Coded Cooperative Data Exchange for a Secret Key

We consider a coded cooperative data exchange problem with the goal of generating a secret key. Specifically, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in traditional cooperative data exchange can be solved in polynomial time. In doing this, we completely characterize the best possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal. Finally, we extend the single-key results to characterize the minimum number of public transmissions required to generate a desired integer number of statistically independent secret keys.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2 figure

Collectivity and manifestations of minimum-bias jets in high-energy nuclear collisions

Collectivity, as interpreted to mean flow of a dense medium in high-energy A-A collisions described by hydrodynamics, has been attributed to smaller collision systems -- p-A and even p-p collisions -- based on recent analysis of LHC data. However, alternative methods reveal that some data features attributed to flows are actually manifestations of minimum-bias (MB) jets. In this presentation I review the differential structure of single-particle $p_t$ spectra from SPS to LHC energies in the context of a two-component (soft + hard) model (TCM) of hadron production. I relate the spectrum hard component to measured properties of isolated jets. I use the spectrum TCM to predict accurately the systematics of ensemble-mean $\bar p_t$ in p-p, p-A and A-A collision systems over a large energy interval. Detailed comparisons of the TCM with spectrum and correlation data suggest that MB jets play a dominant role in hadron production near midrapidity. Claimed flow phenomena are better explained as jet manifestations agreeing quantitatively with measured jet properties.Comment: 10 pages, 8 figures, Proceedings of XLVII International Symposium on Multiparticle Dynamics, Tlaxcala City, Mexico, September 11-15, 201

Low-Q2Q^2 partons in p-p and Au-Au collisions

We describe correlations of low-$Q^2$ parton fragments on transverse rapidity $y_t$ and angles $(\eta,\phi)$ from p-p and Au-Au collisions at $\sqrt{s} =$ 130 and 200 GeV. Evolution of correlations on $y_t$ from p-p to more-central Au-Au collisions shows evidence for parton dissipation. Cuts on $y_t$ isolate angular correlations on $(\eta,\phi)$ for low-$Q^2$ partons which reveal a large asymmetry about the jet thrust axis in p-p collisions favoring the azimuth direction. Evolution of angular correlations with increasing Au-Au centrality reveals a rotation of the asymmetry to favor pseudorapidity. Angular correlations of transverse momentum $p_t$ in Au-Au collisions access temperature/velocity structure resulting from low-$Q^2$ parton scattering. $p_t$ autocorrelations on $(\eta,\phi)$, obtained from the scale dependence of $$ fluctuations, reveal a complex parton dissipation process in heavy ion collisions which includes the possibility of collective bulk-medium recoil in response to parton stopping.Comment: 6 pages, 4 figures, XXXV International Symposium on Multiparticle Dynamics 2005, Krom\^{e}\^{r}\'{i}\^{z}, Czech Republic, August 9-15, 200

Rescuing the nonjet (NJ) azimuth quadrupole from the flow narrative

According to the flow narrative commonly applied to high-energy nuclear collisions a cylindrical-quadrupole component of 1D azimuth angular correlations is conventionally denoted by quantity $v_2$ and interpreted to represent elliptic flow. Jet angular correlations may also contribute to $v_2$ data as "nonflow" depending on the method used to calculate $v_2$, but 2D graphical methods are available to insure accurate separation. The nonjet (NJ) quadrupole has various properties inconsistent with a flow interpretation, including the observation that NJ quadrupole centrality variation in A-A collisions has no relation to strongly-varying jet modification ("jet quenching") in those collisions commonly attributed to jet interaction with a flowing dense medium. In this presentation I describe isolation of quadrupole spectra from pt-differential $v_2(p_t)$ data from the RHIC and LHC. I demonstrate that quadrupole spectra have characteristics very different from the single-particle spectra for most hadrons, that quadrupole spectra indicate a common boosted hadron source for a small minority of hadrons that "carry" the NJ quadrupole structure, that the narrow source-boost distribution is characteristic of an expanding thin cylindrical shell (strongly contradicting hydro descriptions), and that in the boost frame a single universal quadrupole spectrum (L\'evy distribution) on transverse mass $m_t$ accurately describes data for several hadron species scaled according to their statistical-model abundances. The quadrupole spectrum shape changes very little from RHIC to LHC energies. Taken in combination those characteristics strongly suggest a unique {\em nonflow} (and nonjet) QCD mechanism for the NJ quadrupole conventionally represented by $v_2$.Comment: 6 pages, 6 figures, to appear in proceedings of the XLVI International Symposium on Multiparticle Dynamic

The "soft ridge" -- is it initial-state geometry or modified jets?

An $\eta$-elongated same-side 2D peak ("soft ridge") in minimum-bias angular correlations from heavy ion collisions has been attributed both to jet formation and to initial-state geometry structure coupled to radial flow. We consider evidence for both interpretations.Comment: 4 pages, 3 figures, to be published in the Proceedings of the XLI International Symposium on Multiparticle Dynamics (ISMD 2011), 26-30 September, 2011, Miyajima Island, Hiroshima, Japa