Loop algebras, gauge invariants and a new completely integrable system

One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalization of the structure theory of finite-dimensional simple Lie algebras is not the structure theory of loop algebras but the structure theory of affine Kac-Moody algebras. In this paper we use this natural generalization to construct the natural analog of the nonperiodic Toda lattice. Surprisingly, the result is not the periodic Toda lattice but a new completely integrable system on the periodic Toda lattice phase space. This integrable system is prescribed purely in terms of Lie-theoretic data. The commuting functions are precisely the gauge-invariant functions one obtains by viewing elements of the loop algebra as connections on a bundle over $S^1$

Uncovering CDM halo substructure with tidal streams

Models for the formation and growth of structure in a cold dark matter dominated universe predict that galaxy halos should contain significant substructure. Studies of the Milky Way, however, have yet to identify the expected few hundred sub-halos with masses greater than about 10^6 Msun. Here we propose a test for the presence of sub-halos in the halos of galaxies. We show that the structure of the tidal tails of ancient globular clusters is very sensitive to heating by repeated close encounters with the massive dark sub-halos. We discuss the detection of such an effect in the context of the next generation of astrometric missions, and conclude that it should be easily detectable with the GAIA dataset. The finding of a single extended cold stellar stream from a globular cluster would support alternative theories, such as self-interacting dark matter, that give rise to smoother halos.Comment: 7 pages, 7 figures, submitted to MNRA

The effect of leveling coatings on the atomic oxygen durability of solar concentrator surfaces

Space power systems for Space Station Freedom will be exposed to the harsh environment of low earth orbit (LEO). Neutral atomic oxygen is the major constituent in LEO and has the potential of severely reducing the efficiency of solar dynamic power systems through degradation of the concentrator surfaces. Several transparent dielectric thin films have been found to provide atomic oxygen protection, but atomic oxygen undercutting at inherent defect sites is still a threat to solar dynamic power system survivability. Leveling coatings smooth microscopically rough surfaces, thus eliminating potential defect sites prone to oxidation attack on concentrator surfaces. The ability of leveling coatings to improve the atomic oxygen durability of concentrator surfaces was investigated. The application of a EPO-TEK 377 epoxy leveling coating on a graphite epoxy substrate resulted in an increase in solar specular reflectance, a decrease in the atomic oxygen defect density by an order of magnitude and a corresponding order of magnitude decrease in the percent loss of specular reflectance during atomic oxygen plasma ashing

The Role of Cold Flows in the Assembly of Galaxy Disks

We use high resolution cosmological hydrodynamical simulations to demonstrate that cold flow gas accretion, particularly along filaments, modifies the standard picture of gas accretion and cooling onto galaxy disks. In the standard picture, all gas is initially heated to the virial temperature of the galaxy as it enters the virial radius. Low mass galaxies are instead dominated by accretion of gas that stays well below the virial temperature, and even when a hot halo is able to develop in more massive galaxies there exist dense filaments that penetrate inside of the virial radius and deliver cold gas to the central galaxy. For galaxies up to ~L*, this cold accretion gas is responsible for the star formation in the disk at all times to the present. Even for galaxies at higher masses, cold flows dominate the growth of the disk at early times. Within this modified picture, galaxies are able to accrete a large mass of cold gas, with lower initial gas temperatures leading to shorter cooling times to reach the disk. Although star formation in the disk is mitigated by supernovae feedback, the short cooling times allow for the growth of stellar disks at higher redshifts than predicted by the standard model.Comment: accepted to Ap

Cerebral small vessel disease, medial temporal lobe atrophy and cognitive status in patients with ischaemic stroke and transient ischaemic attack

BACKGROUND AND PURPOSE: Small vessel disease (SVD) and Alzheimer's disease (AD) are two common causes of cognitive impairment and dementia, traditionally considered as distinct processes. The relationship between radiological features suggestive of AD and SVD was explored, and the association of each of these features with cognitive status at 1 year was investigated in patients with stroke or transient ischaemic attack. METHODS: Anonymized data were accessed from the Virtual International Stroke Trials Archive (VISTA). Medial temporal lobe atrophy (MTA; a marker of AD) and markers of SVD were rated using validated ordinal visual scales. Cognitive status was evaluated with the Mini Mental State Examination (MMSE) 1 year after the index stroke. Logistic regression models were used to investigate independent associations between (i) baseline SVD features and MTA and (ii) all baseline neuroimaging features and cognitive status 1 year post-stroke. RESULTS: In all, 234 patients were included, mean (±SD) age 65.7 ± 13.1 years, 145 (62%) male. Moderate to severe MTA was present in 104 (44%) patients. SVD features were independently associated with MTA (P < 0.001). After adjusting for age, sex, disability after stroke, hypertension and diabetes mellitus, MTA was the only radiological feature independently associated with cognitive impairment, defined using thresholds of MMSE ≤ 26 (odds ratio 1.94; 95% confidence interval 1.28-2.94) and MMSE ≤ 23 (odds ratio 2.31; 95% confidence interval 1.48-3.62). CONCLUSION: In patients with ischaemic cerebrovascular disease, SVD features are associated with MTA, which is a common finding in stroke survivors. SVD and AD type neurodegeneration coexist, but the AD marker MTA, rather than SVD markers, is associated with post-stroke cognitive impairment

A generalization of Gabriel's Galois covering functors II: 2-categorical Cohen-Montgomery duality

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category construction and of the smash product construction turn out to be 2-equivalences (2-quasi-inverses to each other), which extends the Cohen-Montgomery duality.Comment: 31 pages. I moved the Sec of G-GrCat into Sec 3, and added Lem 5.6. I added more explanations in the proof of Cor 7.6 with (7.5). I added Def 7.7 and Lem 7.8 with the necessary additional assumptions in Props 7.9 and 7.11. I added Lem 8.8 with a short proof, Rmk 8.9 and the proof of Lem 8.10. The final publication is available at Springer via http://dx.doi.org/10.1007/s10485-015-9416-

PATENTS, R&D AND LAG EFFECTS: EVIDENCE FROM FLEXIBLE METHODS FOR COUNT PANEL DATA ON MANUFACTURING FIRMS

Hausman, Hall and Griliches (1984) and Hall, Griliches and Hausman (1986) investigated whether there was a lag in the patent-R&D relationship for the U.S. manufacturing sector using 1970¿s data. They found that there was little evidence of anything but contemporaneous movement of patents and R&D. We reexamine this important issue employing new longitudinal patent data at the firm level for the U.S. manufacturing sector from 1982 to 1992. To address unique features of the data, we estimate various distributed lag and dynamic multiplicative panel count data models. The paper also develops a new class of count panel data models based on series expansion of the distribution of individual effects. The empirical analyses show that, although results are somewhat sensitive to different estimation methods, the contemporaneous relationship between patenting and R&D expenditures continues to be rather strong, accounting for over 60% of the total R&D elasticity. Regarding the lag structure of the patents-R&D relationship, we do find a significant lag in all empirical specifications. Moreover, the estimated lag effects are higher than have previously been found, suggesting that the contribution of R&D history to current patenting has increased from the 1970¿s to the 1980¿s.Innovative activity, Patents and R&D, Individual effects, count panel data methods.

Spin phase diagram of the nu_e=4/11 composite fermion liquid

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.Comment: 5 pages, 3 figure