Hovey, J{\o}rgensen, Neeman, Murfet, Prest, Trlifaj and possibly others.Comment: 38 pages; version 2: major revision, more explanation added at several places, reference list updated and extended, misprints correcte