Approximating a Behavioural Pseudometric without Discount for<br> Probabilistic Systems

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative analogue of probabilistic bisimilarity. Distance zero captures probabilistic bisimilarity. Each pseudometric has a discount factor, a real number in the interval (0, 1]. The smaller the discount factor, the more the future is discounted. If the discount factor is one, then the future is not discounted at all. Desharnais et al. showed that the behavioural distances can be calculated up to any desired degree of accuracy if the discount factor is smaller than one. In this paper, we show that the distances can also be approximated if the future is not discounted. A key ingredient of our algorithm is Tarski's decision procedure for the first order theory over real closed fields. By exploiting the Kantorovich-Rubinstein duality theorem we can restrict to the existential fragment for which more efficient decision procedures exist

Multiwavelength Observations of the Hot DB Star PG 0112+104

We present a comprehensive multiwavelength analysis of the hot DB white dwarf PG 0112+104. Our analysis relies on newly-acquired FUSE observations, on medium-resolution FOS and GHRS data, on archival high-resolution GHRS observations, on optical spectrophotometry both in the blue and around Halpha, as well as on time-resolved photometry. From the optical data, we derive a self-consistent effective temperature of 31,300+-500 K, a surface gravity of log g = 7.8 +- 0.1 (M=0.52 Msun), and a hydrogen abundance of log N(H)/N(He) < -4.0. The FUSE spectra reveal the presence of CII and CIII lines that complement the previous detection of CII transitions with the GHRS. The improved carbon abundance in this hot object is log N(C)/N(He) = -6.15 +- 0.23. No photospheric features associated with other heavy elements are detected. We reconsider the role of PG 0112+104 in the definition of the blue edge of the V777 Her instability strip in light of our high-speed photometry, and contrast our results with those of previous observations carried out at the McDonald Observatory.Comment: 10 pages in emulateapj, 9 figures, accepted for publication in Ap

On Probabilistic Applicative Bisimulation and Call-by-Value λ\lambda-Calculi (Long Version)

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more surprisingly, full-abstraction only holds in a symmetric setting.Comment: 30 page

Loneliness in the United States: A 2018 National Panel Survey of Demographic, Structural, Cognitive, and Behavioral Characteristics

Purpose: To inform health behavior intervention design, we sought to quantify loneliness and its correlates, including social media use, among adults in the United States. Design: Cross-sectional research panel questionnaire. Setting: Responses were gathered from individuals in all 50 states surveyed via Internet from February 2018 to March 2018. Participants: A total of 20 096 US panel respondents aged 18þ. Measures: The University of California at Los Angeles (UCLA) Loneliness Scale (theoretical score range ¼ 20-80) was administered along with demographic, structural, cognitive, and behavioral items. Analysis: After calibrating the sample to population norms, we conducted multivariable linear regression analysis. Results: The overall mean survey-weighted loneliness score was 44.03 (standard error ¼ 0.09). Social support (standardized b [sb] ¼ 0.19) and meaningful daily interactions (sb ¼ 0.14) had the strongest associations with lower loneliness, along with reporting good relationships, family life, physical and mental health, friendships, greater age, being in a couple, and balancing one’s daily time. Social anxiety was most strongly associated with greater loneliness (sb ¼ þ0.20), followed by self-reported social media overuse (sb ¼ þ0.05) and daily use of text-based social media (sb ¼ þ0.03). Conclusion: Our findings confirm that loneliness decreases with age, and that being in a relationship as well as everyday behavioral factors in people’s control are most strongly related to loneliness. Population health promotion efforts to reduce loneliness should focus on improving social support, decreasing social anxiety, and promoting healthy daily behaviors

Probabilistic Mobility Models for Mobile and Wireless Networks

International audienceIn this paper we present a probabilistic broadcast calculus for mobile and wireless networks whose connections are unreliable. In our calculus, broadcasted messages can be lost with a certain probability, and due to mobility the connection probabilities may change. If a network broadcasts a message from a location, it will evolve to a network distribution depending on whether nodes at other locations receive the message or not. Mobility of nodes is not arbitrary but guarded by a probabilistic mobility function (PMF), and we also define the notion of a weak bisimulation given a PMF. It is possible to have weak bisimular networks which have different probabilistic connectivity information. We furthermore examine the relation between our weak bisimulation and a minor variant of PCTL* [1]. Finally, we apply our calculus on a small example called the Zeroconf protocol [2]

The Survival of Water within Extrasolar Minor Planets

We compute that extrasolar minor planets can retain much of their internal H_2O during their host star's red giant evolution. The eventual accretion of a water-rich body or bodies onto a helium white dwarf might supply an observable amount of atmospheric hydrogen, as seems likely for GD 362. More generally, if hydrogen pollution in helium white dwarfs typically results from accretion of large parent bodies rather than interstellar gas as previously supposed, then H_2O probably constitutes at least 10% of the aggregate mass of extrasolar minor planets. One observational test of this possibility is to examine the atmospheres of externally-polluted white dwarfs for oxygen in excess of that likely contributed by oxides such as SiO_2. The relatively high oxygen abundance previously reported in GD 378 plausibly but not uniquely can be explained by accretion of an H_2O-rich parent body or bodies. Future ultraviolet observations of white dwarf pollutions can serve to investigate the hypothesis that environments with liquid water that are suitable habitats for extremophiles are widespread in the Milky Way.Comment: Astronomical Journal, in press, 24 pages, 7 figure

Water Fractions in Extrasolar Planetesimals

With the goal of using externally-polluted white dwarfs to investigate the water fractions of extrasolar planetesimals, we assemble from the literature a sample that we estimate to be more than 60% complete of DB white dwarfs warmer than 13,000 K, more luminous than 3 ${\times}$ 10$^{-3}$ L$_{\odot}$ and within 80 pc of the Sun. When considering all the stars together, we find the summed mass accretion rate of heavy atoms exceeds that of hydrogen by over a factor of 1000. If so, this sub-population of extrasolar asteroids treated as an ensemble has little water and is at least a factor of 20 drier than CI chondrites, the most primitive meteorites. In contrast, while an apparent "excess" of oxygen in a single DB can be interpreted as evidence that the accreted material originated in a water-rich parent body, we show that at least in some cases, there can be sufficient uncertainties in the time history of the accretion rate that such an argument may be ambiguous. Regardless of the difficulty associated with interpreting the results from an individual object, our analysis of the population of polluted DBs provides indirect observational support for the theoretical view that a snow line is important in disks where rocky planetesimals form.Comment: Accepted for publication in the Astronomical Journal, 22 pages, 4 figures, 1 tabl

Two Extrasolar Asteroids with Low Volatile-Element Mass Fractions

Using ultraviolet spectra obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope, we extend our previous ground-based optical determinations of the composition of the extrasolar asteroids accreted onto two white dwarfs, GD 40 and G241-6. Combining optical and ultraviolet spectra of these stars with He-dominated atmospheres, 13 and 12 polluting elements are confidently detected in GD 40 and G241-6, respectively. For the material accreted onto GD 40, the volatile elements C and S are deficient by more than a factor of 10 and N by at least a factor of 5 compared to their mass fractions in primitive CI chondrites and approach what is inferred for bulk Earth. A similar pattern is found for G241-6 except that S is undepleted. We have also newly detected or placed meaningful upper limits for the amount of Cl, Al, P, Ni and Cu in the accreted matter. Extending results from optical studies, the mass fractions of refractory elements in the accreted parent bodies are similar to what is measured for bulk Earth and chondrites. Thermal processing, perhaps interior to a snow line, appears to be of central importance in determining the elemental compositions of these particular extrasolar asteroids.Comment: 37 pages, 13 figures, 5 tables, ApJ, accepte

Simulation-Based Graph Similarity

We present symmetric and asymmetric similarity measures for labeled directed rooted graphs that are inspired by the simulation and bisimulation relations on labeled transition systems. Computation of the similarity measures has close connections to discounted Markov decision processes in the asymmetric case and to perfect-information stochastic games in the symmetric case. For the symmetric case, we also give a polynomial-time algorithm that approximates the similarity to any desired precision

Approximating Markov Processes by Averaging

We recast the theory of labelled Markov processes in a new setting, in a way "dual" to the usual point of view. Instead of considering state transitions as a collection of subprobability distributions on the state space, we view them as transformers of real-valued functions. By generalizing the operation of conditional expectation, we build a category consisting of labelled Markov processes viewed as a collection of operators; the arrows of this category behave as projections on a smaller state space. We define a notion of equivalence for such processes, called bisimulation, which is closely linked to the usual definition for probabilistic processes. We show that we can categorically construct the smallest bisimilar process, and that this smallest object is linked to a well-known modal logic. We also expose an approximation scheme based on this logic, where the state space of the approximants is finite; furthermore, we show that these finite approximants categorically converge to the smallest bisimilar process.Nous reconsidérons les processus de Markov étiquetés sous une nouvelle approche, dans un certain sens "dual'' au point de vue usuel. Au lieu de considérer les transitions d'état en état en tant qu'une collection de distributions de sous-probabilités sur l'espace d'états, nous les regardons en tant que transformations de fonctions réelles. En généralisant l'opération d'espérance conditionelle, nous construisons une catégorie où les objets sont des processus de Markov étiquetés regardés en tant qu'un rassemblement d'opérateurs; les flèches de cette catégorie se comportent comme des projections sur un espace d'états plus petit. Nous définissons une notion d'équivalence pour de tels processus, que l'on appelle bisimulation, qui est intimement liée avec la définition usuelle pour les processus probabilistes. Nous démontrons que nous pouvons construire, d'une manière catégorique, le plus petit processus bisimilaire à un processus donné, et que ce plus petit object est lié à une logique modale bien connue. Nous développons une méthode d'approximation basée sur cette logique, où l'espace d'états des processus approximatifs est fini; de plus, nous démontrons que ces processus approximatifs convergent, d'une manière catégorique, au plus petit processus bisimilaire