Light Elements and Cosmic Rays in the Early Galaxy

We derive constraints on the cosmic rays responsible for the Be and part of the B observed in stars formed in the early Galaxy: the cosmic rays cannot be accelerated from the ISM; their energy spectrum must be relatively hard (the bulk of the nuclear reactions should occur at $>$30 MeV/nucl); and only 10$^{49}$ erg/SNII in high metallicity, accelerated particle kinetic energy could suffice to produce the Be and B. The reverse SNII shock could accelerate the particles.Comment: 5 pages LATEX using paspconf.sty file with one embedded eps figure using psfig. In press, Proc. Goddard High Resolution Spectrograph Symposium, PASP, 199

Microwave whirlpools in a rectangular-waveguide cavity with a thin ferrite disk

We study a three dimensional system of a rectangular-waveguide resonator with an inserted thin ferrite disk. The interplay of reflection and transmission at the disk interfaces together with material gyrotropy effect, gives rise to a rich variety of wave phenomena. We analyze the wave propagation based on full Maxwell-equation numerical solutions of the problem. We show that the power-flow lines of the microwave-cavity field interacting with a ferrite disk, in the proximity of its ferromagnetic resonance, form whirlpool-like electromagnetic vortices. Such vortices are characterized by the dynamical symmetry breaking. The role of ohmic losses in waveguide walls and dielectric and magnetic losses in a disk is a subject of our investigations

Gamma Ray Lines from the Orion Complex

We show that the 4.44 and 6.13 MeV line emission observed with COMPTEL from Orion is consistent with gamma ray spectra consisting of a mixture of narrow and broad lines or spectra containing only broad lines. We employed several accelerated particle compositions and showed that the current COMPTEL data in the 3--7 MeV region alone cannot distinguish between the various possibilities. However, the COMPTEL upper limits in the 1--3 MeV band favor a composition similar to that of the winds of Wolf-Rayet stars of spectral type WC. The power dissipated by the accelerated particles at Orion is about 4 $\times$ 10$^{38}$ erg s$^{-1}$. These particles are not expected to produce significant amounts of $^{26}$Al.Comment: 12 pages, uuencoded compressed postscript with 4 figures ApJL in press 199

Efficient Immunization Strategies for Computer Networks and Populations

We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the susceptible-infected-removed epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases.Comment: Revtex, 5 pages, 4 ps fig

Dynamic Screening in Thermonuclear Reactions

It has recently been argued that there are no dynamic screening corrections to Salpeter's enhancement factor in thermonuclear reactions, in the weak-screening limit. The arguments used were: 1) The Gibbs probability distribution is factorable into two parts, one of which, $exp(-\beta \sum e_{i}e_{j}/r_{ij})$ ($\beta=1/k_{B}T$), is independent of velocity space; and 2) The enhancement factor is $w=1+\beta^{2}e^{2}Z_{1}Z_{2}$ with ${}_{k}={}_{k}/k^{2}$ and ${< E^{2} >}_{k}/(8\pi)=(T/2)[1-\epsilon^{-1} (0,k)]$. We show that both of these arguments are incorrect.Comment: Accepted for publication in The Astrophysical Journa

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge on the network. We determine, for all strategies, the critical fraction p_c of nodes that must be removed for disintegrating the network. We find that for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p_c. At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.Comment: Accepted in PR

Scale-Free Networks are Ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ~ lnN, we show, using analytical arguments, that scale free networks with 2<a<3 have a much smaller diameter, behaving as d ~ lnlnN. For a=3, our analysis yields d ~ lnN/lnlnN, as obtained by Bollobas and Riordan, while for a>3, d ~ lnN. We also show that, for any a>2, one can construct a deterministic scale free network with d ~ lnlnN, and this construction yields the lowest possible diameter.Comment: Latex, 4 pages, 2 eps figures, small corrections, added explanation

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices