Chemically-stabilized allosteric modulators of leucine-rich repeat kinase 2 (lrrk2)

The present disclosure describes synthetic polypeptides for the inhibition or modulation of the activity of leucine-rich repeat kinase 2 (LRRK2) along with methods of using the same in the treatment of medical conditions, for example neurological diseases or disorders

A very luminous, highly extinguished, very fast nova - V1721 Aquilae

Fast novae are primarily located within the plane of the Galaxy, slow novae are found within its bulge. Because of high interstellar extinction along the line of sight many novae lying close to the plane are missed and only the brightest seen. One nova lying very close to the Galactic plane is V1721 Aquilae, discovered in outburst on 2008 September 22. Spectra obtained 2.69 days after outburst revealed very high expansion velocities (FWHM ~6450 km/s). In this paper we have used available pre- and post-outburst photometry and post-outburst spectroscopy to conclude that the object is a very fast, luminous, and highly extinguished A_V=11.6+/-0.2) nova system with an average ejection velocity of ~3400 km/s. Pre-outburst near-IR colours from 2MASS indicate that at quiescence the object is similar to many quiescent CNe and appears to have a main sequence/sub-giant secondary rather than a giant. Based on the speed of decline of the nova and its emission line profiles we hypothesise that the axis ratio of the nova ejecta is ~1.4 and that its inclination is such that the central binary accretion disc is face-on to the observer. The accretion disc's blue contribution to the system's near-IR quiescent colours may be significant. Simple models of the nova ejecta have been constructed using the morphological modelling code XS5, and the results support the above hypothesis. Spectral classification of this object has been difficult owing to low S/N levels and high extinction, which has eliminated all evidence of any He/N or FeII emission within the spectra. We suggest two possibilities for the nature of V1721 Aql: that it is a U Sco type RN with a sub-giant secondary or, less likely, that it is a highly energetic bright and fast classical nova with a main sequence secondary. Future monitoring of the object for possible RN episodes may be worthwhile, as would archival searches for previous outbursts.Comment: 9 pages 10 figures, accepted for publication in A&A. Abstract has been slightly shortened from published versio

Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite

The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity $\chi T^\alpha$ with $\alpha \simeq 0.66$ can be expressed as a universal function of $H/T$ or $\omega/T$. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum critical point.Comment: 5 pages, 3 figures v2: updated to match published version

Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2

We have performed thermodynamic and neutron scattering measurements on the S=1/2 kagome lattice antiferromagnet Zn Cu_3 (OH)_6 Cl_2. The susceptibility indicates a Curie-Weiss temperature of ~ -300 K; however, no magnetic order is observed down to 50 mK. Inelastic neutron scattering reveals a spectrum of low energy spin excitations with no observable gap down to 0.1 meV. The specific heat at low-T follows a power law with exponent less than or equal to 1. These results suggest that an unusual spin-liquid state with essentially gapless excitations is realized in this kagome lattice system.Comment: 4 pages, 3 figures; v2: Updates to authors list and references; v3: Updated version; v4: Published versio

Maximal quadratic modules on *-rings

We generalize the notion of and results on maximal proper quadratic modules from commutative unital rings to $\ast$-rings and discuss the relation of this generalization to recent developments in noncommutative real algebraic geometry. The simplest example of a maximal proper quadratic module is the cone of all positive semidefinite complex matrices of a fixed dimension. We show that the support of a maximal proper quadratic module is the symmetric part of a prime $\ast$-ideal, that every maximal proper quadratic module in a Noetherian $\ast$-ring comes from a maximal proper quadratic module in a simple artinian ring with involution and that maximal proper quadratic modules satisfy an intersection theorem. As an application we obtain the following extension of Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let $c$ be an element of the Weyl algebra $\mathcal{W}(d)$ which is not negative semidefinite in the Schr\" odinger representation. It is shown that under some conditions there exists an integer $k$ and elements $r_1,...,r_k \in \mathcal{W}(d)$ such that $\sum_{j=1}^k r_j c r_j^\ast$ is a finite sum of hermitian squares. This result is not a proper generalization however because we don't have the bound $k \le d$.Comment: 11 page