On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces

Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We recover as special cases several results of Kostant, Panyushev, Suter.Comment: Latex file, 35 pages, minor corrections, some examples added. To appear in Selecta Mathematic

The relationship between invasive annual grasses and biological soil crust across Eastern Washington

Invasive annual grasses cause ecological and economic damage across the western US and are a focal point in restoration and management plans. Managing invasion resistance of natural areas is critical to maintaining their biodiversity and function. Climate change is expected to shift species interactions, including invasive annual grasses, and may alter invasion resistance. One component of invasion resistance is biological soil crust (biocrust), which has been shown to limit Bromus tectorum (cheatgrass) in arid regions. However, biocrust has been less studied in semiarid regions and its effects on other invasive annual grasses, such as Ventenata dubia, have never been studied. The goals of my project were to I) determine how the relationship between invasive annual grasses and biocrust vary across a precipitation gradient and among different invasive annual grass species, 2) determine how patterns of biocrust and Ventenata dubia change over time (3 years), and 3) determine the effects of trampling on biocrust composition and species invasion over 3 years. I surveyed biocrust and invasive annual grasses in 168 plots across 21 sites along a precipitation gradient from arid to semiarid. I also resurveyed vascular plant species and biocrust across a series of transects that were located across a gradient from high to low V. dubia abundance three years after they were established. Finally, I resurveyed vascular plants and biocrust in a series of experimentally trampled and control plots after three years. Biocrust was surveyed using morphological and color groups. I found that the dominant invasive annual grass along the precipitation gradient in eastern Washington shifted from B. tectorum in arid regions to V. dubia in semiarid regions. Biocrust percent cover and lichen richness was negatively correlated with both invasive annual grasses across all sites. Soil depth and topography also affect distribution of invasive annual grasses. Looking at long-term patterns of V. dubia in a semiarid prairie, I found that biocrust abundance or composition did not affect V. dubia. Additionally, trampling applied 3 years ago appeared to have no impact on V. dubia or biocrust abundance. V. dubia abundance over 3 years of sampling was strongly correlated with spring water depth in vernal pond areas. My results can be used to help land managers better understand the relationship between biocrust and invasive annual grass, particularly in the face of climate change which may create more arid climates in the Inland Northwest. Additionally, land managers can focus management of V. dubia in locations where excess spring precipitation persists --Leaves iv-v

Nuove e vecchie periferie popolari. Una ricerca etnografica in due aree di edilizia residenziale pubblica

Public housing suburbs are often an important element in reshaping the social and spatial geography of the city. This article is based on the study of two areas of public housing in Livorno: an historical and a more recent one. In Livorno social housing has led the urban development and the concentration of homogeneous groups of inhabitants. We report some results of an ethnographic research reconstructing how the spatial separation interacts with social relations of inhabitants of physically and socially peripheral areas. This kind of so called weak suburbs, despite possible trajectories of change, present complex patterns of problems. Attention has also been paid to the way concepts of neighborhood, suburb and community are merged in different combinations in the two areas, highlighting the «neighborhood effect», segregation, and encapsulation forms

Closed-Loop Targeted Memory Reactivation during Sleep Improves Spatial Navigation

Sounds associated with newly learned information that are replayed during non-rapid eye movement (NREM) sleep can improve recall in simple tasks. The mechanism for this improvement is presumed to be reactivation of the newly learned memory during sleep when consolidation takes place. We have developed an EEG-based closed-loop system to precisely deliver sensory stimulation at the time of down-state to up-state transitions during NREM sleep. Here, we demonstrate that applying this technology to participants performing a realistic navigation task in virtual reality results in a significant improvement in navigation efficiency after sleep that is accompanied by increases in the spectral power especially in the fast (12\u201315 Hz) sleep spindle band. Our results show promise for the application of sleep-based interventions to drive improvement in real-world tasks

Genetic and morphological variation in a Mediterranean glacial refugium: evidence from Italian pygmy shrews, Sorex minutus (Mammalia: Soricomorpha)

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Root polytopes and abelian ideals

We study the root polytope $\mathcal P_\Phi$ of a finite irreducible crystallographic root system $\Phi$ using its relation with the abelian ideals of a Borel subalgebra of a simple Lie algebra with root system $\Phi$. We determine the hyperplane arrangement corresponding to the faces of codimension 2 of $\mathcal P_\Phi$ and analyze its relation with the facets of $\mathcal P_\Phi$. For $\Phi$ of type $A_n$ or $C_n$, we show that the orbits of some special subsets of abelian ideals under the action of the Weyl group parametrize a triangulation of $\mathcal P_\Phi$. We show that this triangulation restricts to a triangulation of the positive root polytope $\mathcal P_\Phi^+$.Comment: 41 pages, revised version, accepted for publication in Journal of Algebraic Combinatoric