Parameter and Insertion Function Co-synthesis for Opacity Enhancement in Parametric Stochastic Discrete Event Systems

Opacity is a property that characterizes the system's capability to keep its "secret" from being inferred by an intruder that partially observes the system's behavior. In this paper, we are concerned with enhancing the opacity using insertion functions, while at the same time, enforcing the task specification in a parametric stochastic discrete event system. We first obtain the parametric Markov decision process that encodes all the possible insertions. Based on which, we convert this parameter and insertion function co-synthesis problem into a nonlinear program. We prove that if the output of this program satisfies all the constraints, it will be a valid solution to our problem. Therefore, the security and the capability of enforcing the task specification can be simultaneously guaranteed

Complexity of Detectability, Opacity and A-Diagnosability for Modular Discrete Event Systems

We study the complexity of deciding whether a modular discrete event system is detectable (resp. opaque, A-diagnosable). Detectability arises in the state estimation of discrete event systems, opacity is related to the privacy and security analysis, and A-diagnosability appears in the fault diagnosis of stochastic discrete event systems. Previously, deciding weak detectability (opacity, A-diagnosability) for monolithic systems was shown to be PSPACE-complete. In this paper, we study the complexity of deciding weak detectability (opacity, A-diagnosability) for modular systems. We show that the complexities of these problems are significantly worse than in the monolithic case. Namely, we show that deciding modular weak detectability (opacity, A-diagnosability) is EXPSPACE-complete. We further discuss a special case where all unobservable events are private, and show that in this case the problems are PSPACE-complete. Consequently, if the systems are all fully observable, then deciding weak detectability (opacity) for modular systems is PSPACE-complete

Effects of Planetesimal Accretion on the Thermal and Structural Evolution of Sub-Neptunes

A remarkable discovery of NASA's Kepler mission is the wide diversity in the average densities of planets of similar mass. After gas disk dissipation, fully formed planets could interact with nearby planetesimals from a remnant planetesimal disk. These interactions would often lead to planetesimal accretion due to the relatively high ratio between the planet size and the hill radius for typical planets. We present calculations using the open-source stellar evolution toolkit MESA (Modules for Experiments in Stellar Astrophysics) modified to include the deposition of planetesimals into the H/He envelopes of sub-Neptunes (~1-20 MEarth). We show that planetesimal accretion can alter the mass-radius isochrones for these planets. The same initial planet as a result of the same total accreted planetesimal mass can have up to ~5% difference in mean densities several Gyr after the last accretion due to inherent stochasticity of the accretion process. During the phase of rapid accretion these differences are more dramatic. The additional energy deposition from the accreted planetesimals increase the ratio between the planet's radius to that of the core during rapid accretion, which in turn leads to enhanced loss of atmospheric mass. As a result, the same initial planet can end up with very different envelope mass fractions. These differences manifest as differences in mean densities long after accretion stops. These effects are particularly important for planets initially less massive than ~10 MEarth and with envelope mass fraction less than ~10%, thought to be the most common type of planets discovered by Kepler.Comment: 19 Pages, 10 Figures, 1 Table; Accepted for Publication in the Astrophysical Journa

The physical properties of extrasolar planets

Tremendous progress in the science of extrasolar planets has been achieved since the discovery of a Jupiter orbiting the nearby Sun-like star 51 Pegasi in 1995. Theoretical models have now reached enough maturity to predict the characteristic properties of these new worlds, mass, radius, atmospheric signatures, and can be confronted with available observations. We review our current knowledge of the physical properties of exoplanets, internal structure and composition, atmospheric signatures, including expected biosignatures for exo-Earth planets, evolution, and the impact of tidal interaction and stellar irradiation on these properties for the short-period planets. We discuss the most recent theoretical achievements in the field and the still pending questions. We critically analyse the different solutions suggested to explain abnormally large radii of a significant fraction of transiting exoplanets. Special attention is devoted to the recently discovered transiting objects in the overlapping mass range between massive planets and low-mass brown dwarfs, stressing the ambiguous nature of these bodies, and we discuss the possible observable diagnostics to identify these two distinct populations. We also review our present understanding of planet formation and critically examine the different suggested formation mechanisms. We expect the present review to provide the basic theoretical background to capture the essential of the physics of exoplanet formation, structure and evolution, and the related observable signatures.Comment: 62 pages, 15 figures, published in Rep. Prog. Phys, final version available on http://stacks.iop.org/0034-4885/73/01690

Moving inhomogeneous envelopes of stars

Massive stars are extremely luminous and drive strong winds, blowing a large part of their matter into the galactic environment before they finally explode as a supernova. Quantitative knowledge of massive star feedback is required to understand our Universe as we see it. Traditionally, massive stars have been studied under the assumption that their winds are homogeneous and stationary, largely relying on the Sobolev approximation. However, observations with the newest instruments, together with progress in model calculations, ultimately dictate a cardinal change of this paradigm: stellar winds are highly inhomogeneous. Hence, we are now advancing to a new stage in our understanding of stellar winds. Using the foundations laid by V.V. Sobolev and his school, we now update and further develop the stellar spectral analysis techniques. New sophisticated 3-D models of radiation transfer in inhomogeneous expanding media elucidate the physics of stellar winds and improve classical empiric mass-loss rate diagnostics. Applications of these new techniques to multiwavelength observations of massive stars yield consistent and robust stellar wind parameters.Comment: slightly corrected version of the review for the special issue "V.V. Sobolev and his Legacy", Journal of Quantitative Spectroscopy and Radiative Transfe

Optimal Synthesis of Opacity-Enforcing Supervisors for Qualitative and Quantitative Specifications

In this paper, we investigate both qualitative and quantitative synthesis of optimal privacy-enforcing supervisors for partially-observed discrete-event systems. We consider a dynamic system whose information-flow is partially available to an intruder, which is modeled as a passive observer. We assume that the system has a "secret" that does not want to be revealed to the intruder. Our goal is to synthesize a supervisor that controls the system in a least-restrictive manner such that the closed-loop system meets the privacy requirement. For the qualitative case, we adopt the notion of infinite-step opacity as the privacy specification by requiring that the intruder can never determine for sure that the system is/was at a secret state for any specific instant. If the qualitative synthesis problem is not solvable or the synthesized solution is too restrictive, then we further investigate the quantitative synthesis problem so that the secret is revealed (if unavoidable) as late as possible. Effective algorithms are provided to solve both the qualitative and quantitative synthesis problems. Specifically, by building suitable information structures that involve information delays, we show that the optimal qualitative synthesis problem can be solved as a safety-game. The optimal quantitative synthesis problem can also be solved as an optimal total-cost control problem over an augmented information structure. Our work provides a complete solution to the standard infinite-step opacity control problem, which has not been solved without assumption on the relationship between controllable events and observable events. Furthermore, we generalize the opacity enforcement problem to the numerical setting by introducing the secret-revelation-time as a new quantitative measure

On Approximate Opacity of Cyber-Physical Systems

Opacity is an important information-flow security property in the analysis of cyber-physical systems. It captures the plausible deniability of the system's secret behavior in the presence of an intruder that may access the information flow. Existing works on opacity only consider non-metric systems by assuming that the intruder can always distinguish two different outputs precisely. In this paper, we extend the concept of opacity to systems whose output sets are equipped with metrics. Such systems are widely used in the modeling of many real-world systems whose measurements are physical signals. A new concept called approximate opacity is proposed in order to quantitatively evaluate the security guarantee level with respect to the measurement precision of the intruder. Then we propose a new simulation-type relation, called approximate opacity preserving simulation relation, which characterizes how close two systems are in terms of the satisfaction of approximate opacity. This allows us to verify approximate opacity for large-scale, or even infinite systems, using their abstractions. We also discuss how to construct approximate opacity preserving symbolic models for a class of discrete-time control systems. Our results extend the definitions and analysis techniques for opacity from non-metric systems to metric systems

Triangulating Radiation: Radiative Transfer on Unstructured Grids

We present a new numerical approach that is able to solve the multi-dimensional radiative transfer equations in all opacity regimes on a Lagrangian, unstructured network of characteristics based on a stochastic point process. Our method reverses the limiting procedure used to derive the transfer equations, by going back to the original Markov process. Thus, we reduce this highly complex system of coupled differential equations to a simple one-dimensional random walk on a graph, which is shown to be computationally very efficient. Specifically, we use a Delaunay graph, which makes it possible to combine our scheme with a new smoothed particle hydrodynamics (SPH) variant proposed by Pelupessy et al.(2003). We show that the results of applying a two-dimensional implementation of our method with various suitable test cases agree with the analytical results, and we point out the advantages of using our method with inhomogeneous point distributions, showing examples in the progress. Hereafter, we present a supplement to our method, which can be useful in cases where the medium is optically very thin, and we conclude by stating some anticipated properties of this method in three dimensions, and announce future extensions.Comment: 19 pages, 19 figures; substantial revision of conten

Giant Impact: An Efficient Mechanism for the Devolatilization of Super-Earths

Mini-Neptunes and volatile-poor super-Earths coexist on adjacent orbits in proximity to host stars such as Kepler-36 and Kepler-11. Several post-formation processes have been proposed for explaining the origin of the compositional diversity: the mass loss via stellar XUV irradiation, degassing of accreted material, and in-situ accumulation of the disk gas. Close-in planets are also likely to experience giant impacts during the advanced stage of planet formation. This study examines the possibility of transforming volatile-rich super-Earths / mini-Neptunes into volatile-depleted super-Earths through giant impacts. We present the results of three-dimensional giant impact simulations in the accretionary and disruptive regimes. Target planets are modeled with a three-layered structure composed of an iron core, silicate mantle and hydrogen/helium envelope. In the disruptive case, the giant impact can remove most of the H/He atmosphere immediately and homogenize the refractory material in the planetary interior. In the accretionary case, the planet can retain more than half of the gaseous envelope, while a compositional gradient suppresses efficient heat transfer as its interior undergoes double-diffusive convection. After the giant impact, a hot and inflated planet cools and contracts slowly. The extended atmosphere enhances the mass loss via both a Parker wind induced by thermal pressure and hydrodynamic escape driven by the stellar XUV irradiation. As a result, the entire gaseous envelope is expected to be lost due to the combination of those processes in both cases. We propose that Kepler-36b may have been significantly devolatilized by giant impacts, while a substantial fraction of Kepler-36c's atmosphere may remain intact. Furthermore, the stochastic nature of giant impacts may account for the large dispersion in the mass--radius relationship of close-in super-Earths and mini-Neptunes.Comment: 8 pages, 8 figures, 1 table, to be published in ApJ, readability improved according to the proo

On the necessity of composition-dependent low-temperature opacity in metal-poor AGB stars

The vital importance of composition-dependent low-temperature opacity in low-mass (M < 3Msun) asymptotic giant branch (AGB) stellar models of metallicity Z > 0.001 has recently been demonstrated (e.g. Marigo 2002; Ventura & Marigo 2010). Its significance to more metal-poor, intermediate mass (M > 2.5Msun) models has yet to be investigated. We show that its inclusion in lower-metallicity models ([Fe/H] < -2) is essential, and that there exists no threshold metallicity below which composition-dependent molecular opacity may be neglected. We find it to be crucial in all intermediate-mass models investigated ([Fe/H] < -2 and 2.5 < M/Msun < 5), because of the evolution of the surface chemistry, including the orders of magnitude increase in the abundance of molecule-forming species. Its effect on these models mirrors that previously reported for higher-metallicity models - increase in radius, decrease in Teff, faster mass loss, shorter thermally pulsing AGB lifetime, reduced enrichment in third dredge-up products (by a factor of three to ten), and an increase in the mass limit for hot bottom burning. We show that the evolution of low-metallicity models with composition-dependent low-temperature opacity is relatively independent of initial metal abundance because its contribution to the opacity is far outweighed by changes due to dredge-up. Our results imply a significant reduction in the expected number of nitrogen-enhanced metal-poor stars, which may help explain their observed paucity. We note that these findings are partially a product of the macrophysics adopted in our models, in particular the Vassiliadis & Wood (1993) mass loss rate which is strongly dependent on radius.Comment: 13 pages, 13 figures, 2 tables; accepted for publication in The Astrophysical Journa