Study of the local field distribution on a single-molecule magnet-by a single paramagnetic crystal; a DPPH crystal on the surface of an Mn12-acetate crystal

The local magnetic field distribution on the subsurface of a single-molecule magnet crystal, SMM, above blocking temperature (T >> Tb) detected for a very short time interval (~ 10-10 s), has been investigated. Electron Paramagnetic Resonance (EPR) spectroscopy using a local paramagnetic probe was employed as a simple alternative detection method. An SMM crystal of [Mn12O12(CH3COO)16(H2O)4].2CH3COOH.4H2O (Mn12-acetate) and a crystal of 2,2- diphenyl-1-picrylhydrazyl (DPPH) as the paramagnetic probe were chosen for this study. The EPR spectra of DPPH deposited on Mn12-acetate show additional broadening and shifting in the magnetic field in comparison to the spectra of the DPPH in the absence of the SMM crystal. The additional broadening of the DPPH linewidth was considered in terms of the two dominant electron spin interactions (dipolar and exchange) and the local magnetic field distribution on the crystal surface. The temperature dependence of the linewidth of the Gaussian distribution of local fields at the SMM surface was extrapolated for the low temperature interval (70-5 K)

Mg II Absorption Systems in SDSS QSO Spectra

We present the results of a MgII absorption-line survey using QSO spectra from the SDSS EDR. Over 1,300 doublets with rest equivalent widths greater than 0.3\AA and redshifts $0.366 \le z \le 2.269$ were identified and measured. We find that the $\lambda2796$ rest equivalent width ($W_0^{\lambda2796}$) distribution is described very well by an exponential function $\partial N/\partial W_0^{\lambda2796} = \frac{N^*}{W^*} e^{-\frac{W_0}{W^*}}$, with $N^*=1.187\pm0.052$ and $W^*=0.702\pm0.017$\AA. Previously reported power law fits drastically over-predict the number of strong lines. Extrapolating our exponential fit under-predicts the number of $W_0 \le 0.3$\AA systems, indicating a transition in $dN/dW_0$ near $W_0 \simeq 0.3$\AA. A combination of two exponentials reproduces the observed distribution well, suggesting that MgII absorbers are the superposition of at least two physically distinct populations of absorbing clouds. We also derive a new redshift parameterization for the number density of $W_0^{\lambda2796} \ge 0.3$\AA lines: $N^*=1.001\pm0.132(1+z)^{0.226\pm0.170}$ and $W^*=0.443\pm0.032(1+z)^{0.634\pm 0.097}$\AA. We find that the distribution steepens with decreasing redshift, with $W^*$ decreasing from $0.80\pm0.04$\AA at $z=1.6$ to $0.59\pm0.02$\AA at $z=0.7$. The incidence of moderately strong MgII $\lambda2796$ lines does not show evidence for evolution with redshift. However, lines stronger than $\approx 2$\AA show a decrease relative to the no-evolution prediction with decreasing redshift for $z \lesssim 1$. The evolution is stronger for increasingly stronger lines. Since $W_0$ in saturated absorption lines is an indicator of the velocity spread of the absorbing clouds, we interpret this as an evolution in the kinematic properties of galaxies from moderate to low z.Comment: 50 pages, 26 figures, accepted for publication in Ap

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

Star Formation, Supernovae Feedback and the Angular Momentum Problem in Numerical CDM Cosmogony: Half Way There?

We present a smoothed particle hydrodynamic (SPH) simulation that reproduces a galaxy that is a moderate facsimile of those observed. The primary failing point of previous simulations of disk formation, namely excessive transport of angular momentum from gas to dark matter, is ameliorated by the inclusion of a supernova feedback algorithm that allows energy to persist in the model ISM for a period corresponding to the lifetime of stellar associations. The inclusion of feedback leads to a disk at a redshift $z=0.52$, with a specific angular momentum content within 10% of the value required to fit observations. An exponential fit to the disk baryon surface density gives a scale length within 17% of the theoretical value. Runs without feedback, with or without star formation, exhibit the drastic angular momentum transport observed elsewhere.Comment: 4 pages, 3 figures, accepted for publication in ApJ Letter

Longitudinal thalamic white and gray matter changes associated with visual hallucinations in Parkinson’s disease

Objective: Visual hallucinations are common in Parkinson’s disease (PD) and associated with worse outcomes. Large-scale network imbalance is seen in PD-associated hallucinations, but mechanisms remain unclear. As the thalamus is critical in controlling cortical networks, structural thalamic changes could underlie network dysfunction in PD hallucinations. Methods: We used whole-brain fixel-based analysis and cortical thickness measures to examine longitudinal white and grey matter changes in 76 patients with PD (15 hallucinators, 61 non-hallucinators) and 26 controls at baseline, and after 18 months. We compared white matter and cortical thickness, adjusting for age, gender, time-between-scans and intracranial volume. To assess thalamic changes, we extracted volumes for 50 thalamic subnuclei (25 each hemisphere) and mean fibre crosssection (FC) for white matter tracts originating in each subnucleus and examined longitudinal change in PDhallucinators versus non-hallucinators. Results: PD hallucinators showed white matter changes within the corpus callosum at baseline and extensive posterior tract involvement over time. Less extensive cortical thickness changes were only seen after followup. White matter connections from the right medial mediodorsal magnocellular thalamic nucleus showed reduced FC in PD hallucinators at baseline followed by volume reductions longitudinally. After follow-up, almost all thalamic subnuclei showed tract losses in PD hallucinators compared with non-hallucinators. Interpretation: PD hallucinators show white matter loss particularly in posterior connections and in thalamic nuclei, over time with relatively preserved cortical thickness. The right medial mediodorsal thalamic nucleus shows both connectivity and volume loss in PD hallucinations. Our findings provide mechanistic insights into the drivers of network imbalance in PD hallucinations and potential therapeutic targets

Visual dysfunction predicts cognitive impairment and white matter degeneration in Parkinson's disease

Visual dysfunction predicts dementia in Parkinsons disease (PD), but whether this translates to structural change is not known. We aimed to identify longitudinal white matter changes in patients with Parkinsons disease and low visual function and also in those who developed mild cognitive impairment (MCI). We used fixel-based analysis to examine longitudinal white matter change in PD. Diffusion MRI and clinical assessments were performed in 77 patients at baseline (22 low visual function /55 intact vision; and 13 MCI, 13 MCI converters /51 normal cognition) and 25 controls and again after 18 months. We compared micro-structural changes in fibre density, macro-structural changes in fibre bundle cross-section (FC) and combined fibre density and cross-section across white matter, adjusting for age, gender and intracranial volume. Patients with Parkinsons and visual dysfunction showed worse cognitive performance at follow up and were more likely to develop MCI compared with those with normal vision (p=0.008). Parkinsons with poor visual function showed diffuse micro-structural and macro-structural changes at baseline, whereas those with MCI showed fewer baseline changes. At follow-up, Parkinsons with low visual function showed widespread macrostructural changes, involving the fronto-occipital fasciculi, external capsules, and middle cerebellar peduncles bilaterally. No longitudinal change was seen in baseline MCI or in MCI converters, even when the two groups were combined. Parkinsons patients with poor visual function show increased white matter damage over time, providing further evidence for visual function as a marker of imminent cognitive decline

On the Minimum Degree up to Local Complementation: Bounds and Complexity

The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge, the highest known bound on an explicit family of graphs. Probabilistic methods allows us to derive the existence of an infinite number of graphs whose local minimum degree is linear in their order with constant 0.189 for graphs in general and 0.110 for bipartite graphs. As regards the computational complexity of the decision problem associated with the local minimum degree, we show that it is NP-complete and that there exists no k-approximation algorithm for this problem for any constant k unless P = NP.Comment: 11 page

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