We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral lattices of th
e division algebras and associated discrete matrix groups. Our findings can be summarized by saying that the even subgroups, W^+, of the Kac-Moody Weyl groups, W, are isomorphic to generalized modular groups over K for the simply laced algebras, and to certain finite extensions thereof for the non-simply laced algebras. This hints at an extended theory of modular forms and functions.
We study the effect of disorder on the London penetration depth in iron-based superconductors. The theory is based on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between mag
netic and superconducting states in the presence of intraband and interband scattering. Within the quasiclassical approximation we derive and solve Eilenbergers equations, which include a weak external magnetic field, and provide analytical expressions for the penetration depth in the various limiting cases. A complete numerical analysis of the doping and temperature dependence of the London penetration depth reveals the crucial effect of disorder scattering, which is especially pronounced in the coexistence phase. The experimental implications of our results are discussed.
We analyze two multi-chord stellar occultations by Pluto observed on July 18th, 2012 and May 4th, 2013, and monitored respectively from five and six sites. They provide a total of fifteen light-curves, twelve of them being used for a simultaneous fit
that uses a unique temperature profile, assuming a clear (no-haze) and pure N_2 atmosphere, but allowing for a possible pressure variation between the two dates. We find a solution that fits satisfactorily (i.e. within the noise level) all the twelve light-curves, providing atmospheric constraints between ~1,190 km (pressure ~ 11 mubar) and ~ 1,450 km (pressure ~0.1 mubar) from Plutos center. Our main results are: (1) the best-fitting temperature profile shows a stratosphere with strong positive gradient between 1,190 km (at 36 K, 11 mubar) and r = 1,215 km (6.0 mubar), where a temperature maximum of 110 K is reached; above it is a mesosphere with negative thermal gradient of -0.2 K/km up to ~ 1,390 km (0.25 mubar), where, the mesosphere connects itself to a more isothermal upper branch around 81 K; (2) the pressure shows a small (6 %) but significant increase (6-sigma level) between the two dates; (3) without troposphere, Plutos radius is found to be R_P = 1,190 +/- 5km. Allowing for a troposphere, R_P is constrained to lie between 1,168 and 1,195 km; (4) the currently measured CO abundance is too small to explain the mesospheric negative thermal gradient. Cooling by HCN is possible, but only if this species is largely saturated; Alternative explanations like zonal winds or vertical compositional variations of the atmosphere are unable to explain the observed mesospheric trend.
In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we sh
ow the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e. it forms a single light ring. This light ring is generated from a non-homogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual--cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones.
In conical refraction, when a focused Gaussian beam passes along one of the optic axes of a biaxial crystal it is transformed into a pair of concentric bright rings at the focal plane. We demonstrate both theoretically and experimentally that this tr
ansformation is hardly affected by partially blocking the Gaussian input beam with an obstacle. We analyze the influence of the size of the obstruction both on the transverse intensity pattern of the beam and on its state of polarization, which is shown to be very robust.
We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal
plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, being this node found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e. that every two diametrically opposite points of the light ring are linearly orthogonally polarized.
This note studies the use of relays to improve the performance of Kalman filtering over packet dropping links. Packet reception probabilities are governed by time-varying fading channel gains, and the sensor and relay transmit powers. We consider sit
uations with multiple sensors and relays, where each relay can either forward one of the sensors measurements to the gateway/fusion center, or perform a simple linear network coding operation on some of the sensor measurements. Using an expected error covariance performance measure, we consider optimal and suboptimal methods for finding the best relay configuration, and power control problems for optimizing the Kalman filter performance. Our methods show that significant performance gains can be obtained through the use of relays, network coding and power control, with at least 30-40$%$ less power consumption for a given expected error covariance specification.
We present a proof-of-concept of a novel and fully Bayesian methodology designed to detect halos of different masses in cosmological observations subject to noise and systematic uncertainties. Our methodology combines the previously published Bayesia
n large-scale structure inference algorithm, HADES, and a Bayesian chain rule (the Blackwell-Rao Estimator), which we use to connect the inferred density field to the properties of dark matter halos. To demonstrate the capability of our approach we construct a realistic galaxy mock catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a median redshift of approximately 0.05. Application of HADES to the catalogue provides us with accurately inferred three-dimensional density fields and corresponding quantification of uncertainties inherent to any cosmological observation. We then use a cosmological simulation to relate the amplitude of the density field to the probability of detecting a halo with mass above a specified threshold. With this information we can sum over the HADES density field realisations to construct maps of detection probabilities and demonstrate the validity of this approach within our mock scenario. We find that the probability of successful of detection of halos in the mock catalogue increases as a function of the signal-to-noise of the local galaxy observations. Our proposed methodology can easily be extended to account for more complex scientific questions and is a promising novel tool to analyse the cosmic large-scale structure in observations.
We show that in any non-arithmetic rank 1 orbit closure of translation surfaces, there are only finitely many Teichmuller curves. We also show that in any non-arithmetic rank 1 orbit closure, any completely parabolic surface is Veech.
We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is
richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.
