The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents

We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the channel state may be influenced by some of the parties involved. We derive single-letter expressions for the secret key capacity through a type of source emulation analysis. We also derive lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage. These exponents allow us to determine a set of strongly-achievable secret key rates. For degraded eavesdroppers the maximum strongly-achievable rate equals the secret key capacity; our exponents can also be specialized to previously known results. In deriving our strong achievability results we introduce a coding scheme that combines wiretap coding (to excite the channel) and key extraction (to distill keys from residual randomness). The secret key capacity is naturally seen to be a combination of both source- and channel-type randomness. Through examples we illustrate a fundamental interplay between the portion of the secret key rate due to each type of randomness. We also illustrate inherent tradeoffs between the achievable reliability and secrecy exponents. Our new scheme also naturally accommodates rate limits on the public discussion. We show that under rate constraints we are able to achieve larger rates than those that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on Information Theory; Revised in Oct 201

Rank Minimization over Finite Fields: Fundamental Limits and Coding-Theoretic Interpretations

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp and the minimum-rank decoder is asymptotically optimal. The reliability function of this decoder is also derived by appealing to de Caen's lower bound on the probability of a union. The sufficient condition also holds when the sensing matrices are sparse - a scenario that may be amenable to efficient decoding. More precisely, it is shown that if the n\times n-sensing matrices contain, on average, \Omega(nlog n) entries, the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field. Analogies are drawn between the above results and rank-metric codes in the coding theory literature. In fact, we are also strongly motivated by understanding when minimum rank distance decoding of random rank-metric codes succeeds. To this end, we derive distance properties of equiprobable and sparse rank-metric codes. These distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one. Finally, we provide a non-exhaustive procedure to search for the unknown low-rank matrix.Comment: Accepted to the IEEE Transactions on Information Theory; Presented at IEEE International Symposium on Information Theory (ISIT) 201

Physical State of Molecular Gas in High Galactic Latitude Translucent Clouds

The rotational transitions of carbon monoxide (CO) are the primary means of investigating the density and velocity structure of the molecular interstellar medium. Here we study the lowest four rotational transitions of CO towards high-latitude translucent molecular clouds (HLCs). We report new observations of the J = (4-3), (2-1), and (1-0) transitions of CO towards eight high-latitude clouds. The new observations are combined with data from the literature to show that the emission from all observed CO transitions is linearly correlated. This implies that the excitation conditions which lead to emission in these transitions are uniform throughout the clouds. Observed 13CO/12CO (1-0) integrated intensity ratios are generally much greater than the expected abundance ratio of the two species, indicating that the regions which emit 12CO (1-0) radiation are optically thick. We develop a statistical method to compare the observed line ratios with models of CO excitation and radiative transfer. This enables us to determine the most likely portion of the physical parameter space which is compatible with the observations. The model enables us to rule out CO gas temperatures greater than 30K since the most likely high-temperature configurations are 1 pc-sized structures aligned along the line of sight. The most probable solution is a high density and low temperature (HDLT) solution. The CO cell size is approximately 0.01 pc (2000 AU). These cells are thus tiny fragments within the 100 times larger CO-emitting extent of a typical high-latitude cloud. We discuss the physical implications of HDLT cells, and we suggest ways to test for their existence.Comment: 19 pages, 13 figures, 2 tables, emulateapj To be published in The Astrophysical Journa

The Bell Laboratories (13)CO Survey: Longitude-Velocity Maps

A survey is presented of the Galactic plane in the J=1-0 transition of (13)CO. About 73,000 spectra were obtained with the 7 m telescope at Bell Laboratories over a ten-year period. The coverage of survey is (l, b) = (-5 to 117, -1 to +1), or 244 square degrees, with a grid spacing of 3' for |b| < 0.5, and a grid spacing of 6' for |b| > 0.5. The data presented here have been resampled onto a 3' grid. For 0.68 km/s channels, the rms noise level of the survey is 0.1 K on the $T_R^*$ scale. The raw data have been transformed into FITS format, and all the reduction processes, such as correcting for emission in the reference positions, baseline removal and interpolation were conducted within IRAF using the FCRAO task package and additional programs. The reduced data are presented here in the form of longitude-velocity color maps at each latitude. These data allow identification and classification of molecular clouds with masses in excess of ~ 1,000 solar masses throughout the first quadrant of the Galaxy. Spiral structure is manifested by the locations of the largest and brightest molecular clouds.Comment: 23 pages, 7 figures, ApJS submitted (out of 41 frames of Figure4, only one is included becaue of size limit

The Initial Conditions of Clustered Star Formation III. The Deuterium Fractionation of the Ophiuchus B2 Core

We present N2D+ 3-2 (IRAM) and H2D+ 1_11 - 1_10 and N2H+ 4-3 (JCMT) maps of the small cluster-forming Ophiuchus B2 core in the nearby Ophiuchus molecular cloud. In conjunction with previously published N2H+ 1-0 observations, the N2D+ data reveal the deuterium fractionation in the high density gas across Oph B2. The average deuterium fractionation R_D = N(N2D+)/N(N2H+) ~ 0.03 over Oph B2, with several small scale R_D peaks and a maximum R_D = 0.1. The mean R_D is consistent with previous results in isolated starless and protostellar cores. The column density distributions of both H2D+ and N2D+ show no correlation with total H2 column density. We find, however, an anticorrelation in deuterium fractionation with proximity to the embedded protostars in Oph B2 to distances >= 0.04 pc. Destruction mechanisms for deuterated molecules require gas temperatures greater than those previously determined through NH3 observations of Oph B2 to proceed. We present temperatures calculated for the dense core gas through the equating of non-thermal line widths for molecules (i.e., N2D+ and H2D+) expected to trace the same core regions, but the observed complex line structures in B2 preclude finding a reasonable result in many locations. This method may, however, work well in isolated cores with less complicated velocity structures. Finally, we use R_D and the H2D+ column density across Oph B2 to set a lower limit on the ionization fraction across the core, finding a mean x_e, lim >= few x 10^{-8}. Our results show that care must be taken when using deuterated species as a probe of the physical conditions of dense gas in star-forming regions.Comment: ApJ accepte

On the Baryonic Contents of Low Mass Galaxies

The baryonic Tully-Fisher relation is an important observational constraint on cosmological and galactic models. However, it is critical to keep in mind that in observations only stars, molecular, and atomic gas are counted, while the contribution of the ionized gas is almost universally missed. The ionized gas is, however, expected to be present in the gaseous disks of dwarf galaxies simply because they are exposed to the cosmic ionizing background and to the stellar radiation that manages to escape from the central regions of the galactic disks into their outer layers. Such an expectation is, indeed, born out both by cosmological numerical simulations and by simple analytical models.Comment: replaced with the accepted versio

Deconvolution of ASCA X-ray data: II. Radial temperature and metallicity profiles for 106 galaxy clusters

In Paper-I we presented a methodology to recover the spatial variations of properties of the intracluster gas from ASCA X-ray satellite observations of galaxy clusters. We verified the correctness of this procedure by applying it to simulated cluster datasets which we had subjected to the various contaminants common in ASCA data. In this paper we present the results which we obtain when we apply this method to real galaxy cluster observations. We determine broad-band temperature and cooling-flow mass-deposition rates for the 106 clusters in our sample, and obtain temperature, abundance and emissivity profiles (i.e. at least two annular bins) for 98 of these clusters. We find that 90 percent of these temperature profiles are consistent with isothermality at the 3-sigma confidence level. This conflicts with the prevalence of steeply-declining cluster temperature profiles found by Markevitch et al. (1998) from a sample of 30 clusters. In Paper-III (in preparation) we utilise our temperature and emissivity profiles to determine radial hydrostatic-mass properties for a subsample of the clusters presented in this paper.Comment: MNRAS, accpeted. Postscript copy of paper and individual postscript files for plots in Appendix B can be obtained from: http://www-xray.ast.cam.ac.uk/~da

NMR Spectroscopy Reveals the Presence and Association of Lipids and Keratin in Adhesive Gecko Setae

Lipid and protein aggregates are one of the fundamental materials of biological systems. Examples include cell membranes, insect cuticle, vertebrate epidermis, feathers, hair and adhesive structures known as ‘setae’ on gecko toes. Until recently gecko setae were assumed to be composed entirely of keratin, but analysis of footprints left behind by geckos walking on surfaces revealed that setae include various kinds of lipids. However, the arrangement and molecular-level behavior of lipids and keratin in the setae is still not known. In the present study we demonstrate, for the first time, the use of Nuclear Magnetic Resonance (NMR) spectroscopy techniques to confirm the presence of lipids and investigate their association with keratin in ‘pristine\u27 sheds, or natural molts of the adhesive toe pad and non-adhesive regions of the skin. Analysis was also carried on the sheds after they were ‘delipidized’ to remove surface lipids. Our results show a distribution of similar lipids in both the skin and toe shed but with different dynamics at a molecular level. The present study can help us understand the gecko system both biologically and for design of synthetic adhesives, but the findings may be relevant to the characteristics of lipid-protein interactions in other biological systems. http://dx.doi.org/10.1038/srep0959