A long standing problem in quantum mechanics is the minimum number of observables required for the characterisation of unknown pure quantum states. The solution to this problem is specially important for the developing field of high-dimensional quant
um information processing. In this work we demonstrate that any pure d-dimensional state is unambiguously reconstructed by measuring 5 observables, that is, via projective measurements onto the states of 5 orthonormal bases. Thus, in our method the total number of different measurement outcomes (5d) scales linearly with d. The state reconstruction is robust against experimental errors and requires simple post-processing, regardless of d. We experimentally demonstrate the feasibility of our scheme through the reconstruction of 8-dimensional quantum states, encoded in the momentum of single photons.
The Kepler Mission is exploring the diversity of planets and planetary systems. Its legacy will be a catalog of discoveries sufficient for computing planet occurrence rates as a function of size, orbital period, star-type, and insolation flux. The mi
ssion has made significant progress toward achieving that goal. Over 3,500 transiting exoplanets have been identified from the analysis of the first three years of data, 100 of which are in the habitable zone. The catalog has a high reliability rate (85-90% averaged over the period/radius plane) which is improving as follow-up observations continue. Dynamical (e.g. velocimetry and transit timing) and statistical methods have confirmed and characterized hundreds of planets over a large range of sizes and compositions for both single and multiple-star systems. Population studies suggest that planets abound in our galaxy and that small planets are particularly frequent. Here, I report on the progress Kepler has made measuring the prevalence of exoplanets orbiting within 1 AU of their host stars in support of NASAs long-term goal of finding habitable environments beyond the solar system.
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classification of the $3$-filiform Leibniz algebras of maximum length cite{3-filiform}. Moreover, due to the good structure of the algebras of maximum le
ngth, we also tackle some of their cohomological properties. Our main tools are the previous result of Cabezas and Pastor cite{Pastor}, the construction of appropriate homogeneous basis in the considered connected gradation and the computational support provided by the two programs implemented in the software textit{Mathematica}.
Context. LS I +61 303 is a member of the select group of gamma-ray binaries: galactic binary systems that contain a massive star and a compact object, show a changing milliarcsecond morphology and a similar broad spectral energy distribution (SED) th
at peaks at MeV-TeV energies and is modulated by the orbital motion. The nature of the compact object is unclear in LS I +61 303, LS 5039 and HESS J0632+057, whereas PSR B1259-63 harbours a 47.74 ms radio pulsar. Aims. A scenario in which a young pulsar wind interacts with the stellar wind has been proposed to explain the very high energy (VHE, E > 100 GeV) gamma-ray emission detected from LS I +61 303, although no pulses have been reported from this system at any wavelength. We aim to find evidence of the pulsar nature of the compact object. Methods. We performed phased array observations with the Giant Metrewave Radio Telescope (GMRT) at 1280 MHz centred at phase 0.54. Simultaneous data from the multi-bit phased array (PA) back-end with a sampling time of tsamp = 128 microsec and from the polarimeter (PMT) back-end with tsamp = 256 microsec where taken. Results. No pulses have been found in the data set, with a minimum detectable mean flux density of sim 0.38 mJy at 8-sigma level for the pulsed emission from a putative pulsar with period P >2 ms and duty cycle D = 10% in the direction of LS I +61 303. Conclusions. The detection of posible radio pulsations will require deep and sensitive observations at frequencies sim0.5-5 GHz and orbital phases 0.6-0.7. However, it may be unfeasible to detect pulses if the putative pulsar is not beamed at the Earth or if there is a strong absorption within the binary system.
We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and $+infty$. Using these es
timates we prove a spectral gap result by following the technique in [Caceres, Canizo, Mischler 2011, JMPA], which implies that solutions decay to the equilibrium exponentially fast. The growth and fragmentation coefficients we consider are quite general, essentially only assumed to behave asymptotically like power laws.
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales (where the
vorticity is created) to larger scales (where other forces dominate and the turbulence fossilizes). Fossil turbulence is any perturbation in a hydrophysical field produced by turbulence that persists after the fluid is no longer turbulent at the scale of the perturbation. Fossil turbulence patterns and fossil turbulence waves preserve and propagate information about previous turbulence to larger and smaller length scales. Big bang fossil turbulence patterns are identified in anisotropies of temperature detected by space telescopes in the cosmic microwave background. Direct numerical simulations of stratified shear flows and wakes show that turbulence and fossil turbulence interactions are recognizable and persistent.
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than all the other forces that tend to damp the eddies out. Fossil turbulence is a perturbation produced by turbulence that persists
after the fluid ceases to be turbulent at the scale of the perturbation. Because vorticity is produced at small scales, turbulence must cascade from small scales to large, providing a consistent physical basis for Kolmogorovian universal similarity laws. Oceanic and astrophysical mixing and diffusion are dominated by fossil turbulence and fossil turbulent waves. Observations from space telescopes show turbulence and vorticity existed in the beginning of the universe and that their fossils persist. Fossils of big bang turbulence include spin and the dark matter of galaxies: clumps of ~ 10^12 frozen hydrogen planets that make globular star clusters as seen by infrared and microwave space telescopes. When the planets were hot gas, they hosted the formation of life in a cosmic soup of hot-water oceans as they merged to form the first stars and chemicals. Because spontaneous life formation according to the standard cosmological model is virtually impossible, the existence of life falsifies the standard cosmological model.
There is a great deal of work in cognitive psychology, linguistics, and computer science, about using word (or phrase) frequencies in context in text corpora to develop measures for word similarity or word association, going back to at least the 1960
s. The goal of this chapter is to introduce the normalizedis a general way to tap the amorphous low-grade knowledge available for free on the Internet, typed in by local users aiming at personal gratification of diverse objectives, and yet globally achieving what is effectively the largest semantic electronic database in the world. Moreover, this database is available for all by using any search engine that can return aggregate page-count estimates for a large range of search-queries. In the paper introducing the NWD it was called `normalized Google distance (NGD), but since Google doesnt allow computer searches anymore, we opt for the more neutral and descriptive NWD. web distance (NWD) method to determine similarity between words and phrases. It
We present high-sensitivity, high-resolution images of the Ultraluminous Infrared Galaxies (ULIRG; L$_{mathrm{FIR}} > 10^{12}$ L$_odot$) IRAS 23365+3604 and IRAS 07251-0248, taken with the EVN at 6 and 18 cm. The images show a large number of compact
components, whose luminosities are typical of Type IIL and Type IIn Radio Supernovae (RSNe). Further observations of these ULIRGs will allow us to confirm, or to rule out, their nature. The present observations are part of a project that should result in a significant number of SN detections, providing a direct measurement of the Core Collapse Superova (CCSN) rate and allowing us to estimate the Star Formation Rate (SFR) in our sample of ULIRGs .
We show that solutions to Smoluchowskis equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in a weighted
Sobolev norm which implies the L^2 convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove these results through the study of the linearized coagulation equation in self-similar variables, for which we show a spectral gap in a scale of weighted Sobolev spaces. We also take advantage of the fact that the Laplace or Fourier transforms of this equation can be explicitly solved in this case.
