On compression of Bruhat-Tits buildings

We obtain an analog of the compression of angles theorem in symmetric spaces for Bruhat--Tits buildings of the type $A$. More precisely, consider a $p$-adic linear space $V$ and the set $Lat(V)$ of all lattices in $V$. The complex distance in $Lat(V)$ is a complete system of invariants of a pair of points of $Lat(V)$ under the action of the complete linear group. An element of a Nazarov semigroup is a lattice in the duplicated linear space $V\oplus V$. We investigate behavior of the complex distance under the action of the Nazarov semigroup on the set $Lat(V)$.Comment: 6 page

Cosmological Evolution of Supergiant Star-Forming Clouds

In an exploration of the birthplaces of globular clusters, we present a careful examination of the formation of self-gravitating gas clouds within assembling dark matter haloes in a hierarchical cosmological model. Our high-resolution smoothed particle hydrodynamical simulations are designed to determine whether or not hypothesized supergiant molecular clouds (SGMCs) form and, if they do, to determine their physical properties and mass spectra. It was suggested in earlier work that clouds with a median mass of several 10^8 M_sun are expected to assemble during the formation of a galaxy, and that globular clusters form within these SGMCs. Our simulations show that clouds with the predicted properties are indeed produced as smaller clouds collide and agglomerate within the merging dark matter haloes of our cosmological model. We find that the mass spectrum of these clouds obeys the same power-law form observed for globular clusters, molecular clouds, and their internal clumps in galaxies, and predicted for the supergiant clouds in which globular clusters may form. We follow the evolution and physical properties of gas clouds within small dark matter haloes up to z = 1, after which prolific star formation is expected to occur. Finally, we discuss how our results may lead to more physically motivated "rules" for star formation in cosmological simulations of galaxy formation.Comment: Accepted to The Astrophysical Journal; 17 pages, 8 figure

Strongly Enhanced Low Energy Alpha-Particle Decay in Heavy Actinide Nuclei and Long-Lived Superdeformed and Hyperdeformed Isomeric States

Relatively low energy and very enhanced alpha-particle groups have been observed in various actinide fractions produced via secondary reactions in a CERN W target which had been irradiated with 24-GeV protons. In particular, 5.14, 5.27 and 5.53 MeV alpha-particle groups with corresponding half-lives of 3.8(+ -)1.0 y, 625(+ -)84 d and 26(+ -)7 d, have been seen in Bk, Es and Lr-No sources, respectively. The measured energies are a few MeV lower than the known g.s. to g.s. alpha-decays in the corresponding neutron-deficient actinide nuclei. The half-lives are 4 to 7 orders of magnitude shorter than expected from the systematics of alpha-particle decay in this region of nuclei. The deduced evaporation residue cross sections are in the mb region, about 4 orders of magnitude higher than expected. A consistent interpretation of the data is given in terms of production of long-lived isomeric states in the second and third wells of the potential-energy surfaces of the parent nuclei, which decay to the corresponding wells in the daughters. The possibility that the isomeric states in the third minimum are actually the true or very near the true ground states of the nuclei, and consequences regarding the production of the long-lived superheavy elements, are discussed.Comment: 27 pages including 8 figures and 4 table

Fibre-specific white matter reductions in Parkinson’s hallucinations and visual dysfunction

Objective: To investigate the microstructural and macrostructural white matter changes that accompany visual hallucinations and low visual performance in Parkinson’s disease, a risk factor for Parkinson’s dementia. Methods: We performed fixel-based analysis, a novel technique that provides metrics of specific fibre-bundle populations within a voxel (or fixel). Diffusion MRI data was acquired from patients with Parkinson’s disease (n=105, of which 34 low visual performers and 19 hallucinators) and age-matched controls (n=35). We used whole brain fixel-based analysis to compare micro-structural differences in fibre density (FD), macro-structural differences in fibre bundle cross-section (FC) and the combined fibre density and cross-section metric (FDC) across all white matter fixels. We then performed a tract of interest analysis comparing the most sensitive FDC metric across 11 tracts within the visual system. Results: Patients with Parkinson’s disease hallucinations exhibited macrostructural changes (reduced FC) within the splenium of the corpus callosum and the left posterior thalamic radiation compared to patients without hallucinations. Whilst there were no significant changes in FD, we found large reductions in the combined FDC metric in Parkinson’s hallucinators within the splenium (>50% reduction compared to non-hallucinators). Patients with Parkinson’s disease and low visual performance showed widespread microstructural and macrostructural changes within the genu and splenium of the corpus callosum, bilateral posterior thalamic radiations and the left inferior fronto-occipital fasciculus. Conclusions: We demonstrate specific white matter tract degeneration affecting posterior thalamic tracts in patients with Parkinson’s disease with hallucinations and low visual performance, providing direct mechanistic support for attentional models of visual hallucinations

Brain iron deposition is linked with cognitive severity in Parkinson’s disease

Background: Dementia is common in Parkinson’s disease (PD) but measures that track cognitive change in PD are lacking. Brain tissue iron accumulates with age and co-localises with pathological proteins linked to PD dementia such as amyloid. We used quantitative susceptibility mapping (QSM) to detect changes related to cognitive change in PD. Methods: We assessed 100 patients with early-stage to mid-stage PD, and 37 age-matched controls using the Montreal Cognitive Assessment (MoCA), a validated clinical algorithm for risk of cognitive decline in PD, measures of visuoperceptual function and the Movement Disorders Society Unified Parkinson’s Disease Rating Scale part 3 (UPDRS-III). We investigated the association between these measures and QSM, an MRI technique sensitive to brain tissue iron content. Results: We found QSM increases (consistent with higher brain tissue iron content) in PD compared with controls in prefrontal cortex and putamen (p<0.05 corrected for multiple comparisons). Whole brain regression analyses within the PD group identified QSM increases covarying: (1) with lower MoCA scores in the hippocampus and thalamus, (2) with poorer visual function and with higher dementia risk scores in parietal, frontal and medial occipital cortices, (3) with higher UPDRS-III scores in the putamen (all p<0.05 corrected for multiple comparisons). In contrast, atrophy, measured using voxel-based morphometry, showed no differences between groups, or in association with clinical measures. Conclusions: Brain tissue iron, measured using QSM, can track cognitive involvement in PD. This may be useful to detect signs of early cognitive change to stratify groups for clinical trials and monitor disease progression

Organisational and neuromodulatory underpinnings of structural-functional connectivity decoupling in patients with Parkinson's disease

Parkinson's dementia is characterised by changes in perception and thought, and preceded by visual dysfunction, making this a useful surrogate for dementia risk. Structural and functional connectivity changes are seen in humans with Parkinson's disease, but the organisational principles are not known. We used resting-state fMRI and diffusion-weighted imaging to examine changes in structural-functional connectivity coupling in patients with Parkinson's disease, and those at risk of dementia. We identified two organisational gradients to structural-functional connectivity decoupling: anterior-to-posterior and unimodal-to-transmodal, with stronger structural-functional connectivity coupling in anterior, unimodal areas and weakened towards posterior, transmodal regions. Next, we related spatial patterns of decoupling to expression of neurotransmitter receptors. We found that dopaminergic and serotonergic transmission relates to decoupling in Parkinson's overall, but instead, serotonergic, cholinergic and noradrenergic transmission relates to decoupling in patients with visual dysfunction. Our findings provide a framework to explain the specific disorders of consciousness in Parkinson's dementia, and the neurotransmitter systems that underlie these

Magnetic properties of the low-dimensional spin-1/2 magnet \alpha-Cu_2As_2O_7

In this work we study the interplay between the crystal structure and magnetism of the pyroarsenate \alpha-Cu_2As_2O_7 by means of magnetization, heat capacity, electron spin resonance and nuclear magnetic resonance measurements as well as density functional theory (DFT) calculations and quantum Monte Carlo (QMC) simulations. The data reveal that the magnetic Cu-O chains in the crystal structure represent a realization of a quasi-one dimensional (1D) coupled alternating spin-1/2 Heisenberg chain model with relevant pathways through non-magnetic AsO_4 tetrahedra. Owing to residual 3D interactions antiferromagnetic long range ordering at T_N\simeq10K takes place. Application of external magnetic field B along the magnetically easy axis induces the transition to a spin-flop phase at B_{SF}~1.7T (2K). The experimental data suggest that substantial quantum spin fluctuations take place at low magnetic fields in the ordered state. DFT calculations confirm the quasi-one-dimensional nature of the spin lattice, with the leading coupling J_1 within the structural dimers. QMC fits to the magnetic susceptibility evaluate J_1=164K, the weaker intrachain coupling J'_1/J_1 = 0.55, and the effective interchain coupling J_{ic1}/J_1 = 0.20.Comment: Accepted for publication in Physical Review

Roche Lobe Overflow from Dwarf Stellar Systems

We use both analytical analyses and numerical simulations to examine the evolution of residual gas within tidally-limited dwarf galaxies and globular clusters. If the gas sound speed exceeds about 10% of the central velocity dispersion, as is the case for ionized gas within small stellar systems, the gas shall have significant density at the tidal radius, and the gas may be lost on timescales as short as a few times the sound crossing time of the system. In colder systems, the density at the tidal radius is much lower, greatly reducing the mass loss rate, and the system may retain its gas for a Hubble time. The tidally removed gas shall follow an orbit close to that of the original host system, forming an extended stream of ionized, gaseous debris. Tidal mass loss severely limits the ability of dwarf systems to continuously form stars. The ordinary gas content in many dwarf galaxies is fully ionized during high red-shift epochs, possibly preventing star formation in some systems, leading to the formation of starless, dark-matter concentrations. In either the field or in the center of galaxy clusters, ionized gas may be retained by dwarf galaxies, even though its sound speed may be comparable to or even exceed the velocity dispersion. These processes may help to explain some observed differences among dwarf galaxy types, as well as observations of the haloes of massive galaxies.Comment: 28 pages, LaTeX, AASTex macro