Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Process algebra modelling styles for biomolecular processes

We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed

The Extinction Towards the GRB970228 Field

We determine the local galactic extinction towards the field of gamma-ray burst GRB970228 using a variety of methods. We develop a maximum likelihood method for measuring the extinction by comparing galaxy counts in the field of interest to those in a field of known extinction, and apply this method to the GRB970228 field. We also measure the extinction by comparing the observed stellar spectral energy distributions of stars in the GRB970228 field to the spectral energy distribution of library spectra of the same spectral type. Finally we estimate the extinction using the Balmer emission line ratios of a galaxy in the GRB970228 field, and the neutral hydrogen column density and amount of infrared dust emission toward this field. Combining the results of these methods, we find a best-fit galactic extinction in the optical of $A_V=1.19^{+0.10}_{-0.17}$, which implies a a substantial dimming and change of the spectral slope of the intrinsic GRB970228 afterglow.Comment: 22 pages, including 7 figures. Submitted to Ap

Typing in Model Management

International audienceModel management is essential for coping with the complexity introduced by the increasing number and varied nature of artifacts involved in MDE-based projects. Global Model Management (GMM) addresses this issue enabling the representation of artifacts, particularly transformation composition and execution, by a model called a megamodel. Typing information about artifacts can be used for preventing type errors during execution. In this work, we present a type system for GMM that improves its current typing approach and enables formal reasoning about the type of artifacts within a megamodel. This type system is able to capture non-trivial situations such as the use of higher order transformations

Concurrent constraint programming with process mobility

We propose an extension of concurrent constraint programming with primitives for process migration within a hierarchical network, and we study its semantics. To this purpose, we first investigate a "pure " paradigm for process migration, namely a paradigm where the only actions are those dealing with transmissions of processes. Our goal is to give a structural definition of the semantics of migration; namely, we want to describe the behaviour of the system, during the transmission of a process, in terms of the behaviour of the components. We achieve this goal by using a labeled transition system where the effects of sending a process, and requesting a process, are modeled by symmetric rules (similar to handshaking-rules for synchronous communication) between the two partner nodes in the network. Next, we extend our paradigm with the primitives of concurrent constraint programming, and we show how to enrich the semantics to cope with the notions of environment and constraint store. Finally, we show how the operational semantics can be used to define an interpreter for the basic calculus.

The Abundance of Interstellar Nitrogen

Using the HST Goddard High Resolution Spectrograph (GHRS), we have obtained high S/N echelle observations of the weak interstellar N I 1160, 1161 A absorption doublet toward the stars Gamma Cas, Lambda Ori, Iota Ori, Kappa Ori, Delta Sco, and Kappa Sco. In combination with a previous GHRS measurement of N I toward Zeta Oph, these new observations yield a mean interstellar gas phase nitrogen abundance (per 10$^6$ H atoms) of 10$^6$ N/H = 75 +/- 4. There are no statistically significant variations in the measured N abundances from sightline to sightline and no evidence of density-dependent depletion from the gas-phase. Since N is not expected to be depleted much into dust grains in these diffuse sightlines, its gas-phase abundance should reflect the total interstellar abundance. Consequently, the GHRS observations imply that the abundance of interstellar nitrogen (gas plus grains) in the local Milky Way is about 80% of the solar system value of 10$^6$ N/H = 93 +/- 16. Although this interstellar abundance deficit is somewhat less than that recently found for oxygen and krypton with GHRS, the solar N abundance and the N I oscillator strengths are too uncertain to definitively rule out either a solar ISM N abundance or a 2/3 solar ISM N abundance similar to that of O and Kr.Comment: 14 pages, LaTeX, 2 Postscript figures; ApJ Letters, in pres

Graphical Encoding of a Spatial Logic for the pi-Calculus

This paper extends our graph-based approach to the verification of spatial properties of π-calculus specifications. The mechanism is based on an encoding for mobile calculi where each process is mapped into a graph (with interfaces) such that the denotation is fully abstract with respect to the usual structural congruence, i.e., two processes are equivalent exactly when the corresponding encodings yield isomorphic graphs. Behavioral and structural properties of π-calculus processes expressed in a spatial logic can then be verified on the graphical encoding of a process rather than on its textual representation. In this paper we introduce a modal logic for graphs and define a translation of spatial formulae such that a process verifies a spatial formula exactly when its graphical representation verifies the translated modal graph formula

A Photometric Investigation of the GRB970228 Afterglow and the Associated Nebulosity

We carefully analyze the WFPC2 and STIS images of GRB970228. We measure magnitudes for the GRB970228 point source component in the WFPC2 images of $V=26.20^{+0.14}_{-0.13}$, $I_c=23.94^{+0.10}_{-0.09}$ and $V=26.52^{+0.16}_{-0.18}$, $I_c=24.31^{+0.15}_{-0.11}$ on March 26 and April 7, respectively; and $R_c=27.09^{+0.14}_{-0.14}$ on September 4 in the STIS image. For the extended component, we measure magnitudes of $R_c=25.48^{+0.22}_{-0.20}$ in the combined WFPC2 images and $R_c=25.54^{+0.33}_{-0.22}$ in the STIS image, which are consistent with no variation. This value is fainter than previously reported (Galama et al. 98) and modifies the previously assumed magnitudes for the optical transient when it faded to a level where the extended source component contribution was not negligible, alleviating the discrepancy to a power-law temporal behavior. We also measure a color of $V_{606}-I_{814}=-0.18^{+0.51}_{-0.61}$ for the extended source component. Taking into account the extinction measured in this field (Castander & Lamb 1998), this color implies that the extended source is most likely a galaxy with ongoing star formation.Comment: 21 pages, including 8 figures. Submitted to Ap

Combined color indexes and photometric structure of galaxies NGC 834 and NGC 1134

We present the results of BVRI photometry of two galaxies with active star formation: NGC 834 and NGC 1134. Combined color index Q_{BVI} was used to investigate the photometrical structure of the galaxies. Index Q_{BVI} is not affected by internal extinction and is sensitive to the presence of blue stars. Ring-like region with active star formation at 15" from the center reveals itself in the Q_{BVI} map of NGC 834. Three-arm spiral structure is well-seen on the Q_{BVI} map of NGC 1134. We propose to use the combined indexes Q_{BVI} and similarly defined indices as a tracers of Star Formation activity and structure of dusty galaxies.Comment: 3 pages, 4 embedded figures, LaTeX2e, using the EslabStyle.cls file, presented as a poster in the 33rd ESLAB Symp. "Star formation from the small to the large scale", Noordwijk, The Netherlands, 2-5 November 1999, (F. Favata, A.A. Kaas & A. Wilson eds, ESA SP-445

High-Resolution Observations of Interstellar Ca I Absorption -- Implications for Depletions and Electron Densities in Diffuse Clouds

We present high-resolution (FWHM ~ 0.3-1.5 km/s) spectra of interstellar Ca I absorption toward 30 Galactic stars. Comparisons of the column densities of Ca I, Ca II, K I, and other species -- for individual components identified in the line profiles and also when integrated over entire lines of sight -- yield information on relative electron densities and depletions. There is no obvious relationship between the ratio N(Ca I)/N(Ca II) [equal to n_e/(Gamma/alpha_r) for photoionization equilibrium] and the fraction of hydrogen in molecular form f(H2) (often taken to be indicative of the local density n_H). For a smaller sample of sightlines for which the thermal pressure (n_H T) and local density can be estimated via analysis of the C I fine-structure excitation, the average electron density inferred from C, Na, and K (assuming photoionization equilibrium) seems to be independent of n_H and n_H T. While the n_e obtained from the ratio N(Ca I)/N(Ca II) is often significantly higher than the values derived from other elements, the patterns of relative n_e derived from different elements show both similarities and differences for different lines of sight -- suggesting that additional processes besides photoionization and radiative recombination commonly and significantly affect the ionization balance of heavy elements in diffuse IS clouds. Such additional processes may also contribute to the (apparently) larger than expected fractional ionizations (n_e/n_H) found for some lines of sight with independent determinations of n_H. In general, inclusion of ``grain-assisted'' recombination does reduce the inferred n_e, but it does not reconcile the n_e estimated from different elements. The depletion of calcium may have a much weaker dependence on density than was suggested by earlier comparisons with CH and CN.Comment: aastex, 70 pages, accepted to ApJ