Analysis of a convenient information bound for general quantum channels

Open questions from Sarovar and Milburn (2006 J.Phys. A: Math. Gen. 39 8487) are answered. Sarovar and Milburn derived a convenient upper bound for the Fisher information of a one-parameter quantum channel. They showed that for quasi-classical models their bound is achievable and they gave a necessary and sufficient condition for positive operator-valued measures (POVMs) attaining this bound. They asked (i) whether their bound is attainable more generally, (ii) whether explicit expressions for optimal POVMs can be derived from the attainability condition. We show that the symmetric logarithmic derivative (SLD) quantum information is less than or equal to the SM bound, i.e.\ $H(\theta) \leq C_{\Upsilon}(\theta)$ and we find conditions for equality. As the Fisher information is less than or equal to the SLD quantum information, i.e. $F_M(\theta) \leq H(\theta)$, we can deduce when equality holds in $F_M(\theta) \leq C_{\Upsilon}(\theta)$. Equality does not hold for all channels. As a consequence, the attainability condition cannot be used to test for optimal POVMs for all channels. These results are extended to multi-parameter channels.Comment: 16 pages. Published version. Some of the lemmas have been corrected. New resuts have been added. Proofs are more rigorou

Molecfit: A general tool for telluric absorption correction. I. Method and application to ESO instruments

Context: The interaction of the light from astronomical objects with the constituents of the Earth's atmosphere leads to the formation of telluric absorption lines in ground-based collected spectra. Correcting for these lines, mostly affecting the red and infrared region of the spectrum, usually relies on observations of specific stars obtained close in time and airmass to the science targets, therefore using precious observing time. Aims: We present molecfit, a tool for correcting for telluric absorption lines based on synthetic modelling of the Earth's atmospheric transmission. Molecfit is versatile and can be used with data obtained with various ground-based telescopes and instruments. Methods: Molecfit combines a publicly available radiative transfer code, a molecular line database, atmospheric profiles, and various kernels to model the instrument line spread function. The atmospheric profiles are created by merging a standard atmospheric profile representative of a given observatory's climate, of local meteorological data, and of dynamically retrieved altitude profiles for temperature, pressure, and humidity. We discuss the various ingredients of the method, its applicability, and its limitations. We also show examples of telluric line correction on spectra obtained with a suite of ESO Very Large Telescope (VLT) instruments. Results: Compared to previous similar tools, molecfit takes the best results for temperature, pressure, and humidity in the atmosphere above the observatory into account. As a result, the standard deviation of the residuals after correction of unsaturated telluric lines is frequently better than 2% of the continuum. Conclusion: Molecfit is able to accurately model and correct for telluric lines over a broad range of wavelengths and spectral resolutions. (Abridged)Comment: 18 pages, 13 figures, 5 tables, accepted for publication in Astronomy and Astrophysic

On the p-length of some finite p-soluble groups

The main aim of this paper is to give structural information of a finite group of minimal order belonging to a subgroup-closed class of finite groups and whose p-length is greater than 1, p a prime number. Alternative proofs and improvements of recent results about the influence of minimal p-subgroups on the p-nilpotence and p-length of a finite group arise as consequences of our study

Polarizational stopping power of heavy-ion diclusters in two-dimensional electron liquids

The in-plane polarizational stopping power of heavy-ion diclusters in a two-dimensional strongly coupled electron liquid is studied. Analytical expressions for the stopping power of both fast and slow projectiles are derived. To go beyond the random-phase approximation we make use of the inverse dielectric function obtained by means of the method of moments and some recent analytical expressions for the static local-field correction factor.Comment: 9 pages, 5 figures. Published in Physical Review B http://link.aps.org/abstract/PRB/v75/e11510

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Molecular hydrogen, deuterium and metal abundances in the damped Ly-alpha system at z = 3.025 toward QSO 0347-3819

We have detected in high resolution spectra of the quasar Q0347--3819 obtained with the UVES spectrograph at the VLT/Kueyen telescope over 80 absorption features in the Lyman and Werner H2 bands at the redshift of a damped Ly-alpha system at z = 3.025. The z = 3.025 system spans over 80 km/s and exhibits a multicomponent velocity structure in the metal lines. The main component at z = 3.024855 shows a total H2 column density N(H2) = (4.10\pm0.21)*10^{14} cm^{-2} and a fractional molecular abundance f(H2) = (1.94\pm0.10)*10^{-6} derived from the H2 lines arising from J=0 to 5 rotational levels of the ground electronic-vibrational state. For the first time we unambiguously reveal a pronounced [alpha-element/iron-peak] enhancement of [O,Si/Zn] = 0.6\pm0.1 (6 sigma c.l.) at high redshift. The simultaneous analysis of metal and hydrogen lines leads to D/H = (3.75\pm0.25)*10^{-5}. This value is consistent with standard big bang nucleosynthesis if the baryon-to-photon ratio, eta, lies within the range 4.37*10^{-10} <= eta <= 5.32*10^{-10}, implying 0.016 <= Omega_b h^2_100 <= 0.020.Comment: 32 pages, 16 ps figures, accepted to Ap

On certain products of permutable subgroups

[EN] In this paper, we study the structure of finite groups G = AB which are a weakly mutually sn-permutable product of the subgroups A and B, that is, A permutes with every subnormal subgroup of B containing A boolean AND B and B permutes with every subnormal subgroup of A containing A boolean AND B. We obtain generalisations of known results on mutually sn-permutable products.The first and fourth authors have been supported by the research grant PGC2018- 095140-B-I00 from the Ministerio de Ciencia, Innovación y Universidades and the Agencia Estatal de Investigación (Spanish Government) and FEDER (European Union), and PROMETEO/2017/057 from Generalitat (Valencian Community, Spain).Ballester-Bolinches, A.; Madanha, SY.; Mudziiri Shumba, TM.; Pedraza Aguilera, MC. (2022). On certain products of permutable subgroups. Bulletin of the Australian Mathematical Society. 105(2):278-285. https://doi.org/10.1017/S0004972721000617278285105

HST hot-Jupiter transmission spectral survey: Haze in the atmosphere of WASP-6b

We report Hubble Space Telescope (HST) optical to near-infrared transmission spectroscopy of the hot Jupiter WASP-6b, measured with the Space Telescope Imaging Spectrograph (STIS) and Spitzer's InfraRed Array Camera (IRAC). The resulting spectrum covers the range $0.29-4.5\,\mu$m. We find evidence for modest stellar activity of WASP-6b and take it into account in the transmission spectrum. The overall main characteristic of the spectrum is an increasing radius as a function of decreasing wavelength corresponding to a change of $\Delta (R_p/R_{\ast})=0.0071$ from 0.33 to $4.5\,\mu$m. The spectrum suggests an effective extinction cross-section with a power law of index consistent with Rayleigh scattering, with temperatures of $973\pm144$ K at the planetary terminator. We compare the transmission spectrum with hot-Jupiter atmospheric models including condensate-free and aerosol-dominated models incorporating Mie theory. While none of the clear-atmosphere models is found to be in good agreement with the data, we find that the complete spectrum can be described by models that include significant opacity from aerosols including Fe-poor Mg$_2$SiO$_4$, MgSiO$_3$, KCl and Na$_2$S dust condensates. WASP-6b is the second planet after HD189733b which has equilibrium temperatures near $\sim1200$ K and shows prominent atmospheric scattering in the optical.Comment: 18 pages, 15 figures, 7 table

HST hot Jupiter transmission spectral survey: evidence for aerosols and lack of TiO in the atmosphere of WASP-12b

We present HST optical transmission spectra of the transiting hot Jupiter WASP-12b, taken with the STIS instrument. From the transmission spectra, we are able to decisively rule out prominent absorption by TiO in the exoplanet's atmosphere. Strong pressure-broadened Na and K absorption signatures are also excluded, as are significant metal-hydride features. We compare our combined broadband spectrum to a wide variety of existing aerosol-free atmospheric models, though none are satisfactory fits. However, we do find that the full transmission spectrum can be described by models which include significant opacity from aerosols: including Rayleigh scattering, Mie scattering, tholin haze, and settling dust profiles. The transmission spectrum follows an effective extinction cross section with a power-law of index alpha, with the slope of the transmission spectrum constraining the quantity alphaT = -3528+/-660 K, where T is the atmospheric temperature. Rayleigh scattering (alpha=-4) is among the best fitting models, though requires low terminator temperatures near 900 K. Sub-micron size aerosol particles can provide equally good fits to the entire transmission spectrum for a wide range of temperatures, and we explore corundum as a plausible dust aerosol. The presence of atmospheric aerosols also helps to explain the modestly bright albedo implied by Spitzer observations, as well as the near black body nature of the emission spectrum. Ti-bearing condensates on the cooler night-side is the most natural explanation for the overall lack of TiO signatures in WASP-12b, indicating the day/night cold-trap is an important effect for very hot Jupiters. These finding indicate that aerosols can play a significant atmospheric role for the entire wide range of hot-Jupiter atmospheres, potentially affecting their overall spectrum and energy balance.(abridged)Comment: 19 pages, 14 figures, 5 tables. Accepted for publication in MNRA