Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of non-zero elements, is presented and analysed using methods of statistical physic
s. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code.
In the study of differential privacy, composition theorems (starting with the original paper of Dwork, McSherry, Nissim, and Smith (TCC06)) bound the degradation of privacy when composing several differentially private algorithms. Kairouz, Oh, and Vi
swanath (ICML15) showed how to compute the optimal bound for composing $k$ arbitrary $(epsilon,delta)$-differentially private algorithms. We characterize the optimal composition for the more general case of $k$ arbitrary $(epsilon_{1},delta_{1}),ldots,(epsilon_{k},delta_{k})$-differentially private algorithms where the privacy parameters may differ for each algorithm in the composition. We show that computing the optimal composition in general is $#$P-complete. Since computing optimal composition exactly is infeasible (unless FP=$#$P), we give an approximation algorithm that computes the composition to arbitrary accuracy in polynomial time. The algorithm is a modification of Dyers dynamic programming approach to approximately counting solutions to knapsack problems (STOC03).
The a-function is a proposed quantity defined in even dimensions which has a monotonic behaviour along RG flows, related to the beta-functions via a gradient flow equation. We study the a-function for a general scalar theory in six dimensions, using
the beta-functions up to three-loop order for both the MSbar and MOM schemes (the latter presented here for the first time at three loops).
We study indented spherical colloids, interacting via depletion forces. These systems exhibit liquid-vapor phase transitions whose properties are determined by a combination of strong lock-and-key bonds and weaker non-specific interactions. As the pr
opensity for lock-and-key binding increases, the critical point moves to significantly lower density, and the coexisting phases change their structure. In particular, the liquid phase is porous, exhibiting large percolating voids. The properties of this system depend strongly on the topological structure of an underlying bond network: we comment on the implications of this fact for the assembly of equilibrium states with controlled porous structures.
We use surface brightness contour maps of nearby edge-on spiral galaxies to determine whether extended bright radio halos are common. In particular, we test a recent model of the spatial structure of the diffuse radio continuum by Subrahmanyan and Co
wsik which posits that a substantial fraction of the observed high-latitude surface brightness originates from an extended Galactic halo of uniform emissivity. Measurements of the axial ratio of emission contours within a sample of normal spiral galaxies at 1500 MHz and below show no evidence for such a bright, extended radio halo. Either the Galaxy is atypical compared to nearby quiescent spirals or the bulk of the observed high-latitude emission does not originate from this type of extended halo.
We reconstruct the abundance of thorium near the Compton-Belkovich Volcanic Complex on the Moon, using data from the Lunar Prospector Gamma Ray Spectrometer. We enhance the resolution via a pixon image reconstruction technique, and find that the thor
ium is distributed over a larger ($40 mathrm{km}times 75$ km) area than the ($25 mathrm{km}times 35$ km) high albedo region normally associated with Compton-Belkovich. Our reconstructions show that inside this region, the thorium concentration is $14!-!26$ ppm. We also find additional thorium, spread up to $300$ km eastward of the complex at $sim!2$ ppm. The thorium must have been deposited during the formation of the volcanic complex, because subsequent lateral transport mechanisms, such as small impacts, are unable to move sufficient material. The morphology of the feature is consistent with pyroclastic dispersal and we conclude that the present distribution of thorium was likely created by the explosive eruption of silicic magma.
We report the first comprehensive study of the high temperature form ($alpha$-phase) of iron disilicide. Measurements of the magnetic susceptibility, magnetization, heat capacity and resistivity were performed on well characterized single crystals. W
ith a nominal iron $d^6$ configuration, and a quasi-two dimensional crystal structure that strongly resembles that of LiFeAs, $alpha$-FeSi$_2$ is a potential candidate for unconventional superconductivity. Akin to LiFeAs, $alpha$-FeSi$_2$ does not develop any magnetic order, and we confirm its metallic state down to the lowest temperatures ($T$=1.8 K). However, our experiments reveal that paramagnetism and electronic correlation effects in $alpha$-FeSi$_2$ are considerably weaker than in the pnictides. Band theory calculations yield small Sommerfeld coefficients of the electronic specific heat $gamma=C_e/T$ that are in excellent agreement with experiment. Additionally, realistic many-body calculations further corroborate that quasi-particle mass enhancements are only modest in $alpha$-FeSi$_{2}$ . Remarkably, we find that the natural tendency to vacancy formation in the iron sublattice has little influence on the iron valence and the density of states at the Fermi level. Moreover, Mn doping does not significantly change the electronic state of the Fe ion. This suggests that the iron valence is protected against hole doping, and indeed the substitution of Co for Fe causes a rigid-band like response of the electronic properties. As a key difference from the pnictides, we identify the smaller inter-iron layer spacing, which causes the active orbitals near the Fermi level to be of a different symmetry in $alpha$-FeSi$_2$. This change in orbital character might be responsible for the lack of superconductivity in this system, providing constraints on pairing theories in the iron based pnictides and chalcogenides.
$HC_*(A rtimes G)$ is the cyclic homology of the crossed product algebra $A rtimes G.$ For any $g epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A rtimes G).$ If $G$ is the f
inite cyclic group generated by $g$ and $|G|=r$ is invertible in $k,$ then $HC_*(A rtimes G)$ will be isomorphic to a direct sum of $r$ copies of $HC_*^g(A).$ For the case where $|G|$ is finite and $Q subset k$ we will generalize the Karoubi and Connes periodicity exact sequences for $HC_*^g(A)$ to Karoubi and Connes periodicity exact sequences for $HC_*(A rtimes G)$ .
We present the redshift evolutions and distributions of the gamma-ray luminosity and photon spectral index of flat spectrum radio quasar (FSRQ) type blazars, using non-parametric methods to obtain the evolutions and distributions directly from the da
ta. The sample we use for analysis consists of almost all FSRQs observed with a greater than approximately 7 sigma detection threshold in the first year catalog of the Fermi Gamma-ray Space Telescopes Large Area Telescope, with redshfits as determined from optical spectroscopy by Shaw et al. We find that FSQRs undergo rapid gamma-ray luminosity evolution, but negligible photon index evolution, with redshift. With these evolutions accounted for we determine the density evolution and luminosity function of FSRQs, and calculate their total contribution to the extragalactic gamma-ray background radiation, resolved and unresolved, which is found to be 16(+10/-4)%, in agreement with previous studies.
We extend the statistical analysis of Lissauer et al. (2012, ApJ 750, 112), which demonstrates that the overwhelming majority of Kepler candidate multiple transiting systems (multis) represent true transiting planets, and develop therefrom a procedur
e to validate large numbers of planet candidates in multis as bona fide exoplanets. We show that this statistical framework correctly estimates the abundance of false positives already identified around Kepler targets with multiple sets of transit-like signatures based on their abundance around targets with single sets of transit-like signatures. We estimate the number of multis that represent split systems of one or more planets orbiting each component of a binary star system. We use the high reliability rate for multis to validate more than one dozen particularly interesting multi-planet systems are validated in a companion paper by Rowe et al. (2014, ApJ, this issue). We note that few very short period (P < 1.6 days) planets orbit within multiple transiting planet systems and discuss possible reasons for their absence. There also appears to be a shortage of planets with periods exceeding a few months in multis.
