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Traditional security analyses are often geared towards cryptographic primitives or protocols. Although such analyses are necessary, they cannot address a defender's need for insight into {\em which aspects of a networked system having a significant impact on its security, and how to tune its configurations or parameters so as to improve security}. This question is known to be notoriously difficult to answer, and the state-of-the-art is that we know little about it. Towards ultimately addressing this question, this paper presents a stochastic model for quantifying security of networked systems. The resulting model captures two aspects of a networked system: (1) the strength of deployed security mechanisms such as intrusion detection systems, and (2) the underlying {\em vulnerability graph}, which reflects how attacks may proceed. The resulting model brings the following insights: (1) How should a defender "tune" system configurations (e.g., network topology) so as to improve security? (2) How should a defender "tune" system parameters (e.g., by upgrading which security mechanisms) so as to improve security? (3) Under what conditions is the steady-state number of compromised entities of interest below a given threshold with a high probability? Simulation studies are conducted to confirm the analytic results, and to show the tightness of the bounds of certain important metric that cannot be resolved analytically.

The envelopes of AGB stars are irradiated externally by ultraviolet photons; hence, the chemistry is sensitive to the photodissociation of N$_2$ and CO, which are major reservoirs of nitrogen and carbon, respectively. The photodissociation of N$_2$ has recently been quantified by laboratory and theoretical studies. Improvements have also been made for CO photodissociation. For the first time, we use accurate N$_2$ and CO photodissociation rates and shielding functions in a model of the circumstellar envelope of the carbon-rich AGB star, IRC +10216. We use a state-of-the-art chemical model of an AGB envelope, the latest CO and N$_2$ photodissociation data, and a new method for implementing molecular shielding functions in full spherical geometry with isotropic incident radiation. We compare computed column densities and radial distributions of molecules with observations. The transition of N$_2$ $\to$ N (also, CO $\to$ C $\to$ C$^+$) is shifted towards the outer envelope relative to previous models. This leads to different column densities and radial distributions of N-bearing species, especially those species whose formation/destruction processes largely depend on the availability of atomic or molecular nitrogen, for example, C$_n$N ($n$=1, 3, 5), C$_n$N$^-$ ($n$=1, 3, 5), HC$_n$N ($n$=1, 3, 5, 7, 9), H$_2$CN and CH$_2$CN. The chemistry of many species is directly or indirectly affected by the photodissociation of N$_2$ and CO, especially in the outer shell of AGB stars where photodissociation is important. Thus, it is important to include N$_2$ and CO shielding in astrochemical models of AGB envelopes and other irradiated environments. In general, while differences remain between our model of IRC +10216 and the observed molecular column densities, better agreement is found between the calculated and observed radii of peak abundance., Comment: 13 pages, 17 figures, 3 tables. Accepted for publication in Astronomy and Astrophysics

The dynamics of the reaction H + OH $\to$ O (3P) + H2 have been studied in a series of quasi-classical trajectory (QCT) calculations and transition state theory (TST) methods using high quality 3A' and 3A'' potential energy surfaces (PESs). Accurate OH (v, j) state resolved cross sections and rate constants on both potential energy surfaces are presented and fitted for OH at (v = 0, j = 0-16) and (v = 1, j = 0-6). The cross sections were calculated for different collisional energies (Ec), ranging from the threshold energy at each specific rovibrational state up to 1.0 eV with step sizes of 0.1 eV or less. They increase steeply with collision energy when the barrier to reaction can be overcome, after which the cross sections stay nearly constant with energy. State resolved rate constants in the temperature range 200-2500 K are presented based on the cross sections. Total thermal rate constants were calculated by summing the rates for reaction on the 3A' and 3A'' potential energy surfaces weighted by 1/3 and taking into account the thermal populations of the rovibrational states of the OH molecules. It is shown that the improved canonical variational transition (CVT) treatments with the approximation of zero-curvature tunneling (ZCT) or small-curvature tunneling (SCT) produce results more in accord with the QCT results than the TST and CVT methods. The reactions are governed by the direct reaction mechanism. The rate constants for OH in excited vibrational and rotational states are orders of magnitude larger than the thermal rate constants, which needs to be taken into account in astrochemical models., Comment: Current version: 35 pages with 7 figures and 2 tables. Online version: 8 pages, see http://pubs.acs.org/doi/abs/10.1021/jp4068153